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  • 2017
    • John Hay, Michael - Ph.D. Dissertation
      Stability and Uncertainty of Ice-Sheet Crystal Fabrics 2017, John Hay,Michael ,Michael John Hay Stability and Uncertainty of Ice-Sheet Crystal Fabrics Michael John Hay A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: Edwin Waddington Chair Howard Conway Gerard Roe Randall J LeVeque Program Authorized to Offer Degree: Department of Earth and Space Sciences c Copyright 2017 Michael John Hay University of Washington Abstract Stability and Uncertainty of Ice-Sheet Crystal Fabrics Michael John Hay Chair of the Supervisory Committee: Professor Edwin Waddington Department of Earth and Space Sciences Ice crystal orientation fabric has a large effect on polycrystalline ice flow In this thesis I explore uncertainty of ice fabric measurements and the related question of stability of ice crystal fabrics and anisotropic ice flow in ice sheets I develop new estimates of uncertainty of fabric parameter estimates from thin-section data and connect this to uncertainty in ice flow characteristics To reduce this sampling error I develop a new inverse method to infer fabric parameters from sonic velocity measurements and thin-section samples I show a number of results concerning the stability of ice crystal fabrics in ice sheets First I show that small velocity gradient perturbations can induce large changes in ice fabric which in turn affects anisotropic ice viscosity significantly Next I analyze the development of incipient fabric perturbations in coupled flow I develop an analytical coupled model of anisotropic ice flow and fabric evolution and show that the coupled system is unstable in many circumstances under ice-sheet flank flow and divide flow TABLE OF CONTENTS Page List of Figures iii Glossary viii Chapter 1: Introduction 1 1 1 Introduction 1 1 2 Background 2 1 2 1 Ice crystal deformation rotation and growth 2 1 2 2 Homogenization 6 1 2 3 Orientation distribution functions ODFs 7 1 2 4 Continuum fabric evolution models 10 Outline 12 1 3 Chapter 2: Statistical Aspects of Ice-Crystal Orientation Fabrics 14 2 1 Introduction 14 2 2 Parameterized orientation-density functions PODFs 18 2 2 1 Fisher and Watson distributions 18 2 2 2 The Bingham Distribution 20 2 2 3 The Dinh-Armstrong distribution 21 2 2 4 Comparison of PODFs 22 Sampling error in thin sections 25 2 3 1 Bootstrap estimates of sampling error 27 2 3 2 Sampling-error estimates for WAIS Divide 28 2 3 3 Sampling error in enhancement factor 29 Conclusions 34 2 3 2 4 i Chapter 3: 3 1 3 2 3 3 3 4 3 5 3 6 Ice Fabric Inference with Thin-Section Measurements ities with Application to the NEEM Ice Core Introduction Velocity model for sound waves in ice Fabric inference model Eigenvalue inference on synthetic data Application to sonic measurements at NEEM Conclusions and Sonic Veloc Chapter 4: 4 1 4 2 4 3 4 4 The response of ice-crystal orientation fabric to velocity-gradient turbations Introduction 4 1 1 Fabric evolution First-order perturbations to strong single-maximum fabrics Monte-Carlo analysis of stress perturbations Conclusions Chapter 5: Perturbations of Fabric Evolution and Flow of 5 1 Introduction 5 1 1 Background 5 2 Fabric Model 5 3 Flow Model 5 4 Perturbation approximation 5 5 Results 5 5 1 Layered perturbations in simple shear 5 5 2 Layered perturbations in pure shear 5 5 3 Discussion 5 6 Conclusions Anisotropic Chapter 6: Conclusions 6 1 Summary 6 2 Implications 1 Appendix A: Derivation of analytical estimates of sampling ii error 36 37 40 42 47 49 52 per 55 55 61 63 67 70 Ice 71 71 73 77 78 79 84 84 87 88 90 91 91 92 94 LIST OF FIGURES Figure Number Page 1 1 Cartoon of an individual ice crystal with the basal plane and c-axis shown 1 2 Schmid plots of thin sections taken from the WAIS divide ice core Each dot represents the c-axis orientation of a single grain An azimuthal equal-area projection is used such that a grain in the center of the circle is vertical and a grain on the edge has a horizontal c-axis A is an approximately isotropic fabric 3 2 1 B is a girdle fabric 3 2 1 C is a singlemaximum fabric 3 2 1 2 1 2 2 2 3 2 4 7 9 Log-likelihood of maximum-likelihood fits of the Dinh-Armstrong Equation 2 4 Bingham Equation 2 3 and Fisherian Equation 2 1 distributions to WAIS and Siple Dome thin-sections Higher log-likelihood indicates a better fit The likelihoods are normalized by grain area for WAIS For Siple Dome they are normalized by the number of grains The Dinh-Armstrong and Bingham distributions perform similarly with the Lliboutry s Fisherian distribution having lower likelihood for almost all thin sections 24 Estimates of the diagonal elements Aii no sum of the second-order orientation tensor Aij from fabric thin sections from the WAIS Divide core The error bars are the 95% bootstrap confidence intervals of the observed area-weighted thin section Aii 30 Bootstrap resampling and analytical estimates of the sample distributions of the eigenvalues of the thin section fabric at 140m The analytical dashed lines and resampled bootstrap estimates solid lines match closely Because the fabric is rather weak there is still a moderate amount of uncertainty despite this sample having 1405 grains 31 Bootstrap resampling and analytical estimates of the sample distributions of the error in fabric Euler angles of the thin section fabric at 140m The analytical and resampled bootstrap estimates match closely The smallest eigenvalue has a wide distribution in the associated Euler angle because the other two eigenvalues are close 32 iii 2 5 3 1 3 2 3 3 3 4 4 1 4 2 Bootstrap 95% confidence intervals for enhancement factor for the 83 WAIS thin sections Due to the dependence on the fourth power of the average Schmid factor the confidence intervals are wide 33 Application of the statistical model to synthetically generated fabric Thinsection eigenvalues with 30m spacing are generated by adding noise to the true eigenvalues The modeled eigenvalues are close to the true eigenvalues over the majority of the depth Error is primarily due to error in the velocitycorrection term 48 Velocity corruption dashed and estimated velocity corrections solid lines for vp vsh and vsv Estimation of the velocity corruption depends on the thin-section eigenvalues Due to the large degree of spatial variability of the fabric and the noise in the thin sections inaccuracies on the order of 10m s occur More thin-section samples and more accurate samples can reduce this error substantially 50 P-wave velocities modeled from thin sections dots and observed P-wave velocities line The observed P-wave velocities are smoothed over 3m and are averaged over multiple runs Due to a combination of model error and velocity drift the observed velocities are on the order of 100m s 1 less than the modeled velocities 52 Eigenvalues derived from thin sections at NEEM dots 61 together with spatially-continuous estimates from the assimilation procedure The variability of eigenvalues over shorter length scales in the upper core appears to be due to sampling error The large variations seen in the thin sections in the deep ice are confirmed by the sonic velocity data 53 The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with pure shear and a strain perturbation whose components average 2% of the background pure shear and 1 The central 95% of realizations are shaded Significant deviations of A13 and A23 occur These correspond to tilted cone fabrics whose direction of greatest concentration differs on the order of 5 from vertical 59 The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with pure shear and a strain perturbation whose components average 5% of the background pure shear with 1 the central 95% of realizations are shaded Larger deviations of A13 and A23 occur than under 2% average perturbations These correspond to tilted cone fabrics tilted on the order of 10 from vertical The background pure shear is very effective at restraining perturbations of other components of A 64 iv 4 3 4 4 5 1 5 2 5 3 5 4 The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with simple shear and a strain perturbation whose components average 2% of the background pure shear with 1 The central 95% of realizations are shaded Smaller perturbations develop than with pure shear However they still may be enough to seed further fabric and flow disturbances The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with simple shear and a strain perturbation whose components average 5% of the background pure shear using 1 The central 95% of realizations are shaded Large deviations in A13 and A23 occur than with 2% average velocity-gradient perturbations corresponding to tilted cone fabrics deviating on the order of 5 from vertical Smaller deviations occur in other components Cartoon of the form of a sinusoidal perturbation in space with spatial wavevector The shading represents the sign and magnitude of cos x for a perturbation of the form v cos x where v is the Fourier coefficient of the perturbation The sinusoidal perturbation extends throughout three-dimensional space The plane of the perturbation is given by the plane which is normal to the wavevector In this diagram the positive x-axis extends outwards from the page The largest real part of the eigenvalues of the Jacobian matrix 5 27 under simple shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the y-axis The largest real part of the eigenvalues of the Jacobian matrix 5 27 under pure shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the x-axis The largest real part of the eigenvalues of the Jacobian matrix 5 27 under pure shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the y-axis v 66 68 80 85 85 86 DEDICATION This thesis is dedicated to my dog Eli Outside of a dog a book is a man s best friend Inside of a dog it s too dark to read - Groucho Marx vi ACKNOWLEDGMENTS This thesis and my Ph D studies have only been possible due to the amazing help and support I have had from people around me First and foremost Ed Waddington has been the best advisor any grad student could hope for His support and insight have been integral to my success Thanks also to the rest of my committee Twit Conway has been a great co-advisor The work on Beardmore glacier is a highlight of my Ph D Gerard Roe has greatly improved this thesis with his critical eye on my work Also thanks to Randy LeVeque for serving as my GSR My fellow grad students and my officemates in particular have been a great source of support scientific and otherwise Thanks to Dan Kluskiewicz Rob Sheerer Trevor Thomas Adam Campbell Max Stevens Elena Amador John Christian Taryn Black and everyone else Thanks also to faculty and postdocs T J Fudge Michelle Koutnik Al Rasmussen Clement Miege A big thanks to ESS staff Thanks to Ed Mulligan for computer support and Noell Bernard for her help advising me Lastly thanks to my partner Nick my parents and my brother Tom You don t choose your family but I couldn t have chosen a better one vii GLOSSARY ICE CRYSTAL: A region of ice where the crystallographic structure is sufficiently uniformly oriented GRAIN: Synonym for ice crystal BASAL PLANE: C-AXIS: Crystallographic plane in ice with easy shear Direction orthogonal to the basal plane POLYCRYSTAL: A multicrystalline aggregate ORIENTATION DISTRIBUTION FUNCTION: Probability distribution of c-axis orientations of a polycrystal SECOND-ORDER ORIENTATION TENSOR: FABRIC EIGENVALUE: Second moment Aij ci cj of an ODF An eigenvalue of Aij A method of reconciling bulk stress and strain of a polycrystal to stress and strain of individual grains HOMOGENIZATION SCHEME: POLYGONIZATION: Splitting of ice grains due to progressive rotation of subgrains DYNAMIC RECRYSTALLIZATION: ICE DIVIDE: The nucleation and growth of new grains A point where ice flows from in different directions similarly to hydrographic divides Flow of ice on ice-sheet flanks away from ice divides Surface slope provides the driving stress Movement is mainly due to simple shear concentrated in the lower layers FLANK FLOW: DIVIDE FLOW: Flow of ice near ice divides Dominated by longitudinal extension viii A random function where finite samples of the function follow a multivariate Gaussian distribution GAUSSIAN PROCESS: ix 1 Chapter 1 INTRODUCTION 1 1 Introduction Individual ice crystals have an unusual amount of plastic anisotropy with deformation by shear along the basal plane being around 100 times easier than strain in other orientations e g Duval et al 28 Due to this the aggregate orientations of crystals the crystal fabric has a large effect on bulk ice flow in ice sheets If the orientations are anisotropic the ice has a bulk anisotropic response to stress Conversely ice flow drives development of crystal orientation fabric in ice sheets Aside from understanding ice rheology ice fabric may be useful itself for paleoclimate interpretation Kennedy et al 49 found that initial differences in fabric at snow deposition can persist deep into ice sheets In the NEEM core in Greenland there is an abrupt change in fabric corresponding to the Holocene transition 60 Anisotropic ice flow due to anisotropic crystal fabric can itself hinder paleoclimate interpretation by causing stratigraphic disruption where isochronous layers can become folded or removed Alley et al 7 found recumbent z-folds in the GISP2 core associated with stripes of anomalously oriented grains Fudge et al 32 found evidence of small-scale boudinage about 750m above the bed in the WAIS divide core These features may be due to anisotropic flow This thesis is not primarily focused on the detailed microstructural physics of ice nor is it directly focused on empirical observations of ice crystal orientation fabrics Instead it is focused on answering the question of what we do not know about ice fabric and anisotropic ice flow I explore uncertainties in fabric measurement methods and also how these un- 2 certainties may be reduced I examine the effects of velocity-gradient perturbations on ice fabric In addition I study perturbations to fabric as part of a coupled system and show that stratigraphic disturbances could occur due to initial fabric perturbations in coupled ice flow and fabric development 1 2 Background In this section I will give a brief overview of the background material related to this thesis I first discuss small-scale ice physics I review homogenization methods to derive continuum approximations to polycrystalline ice as well as fabric evolution 1 2 1 Ice crystal deformation rotation and growth A cartoon of an individual ice crystal is shown in Fig 1 1 with the crystallographic c-axis labeled An individual ice crystal deforms primarily by dislocation creep in glacial settings 81 A dislocation is a defect in the crystal lattice Since the regular atomic structure of the crystal is distorted by the dislocation there is an associated strain and stress field For edge dislocations this takes the form of a dipole with one pole being compressive and the other tensile If an external stress is applied to the crystal this produces a net driving force on the dislocation which can induce the dislocation to move if sufficient stress is realized When a dislocation reaches a grain boundary the crystal is sheared Dislocations are generated during strain As grains become highly strained dislocations begin to interfere causing deformation to become more difficult This is known as work-hardening in common with the metallurgical definition Dislocations may be removed through the process of recovery where dislocations move to minimize their free energy This occurs partly through the annihilation of dislocations of opposite sign and arrangement of dislocations into subgrain boundaries or to the grain boundaries themselves The combined effects of dislocation generation recovery and work hardening produces a steady-state density of dislocations at higher strains and a steady-state strain rate for constant stress This steady state is known as secondary creep 81 3 The direction of movement of a dislocation is the Burgers vector denoted by bi We will denote the normal to the slip plane by mi A slip system is the same Burgers vector and slip plane normal repeated over the crystal structure Slip systems are defined by the Schmid tensor Eij bi mj The resolved shear stress on each slip system is given by s Eij Sij 1 1 where Sij is the deviatoric stress experienced by the crystal The rate of shearing on the slip system is given by the following relation B sn 1 s Q exp RT 1 2 Here B is a constant Q is the activation energy of the slip system R is the universal gas constant and T is the temperature The exponent n is roughly 3 for steady-state dislocation creep in ice 81 which is the regime glacial ice is usually in In ice easy slip only occurs on the basal plane where the normal to the plane mi is given by the c-axis ci Slip in either prismatic or pyramidal planes is on the order of 100 times harder 28 This is the mechanism behind the extreme level of plastic anisotropy of ice compared to most other materials Other deformation mechanisms besides basal dislocation slip are usually active in deforming ice Dislocation glide on the basal plane provides two independent slip systems corresponding to the two degrees of freedom of the plane However a minimum of five independent slip systems is needed to accomodate arbitrary deformations 80 During deformation grains well-oriented towards basal slip will begin to deform but are blocked by hard-oriented grains The resulting stress may be relieved through several mechanisms Grain boundary sliding can occur to maintain compatibility between adjacent grains Nonuniform deformation involving bending of the lattice may occur within grains This can result in the formation of subgrain boundaries 65 In addition slip along prismatic planes may occur in some circumstances 65 The most commonly used constitutive relation for isotropic ice is Glen s flow law 39 4 which is closely related to Eq 1 2 : Dij BSij en 1 Q exp RT 1 3 where e is the effective stress and Dij is the strain-rate tensor The exponent n is usually set to 3 in common with the exponent for steady-state dislocation creep To maintain compatibility with other grains and the externally applied strain lattice rotation occurs during dislocation creep This induces c-axes to rotate towards directions of principal compression For example in vertical compression prominent near ice divides c-axes rotate towards vertical This makes the ice harder under applied vertical compression since there is is a smaller component of shear stress along the basal plane In the extreme case where a grain pointed exactly vertically is subjected to vertical compression there is no resolved shear stress on the basal plane Thus the crystal does not deform through basal glide at all In the case where deformation occurs solely due to slip on the basal plane the rate of c-axis rotation due to lattice rotation is given by a modified Jeffery s equation 58 g g c i Vij cj Dij cj ci cj ck Djk 1 4 Here Vij is the bulk vorticity tensor corresponding to externally applied spin The quantity g is a component of the strain-rate tensor experienced by the grain rather than the global Dij strain rate The last term of Equation 1 4 ensures that the rotation of the c-axis is tangent to the sphere to maintain unit length This can be seen by noting that the Vij cj term does not affect the magnitude of ci leaving only the Dij cj term Assume that at time t 0 the c-axis is given by c0 After a short length of time t the magnitude of the new c-axis c t is without the final term in Equation 1 4 c t c0 tDc 1 5 c0 cT0 Dc0 t 1 6 1 cT0 Dc0 t 1 7 5 to first order in t Thus for the c-axis to maintain unit length we must add the quantity cT Dc t projected onto c by multiplying by c This then gives the last term of Equation 1 4 While deformation-induced grain rotation is the most important process governing fabric development in ice sheets other processes play a role in both fabric development and ice rheology There is evidence that grain size plays a significant role in ice deformation Cuffey et al 18 used observations from the Meserve Glacier in Antarctica to argue that grain-size variations explain a significant amount of enhanced shear in ice-age ice in Greenland Grain growth in which some grains grow at the expense of others occurs throughout ice sheets Normal grain growth is most prominent in upper layers of ice sheets where grains are not yet highly strained Here large grains grow at the expense of small grains due to differences of curvature Grain boundaries with high curvatures have more unmade bonds per unit area these unmade bonds possess free energy Smaller grains have higher positive curvature over more of their boundary than large grains making it energetically favorable for large grains to consume small ones 59 As grains become more highly strained the process of polygonization also known as rotation recrystallization works against normal grain growth As noted previously bending of the crystal lattice induces the formation of subgrain boundaries because dislocations lying in different basal planes can minimize their strain energy fields by lining up As this process continues and the subgrain misorientation increases the subgrains become distinct grains This process also reduces the work-hardening of grains since dislocations are moved from grain interiors to the new grain boundaries Polygonization causes changes in grain orientation of no more than a few degrees 6 It does not significantly change the resolved shear stress of the resulting child grains In contrast to polygonization dynamic recrystallization also known as migration recrystallization or discontinuous recrystallization can greatly change grain orientations Highly strained grains have a high dislocation density which carries a great amount of strain energy Newly nucleated grains with low dislocation densities can then easily grow with the reduc- 6 tion in dislocation density providing the main driving force These grains are typically well oriented for basal glide Dynamic recrystallization typically occurs in waves as new grains rapidly grow and consume the older more strained grains e g Montagnat and Duval 59 This produces an interlocking texture of irregular very large up to several cm3 grains This provides an important mechanism to control the strength of ice fabrics deep in ice cores In particular near ice divides it limits the tendency of c-axes to line up to vertical under the applied vertical compression This limits the hardness of the ice under the applied stress Dynamic recrystallization is usually active only above about 10 C which occurs in deeper layers in most ice-sheet locations Although dynamic recrystallization is evident in layers as shallow as 200m at Siple Dome at temperatures of around 20 C 21 1 2 2 Homogenization A key difficulty of any continuum treatment of anisotropic ice is stress and strain homogenization: Stress and strain of individual grains must be consistent with the global stress and strain of the entire polycrystal The homogenization scheme must also be tractable There are two possible end-members First the Taylor-Bishop-Hill model 74 assumes homogeneous strain among grains while allowing stress between grains to vary so as to produce the required global strain This method is well-suited to materials with several active slip systems It also has the advantage of avoiding overlap between grains: because every grain has the same strain compatibility is guaranteed An alternative approach is the Sachs model 69 which assumes homogeneous stress among grains The strain of each grain is such that the global stress is maintained This model does not produce strain compatibility which can produce nonphysical overlaps between grains Nonetheless it produces better bulk strain and stress predictions for ice than the homogeneous strain model because ice typically has only two active slip systems In the middle between these two are visco-plastic self-consistent VPSC schemes 52 Here each individual grain is treated as an ellipsoidal inclusion in an infinite homogeneous matrix with the average properties of the polycrystal the homogeneous equivalent medium 7 Figure 1 1: Cartoon of an individual ice crystal with the basal plane and c-axis shown c-axis basal plane This allows for stress and strain to be dependent on grain orientation which is more realistic than the homogeneous stress or homogeneous strain assumptions However it requires iterative solutions: the deformation of each grain is dependent on the properties of the homogenenous equivalent medium which is in turn dependent on the properties of every other grain This makes the VPSC scheme difficult to directly apply in many applications such as ice flow models or continuum fabric evolution models However Gillet-Chaulet et al 38 sidestepped this problem by instead fitting a parameterized constitutive relation to the results of a VPSC model over a grid of fabric parameters 1 2 3 Orientation distribution functions ODFs The distribution of ice-crystal c-axes may be described by an orientation distribution function or ODF These are also known as crystal orientation distribution functions COFs ODFs are probability distributions of c-axes defined on the unit sphere Despite the name ODFs are not necessarily true fuctions as is the case with the discrete ODF given by the crystals of a thin-section sample Since a c-axis c cannot be distinguished from c due to ice crystals having reflectional symmetry about the basal plane ODFs are antipodally symmetric Due to this antipodal symmetry ODFs are commonly restricted to the upper hemisphere Throughout most of this thesis we instead treat the ODF as being defined on the entire sphere for mathematical convenience 8 Orientation tensors Orientation distribution functions are often summarized using symmetric orientation or moment tensors 2 These tensors are used throughout this thesis The element with index i1 in of the nth order orientation tensor Ti1 in is given by the outer product of of the c-axis with itself n times averaged over the ODF Ti1 in n Y ci j 1 8 j 1 Since ODFs are antipodally symmetric odd-order tensors are zero Usually the fabric is described with only the second-order orientation tensor Aij ci cj This is a symmetric 3 3 tensor The second-order orientation tensor is also the covariance tensor of the ODF if it is viewed as a distribution in Cartesian space with support confined to the sphere The definition of covariance of a distribution is the second moment about the mean given by Cov ci cj ci ci cj cj 1 9 Since the mean or first-order orientation tensor ci is zero due to antipodal symmetry this reduces to Aij ci cj Because it is symmetric there exists a reference frame where Aij is diagonal with eigenvalues 1 2 3 which sum to unity They sum to unity by construction because all c-axes lie on the unit sphere The corresponding eigenvectors are also known as fabric principal directions The eigenvalues correspond to concentrations of fabric in each principal direction The principal direction associated with the largest eigenvalue 3 has the highest concentration of c-axes and the principal direction association with 1 has the lowest concentration The eigenvalue 2 is associated with the direction orthogonal to the other two If 3 2 1 then the fabric is isotropic with c-axes distributed nearly uniformly across the sphere If instead 3 2 1 then the fabric is known as a single-maximum or pole fabric In the case where 3 2 1 then the fabric is a girdle fabric with a 9 Figure 1 2: Schmid plots of thin sections taken from the WAIS divide ice core Each dot represents the c-axis orientation of a single grain An azimuthal equal-area projection is used such that a grain in the center of the circle is vertical and a grain on the edge has a horizontal c-axis A is an approximately isotropic fabric 3 2 1 B is a girdle fabric 3 2 1 C is a single-maximum fabric 3 2 1 A C B concentration of c-axes lying near the great circle orthogonal to 1 Examples of each of these fabric types from the West Antarctic Ice Sheet WAIS divide ice-core 30 are shown in Figure 1 2 The fourth-order orientation tensor Aijkl ci cj ck cl is also necessary for many flow and fabric evolution calculations While it is not typically used to describe ice fabrics it can account for more complex fabric types such as fabrics with multiple maxima In practice this is usually estimated from the second-order orientation tensor through closure approximations see next section Zheng and Zou 84 showed that an ODF may be expressed as as an expansion of orthogonal traceless basis-functions with coefficients derived from orientation tensors The first two terms of this expansion are given by 1 15 c 4 2 1 Aij ij ci cj 3 1 10 If we are working in the reference frame defined by the fabric principal directions such that the second-order orientation tensor is diagonal the link between fabric eigenvalues and ODF 10 density can be readily seen Unfortunately this series expansion approach is not usually useful to describe most fabrics If the expansion is truncated at the second-order as above the second-order orientation tensor of the truncated distribution is not necessarily the same Aij it is parameterized by i e Ai j on the right-hand side of Eq 1 10 In particular the second and fourth-order trunctions cannot represent very strong single-maximum fabrics Basis functions and coefficients beyond the fourth order have unfeasibly many terms 1 2 4 Continuum fabric evolution models Eq 1 4 gives the rotation rate of a single grain When modeling bulk fabric it is not practical to treat each grain individually Instead we may derive an evolution equation for the second-order orientation tensor Aij This has only six unique components reducing an expensive computational problem to a small ODE system Suppose that we have an ODF c giving the density of c-axes at c dAij c i cj ci c j dt 1 11 Replacing c in the above equation with Eq 1 4 we arrive at the following evolution equation for the material derivative of Aij : dAij Vik Akj Aik Vkj Dik Akj Aik Dkj 2Aijkl Dkl dt 1 12 The last term involves the fourth-order orientation tensor Aijkl which introduces the closure problem: to determine the evolution of the second-order orientation tensor we need the fourth-order orientation tensor We could similarly use an evolution equation for the fourthorder orientation tensor but the sixth-order orientation tensor would appear in that equation and so on Thus we need some way to approximate the fourth-order tensor Aijkl in terms of Aij In the fiber literature a vast array of closure approximations have been proposed to solve this problem I will discuss a few here Perhaps the simplest is the quadratic closure where Aijkl Aij Akl This is exact in the case of perfectly concentrated fabrics where 3 1 It is quite accurate whenever 11 3 0 8 and produces reasonably accurate predictions for the c-axis rotation rate even for diffuse fabrics The quadratic closure is still the most common closure used for industrial fiber-orientation models due to its simplicity and reasonable accuracy Another simple closure is the linear closure Aijkl 1 ij ij ij ij ij ij 35 1 Aij kl Aik jl Ail jk Akl ij Ajl ik Ajk il 1 13 7 The linear closure is exact for isotropic fabrics but produces invalid predictions for strong single-maximum fabrics Therefore it is not a good choice itself as a closure approximation in ice because strong single-maximum fabrics are common in deeper layers of ice sheets The hybrid closure 3 instead takes a weighted average of the linear and quadratic closures where the weighting is usually dependent on the largest eigenvalue 3 This can exactly represent both isotropic fabrics and perfect single-maximum fabrics Other more sophisticated closures exist Chung and Kwon 16 proposed the invariantbased orthotropic fitted IBOF closure This closure writes Aijkl using polynomial functions of the invariants of Aij The coefficients of the polynomial functions are fitted to a particular assumption of the form of the ODF or to empirical data This closure approximation was used by Gillet-Chaulet et al 38 by fitting to an analytical distribution Lastly I examine the fast exact closure 63 If a fabric is initially isotropic and evolves only due to lattice rotation from basal slip then the ODF has the following form: c 1 4 cT Bc 3 2 1 14 where B CT C has a determinant of unity and C follows the equation dC C D W dt 1 15 Rather than solving the Jeffery s equation 1 12 directly only the previous ODE 1 15 must be integrated This sidesteps the closure problem entirely The orientation tensors Aij and Aijkl can be easily recovered using Carlson symmetric integrals However it is not 12 necessary to compute Aijkl in order to integrate the evolution of the fabric through time This closure is not exact in the case of ice fabrics since they typically are not initially isotropic and do not follow the distribution given by Eq 1 14 exactly However I have found that this distribution does an excellent job of approximately fitting thin-section data This suggests that this closure approximation would be accurate in practice for predicting ice fabric development The IBOF closure used by Gillet-Chaulet et al 38 is in fact a polynomial approximation to this closure Compared to the IBOF closure the fast exact closure has a simpler implementation and better theoretical motivation In addition it is also more computationally efficient if Aij and Aijkl do not need to be computed at every timestep 1 3 Outline This thesis is divided into four main chapters corresponding to four manuscripts In the second chapter I examine statistics and sampling error in ice-core thin sections I derive novel estimates of sampling error in fabric and apply these estimates to thin-section data from the WAIS divide ice-core 30 I show that thin-section sampling error can be large under area-weighted thin sections I also introduce a new parameterized ODF to glaciology and compare the fits of this and other distributions in the WAIS and Siple Dome ice cores The last two main chapters examine the sensitivity of anisotropic flow to perturbations of flow and fabric In the fourth chapter I examine the sensitivity of ice fabrics to velocity gradient perturbations I show that small velocity-gradient perturbations can induce tilted-cone fabrics in simple shear and pure shear where the direction of greatest c-axis concentration is not vertical These fabrics can induce vertical motion in horizontal simple shear The fifth chapter is an expansion on the third: given that small velocity perturbations can cause significant fabric perturbations can the dynamics of coupled ice flow and fabric evolution cause these perturbations to grow further I examine this by developing an analytical first-order model of coupled anisotropic ice flow and fabric perturbations I show that under pure shear and simple shear fabric perturbations in single-maximum fabrics can be 13 unstable The contributions of this thesis are significant in several ways I provide a thorough examination of methods of measuring crystal orientation fabrics in boreholes The rigorous estimates of thin-section sampling error I developed are generally larger and more realistic than previous estimates Accurate estimates of uncertainties will aid usage of fabric data for paleoclimate interpretation In addition my uncertainty estimates may also be useful to inform thin-section sampling done in future ice cores Finding the best number and the best locations of thin-section samples for an ice core is a trade-off between consumption of limited core ice labor accuracy and spatial coverage By providing accurate estimates of uncertainty based on grain-size distributions and fabric eigenvalues these decisions can be better justified Inference of fabric using sonic velocities and thin-section measurements is a promising technique to combat sampling error or bias in sonic measurements and sampling error in thin sections Borehole sonic logging has received increased interest over the past several years Given that thin-section measurements usually taken from ice cores anyway this technique can improve accuracy with little cost My statistical approach to fabric inversion also makes fewer assumptions on the form of the ODF compared to previous work It is also an innovative use of the Google Tensorflow machine learning library for a geophysical inversion problem This has the potential to be a convenient tool to use in other similar problems The last two chapters of this thesis provide the most comprehensive examination of stability of ice-crystal fabrics to date Stratigraphic disruption due to anisotropy has received little attention despite being the most plausible cause of smaller-scale stratigraphic disturbances seen off the bed In addition anisotropy probably plays a strong role in large-scale folding and stratigraphic disruption in basal ice due to its ability to create very large differences in viscosity The work in this thesis is a start to understanding this complicated topic 14 Chapter 2 STATISTICAL ASPECTS OF ICE-CRYSTAL ORIENTATION FABRICS This chapter is in review at the Journal of Glaciology with Ed Waddington as co-author I developed the statistical results and wrote this manuscript Ed Waddington helped edit the manuscript and contributed useful discussions Abstract: Ice crystal orientation fabric has a large effect on polycrystalline ice flow due to the strong plastic anisotropy of individual grains The crystal orientation fabric can be described as an orientation distribution function ODF which is a probability distribution defined on the sphere for the direction of crystal c-axes From this viewpoint we present several statistical results for ODFs We introduce a parameterized ODF PODF the Bingham distribution to glaciology We compare the performance of this and other PODFs against measurements from the West Antarctic Ice Sheet WAIS and Siple Dome ice cores We also examine the sampling error introduced by attempting to infer the larger-scale bulk ODF from a thin-section sample We introduce new analytical expressions for sampling error and examine the use of bootstrapping for estimation of sampling error We show that sampling error of fabric parameters can be substantial Finally we examine sampling error from inferring enhancement factor in Glen s flow law from thin sections We show that rheological properties of ice are very poorly constrained by thin-section measurements due to the power-law constitutive relation of ice in the dislocation-creep regime 2 1 Introduction An individual ice crystal has an anisotropic creep response deforming most easily in shear parallel to the crystal basal-plane orthogonal to the crystallographic c-axis Plastic deforma- 15 tion of an ice polycrystal depends on the orientations of its constituent grains e g Azuma 8 which is described by the c-axis orientation distribution function ODF The ODF is a probability distribution of c-axis density often defined on the upper hemisphere because a c-axis vector c is indistinguishable from c In this paper we will instead treat the ODF as being an even function defined on the entire sphere for mathematical convenience A polycrystal with an isotropic ODF will have a bulk isotropic response to applied stress However polycrystals develop an anisotropic ODF in response to applied strain The development of a preferred orientation is guided primarily by intracrystalline slip Due to interference among grains there is a tendency for the c-axes to rotate away from the directions of principal extensional strain 10 ODFs are often summarized using orientation or moment tensors e g Svendsem and Hutter 73 We will make extensive use of index notation in this paper due to the use of higher-order tensors However at times we will not follow the summation convention for notational convenience this is noted when it occurs In addition throughout this paper indices 1 2 and 3 are associated with the x y and z directions respectively The second-order orientation tensor Aij is the expectation ci cj where i j 1 2 3 The mean of the ODF ci is always zero because of antipodal symmetry Therefore Aij is also the covariance matrix of the distribution by definition of covariance as Cov ci cj ci ci cj cj The diagonal elements A11 A22 and A33 give a measure of the c-axis concentration on the x y and z axes respectively Similar to the second-order orientation tensor the fourth-order tensor is the expected value Aijkl ci cj ck cl Since ODFs over the sphere are antipodally symmetric odd-order tensors are zero The symmetric second-order orientation tensor may be decomposed into non-negative eigenvalues and three orthogonal eigenvectors The eigenvalues of A sum to unity by construction The eigenvectors or fabric principal directions denote the directions of greatest density corresponding to the largest eigenvalue smallest density the smallest eigenvalue and a direction orthogonal to the other two An isotropic fabric has three equal eigenvalues A girdle fabric in which there is a band of high concentration along a great circle has two nearly equal eigenvalues and one small eigenvalue A single-maximum fabric 16 Table 2 1: List of symbols Symbol Definition qi Component of a tensor in index notation q Same tensor in vector notation x Sample estimate of a quantity x ci ice-crystal c-axis for i 1 2 3 in x y z directions c Ice-crystal orientation dist func qi Expected value of qi under aij Grain structure-tensor ci cj Aij Comp of the 2th order orient tensor aij Aijkl Comp of the 4th order orient tensor aij akl i Fabric eigenvalue of A V Matrix of eigenvectors of A Zenith angle Azimuth angle ij Kronecker delta symbol S2 Unit sphere A standard deviation Sij Stress tensor B Bingham distribution Equation 2 3 L Diagonal concentration matrix of B D Dinh-Armstrong distribution Equation 2 4 R Parameter matrix of D F Lliboutry s Fisherian distribution Equation 2 1 W Watson distribution Equation 2 2 Scalar concentration parameter for F Scalar concentration parameter for W 17 has one large eigenvalue and two small ones Small-girdle fabrics can also occur during active recrystallization where a small ring of high density exists around the axis-preferred orientation of the applied strain and vorticity typically centered around vertical It is common to approximate the unknown true ODF with a parametric ODF PODF which can normally be fit to observed fabric data This reduces the number of parameters Among other uses it is usually necessary to assume a specific PODF to numerically model fabric evolution Numerous PODFs have been proposed The majority have an axis of rotational symmetry which is valid for single-maximum fabrics and symmetric girdle fabrics Several PODFs have been developed that are motivated by analytical solutions to c-axis evolution valid in specific flow regimes e g Staroszczyk and Gagliardini 72 Svendsem and Hutter 73 Gagliardini and Meyssonnier 33 G odert and Hutter 41 However Gagliardini et al 36 noted that these are special cases of the Dinh-Armstrong distribution 20 This is a very flexible distribution that does not assume axial symmetry Any initially isotropic fabric which evolves due only to deformation-induced grain rotation has this ODF Other distributions have been proposed based on heuristic considerations e g Thorsteinsson 75 Lliboutry 54 More recently Kennedy et al 49 proposed the axially symmetric Watson distribution for use as PODF For a complete overview of this topic see Gagliardini et al 36 In this paper we propose the Bingham distribution as an ODF motivated primarily by statistical considerations The Bingham distribution is a generalization of the Watson distribution Sampling error can be significant when inferring bulk properties of ice from a small thinsection sample By bulk properties we mean those averaged out over large ice volumes What constitutes a larger volume is somewhat arbitrary but is at least as large as to render sampling error insignificant over the length scales of the larger volume Sampling error is the error from approximating something here the bulk properties of ice from a limited sample size Therefore it is important to take sampling error into account when interpreting ice-sheet thin sections in order to properly interpret thin-section data In addition this sampling error can also be viewed as variability in the underlying ODF on the scale of thin 18 sections This can cause variability of anisotropic viscosity on the scale of thin sections Thorsteinsson 75 found that around 5000 grains are needed to effectively eliminate sampling error in a fabric model Later on Durand et al 24 fit a quadratic estimate of the sampling error of A by generating an array of fabrics of 10 000 grains each and resampling from these fabrics Unfortunately this method is not directly applicable to per-pixel measurements such as with electron backscatter diffraction or automatic fabric analyzers since it does not take into account the correlation of nearby measurements Here we introduce an analytical estimate for the sampling distribution of fabric eigenvalues and eigenvectors based on data taken from a discrete thin-section sample with either equal weighting of grains or weighting by area Generally area weighting should be preferred as it more accurately reflects the true fabric by giving a larger weight to larger grains 35 When fabric eigenvectors and eigenvalues are derived using area weighting of crystals in thin sections we show that sampling error can be greatly increased We also numerically derive an estimate of the sampling distribution of enhancement factor 53 under simple shear from thin sections This random variability for regions of several hundred grains can also affect small-scale flow This may be a source of incipient layer folds which can then be overturned by anisotropically-enhanced shearing deep in ice sheets 76 2 2 Parameterized orientation-density functions PODFs We now examine the use of PODFs We discuss several previously used PODFs which we consider to be especially statistically and physically plausible We introduce the Bingham distribution as a PODF We then compare the log-likelihoods of the distributions fitted to thin-section data at the West Antarctic Ice Sheet WAIS Divide ice core and the Siple Dome ice core to assess their performance 2 2 1 Fisher and Watson distributions Lliboutry 54 first suggested the use of an axially-symmetric Von Mises-Fisher type distribution Expressed in a reference frame where the vertical axis is aligned with the symmetry 19 axis this is F exp cos e 1 2 1 where is the zenith angle and is a scalar concentration parameter Gagliardini et al 36 found that this distribution provided the best fit for fabric in a thin section from the Dome C core As a modification to the Lliboutry s Fisherian distribution Kennedy et al 49 introduced the Watson distribution for use as a PODF: W a exp cos2 2 2 where is a concentration parameter is the zenith angle and a is a normalization constant Note that by the double-angle formula if the concentration parameters for the Watson distribution and for the Fisher distribution are equal then F 2 W Both of these distributions can represent single-maximum fabrics with positive concentration parameters and the axis of symmetry parallel to the eigenvector associated with the largest eigenvalue Likewise girdle fabrics can be represented with negative concentration parameters with the axis of symmetry parallel to the eigenvector associated with the smallest eigenvalue The Watson distribution has the important advantage of being antipodally symmetric Because individual ice-crystal orientations cannot be distinguished between c and c any ice ODF defined on the sphere should also be antipodally symmetric It is common practice to define ODFs only on the upper hemisphere Any ODF defined on the upper hemisphere can trivially be extended to the whole sphere However this does not in general preserve smoothness which is usually desirable For the Von Mises-Fisher distribution of Lliboutry the derivative of density with respect to does not vanish at the equator If we extend this ODF to the whole sphere the derivative is discontinuous at the equator The discontinuity does not have a physical basis This same difficulty appears when extending any distribution on the half to the full sphere whose density gradient does not vanish at the equator 20 2 2 2 The Bingham Distribution We now introduce the Bingham distribution 13 as a generalization of the Watson distribution The density in Cartesian coordinates is B c L exp cT VLVT c 2 3 where V is the matrix of eigenvectors of the second-order orientation tensor A and is a normalization constant Also L is a diagonal matrix containing three concentration parameters i such that 1 2 3 This distribution is invariant for changes in the sum of concentration parameters because any change in the sum of concentration parameters is negated by a change in the normalizing constant L Because of this we may set 1 0 since if the parameters are i with 1 6 0 the distribution with concentration parameters i 1 is identical This reduces the number of free parameters from three to two If we set 2 0 as well the Watson distribution Equation 2 2 is recovered This distribution has a number of desirable properties It is able to represent single-maximum fabric and girdle fabrics but is also able to capture fabrics with three distinct eigenvalues such as oblong maxima or girdles that are concentrated in one direction In addition the Bingham distribution is parsimonious If we seek a PODF with a given A then the Bingham distribution avoids introducing spurious structures that are unnecessary to satisfy the assumption of a particular value of A Specifically the Bingham distribution is the maximum-entropy distribution for any spherical distribution with a given second-order orientation tensor or covariance matrix 55 Distributional entropy is defined very similarly to thermodynamic entropy the latter can be seen as a special case of the former The entropy of a probability distribution q is the expectation log q Distributions that have high entropy contain less information Higher-entropy distributions are therefore more parsimonious due to having less information Thus when selecting a parametric distribution the distribution with the highest entropy that adequately fits the given data is the most parsimonious explanation of the observations Such a distribution fits the data well but without assuming extraneous 21 information In this sense the Bingham distribution is similar to the multivariate normal distribution which has maximum entropy of any distribution over n-dimensional Euclidean space possessing a given covariance matrix or the exponential distribution which has the maximum entropy of any distribution on the line with a given mean The Bingham distribution is in fact the multivariate normal distribution with zero mean conditioned to lie on the unit sphere The Bingham distribution has found use in paleomagnetics 64 and other fields However its wider adoption has been hampered by a lack of closed-form analytical expressions for the normalization constant and the maximum-likelihood estimator of i given the data necessitating a greater use of slower numerical methods than many other distributions However this is not as great of a challenge as it once was In addition since the distribution is determined by two parameters it is amenable to methods based on lookup tables In fitting a Bingham distribution to an observed fabric only the second moment of the observed fabric A is needed Higher moments are neglected which means the Bingham distribution cannot fit complex fabric distributions such as those with multiple maxima It is possible to derive distributions fitting higher moments However this would quickly become unwieldy In addition if the goal is to estimate a bulk fabric distribution from a limited thin-section sample more complex distributions would tend to overfit the data 2 2 3 The Dinh-Armstrong distribution We now examine another distribution which we will refer to as the Dinh-Armstrong distribution 20 This is given by D c 1 3 4 cT Rc 2 2 4 where R is a symmetric second-order tensor with a determinant of unity Gillet-Chaulet et al 38 introduced this distribution to glaciology for fabric evolution If c rotates due only to slip on the basal plane and if the ODF was at one time isotropic then the ODF has this distribution with R FFT where F the bulk deformation gradient In the reference frame 22 defined by the fabric principal-directions R is a diagonal matrix with diagonal entries bi The three elements bi possess only two degrees of freedom due to the constraint that the determinant is unity 2 2 4 Comparison of PODFs We now compare the Dinh-Armstrong distribution Equation 2 4 the Fisherian distribution Equation 2 1 and the Bingham distribution Equation 2 3 using thin-section data from the WAIS Divide ice core 30 and the Siple Dome ice core 82 We found a maximum-likelihood fit of each of these three distributions for each thin section The data likelihood of a parameter value of a parameterized distribution f is the probability of those observed data arising under the distribution f with the parameter value The maximum-likelihood value of is the value of that maximizes this likelihood That is the maximum-likelihood estimator maximizes Pr d where d is the observed data In practice the log-likelihood is maximized instead of directly maximizing the likelihood Maximum-likelihood estimation is a standard way to fit distributions to data for many statistical tasks It provides a coherent measure of the fitness of a distribution to data Thus comparing log-likelihoods of data for the maximum likelihood fits of these distributions is a fair way of comparing their performance For the Bingham distribution Equation 2 3 we computed the maximum-likelihood density estimates of L numerically given the observed grain orientations from the WAIS and Siple Dome ice-cores For the Dinh-Armstrong distribution Equation 2 4 we numerically found the maximum-likelihood estimates for the parameter R For Lliboutry s Fisherian distribution with a single-maximum fabric we first rotated the reference frame into the fabric principal reference frame such that the eigenvector corresponding to the largest eigenvalue points vertical For Lliboutry s Fisherian distribution with a girdle fabric we rotated the reference frame such that the eigenvector associated with the smallest eigenvalue is vertical We then numerically found the maximum-likelihood estimates for the concentration parameter The results for all three PODFs for both WAIS and Siple Dome are plotted in Figure 2 1 23 We consider the normalized log-likelihoods of thin-sections normalized by either thinsection area or number of grains rather than the likelihood of observing all grains in each thin section Normalized log-likelihood gives the average likelihood of observing a grain from a thin section This is necessary because the thin sections differ in the number of grains so the likelihoods of each thin section with all grains taken together are not directly comparable Everything else being equal a sample with more grains will have lower likelihood than a sample with few grains Note that we are plotting the log-likelihood of each distribution for the maximum-likelihood values of the parameters L and R We are not plotting the values of these parameters themselves since they are not comparable between distributions and they themselves give no information on the goodness of fit The Fisherian distribution has the lowest log-likelihood for nearly all thin sections The Bingham and Dinh-Armstrong distributions perform similarly with the Bingham distribution slightly outperforming the Dinh-Armstrong distribution overall For these data as a whole this indicates that the Bingham distribution is the best choice due to its maximum-entropy property However the Dinh-Armstrong distribution does not have a normalization constant that must be found numerically as the Bingham distribution does Therefore it may be a better choice for many applications Different physical situations are not likely to be fit by a single ODF However both the Dinh-Armstrong Equation 2 4 and Bingham Equation 2 3 distributions have physical motivation and may serve as good default PODFs All three PODFs are capable of exactly representing isotropic fabrics and in the limit perfect single maximum fabrics Thus they perform similarly in the less-anisotropic fabric near the top of the WAIS divide ice core Log-likelihoods are usually lower for diffuse fabrics than for concentrated fabrics In concentrated fabrics most of the grains lie in orientation which have high ODF density resulting in high likelihoods In the limit of grains taken from a perfect single-maximum fabric the likelihood of each grain is positive infinite On the other hand in the limit of an isotropic fabric the unnormalized log-likelihood of every grain is always log 4 This is because the area of the surface of the sphere is 4 24 Figure 2 1: Log-likelihood of maximum-likelihood fits of the Dinh-Armstrong Equation 2 4 Bingham Equation 2 3 and Fisherian Equation 2 1 distributions to WAIS and Siple Dome thin-sections Higher log-likelihood indicates a better fit The likelihoods are normalized by grain area for WAIS For Siple Dome they are normalized by the number of grains The Dinh-Armstrong and Bingham distributions perform similarly with the Lliboutry s Fisherian distribution having lower likelihood for almost all thin sections WAIS Divide 1 0 Average log likelihood A Bingham Dinh-Armstrong Fisherian 0 5 0 0 0 5 1 0 1 5 2 0 2 5 3 0 0 1000 1500 2000 Depth m 2500 3000 Siple Dome 1 0 0 0 3500 B Bingham Dinh-Armstrong Fisherian 0 5 Average log likelihood 500 0 5 1 0 1 5 2 0 2 5 3 0 0 200 400 Depth m 600 800 1000 25 2 3 Sampling error in thin sections C-axis measurements from ice-sheet thin-section samples provide a way of directly sampling c-axes from ice sheets Sampled crystal c-axes can be assumed to be taken from some orientation distribution function Thin-section samples are small in area typically with a few hundred grains Therefore inferring the bulk fabric of the surrounding ice from thinsection samples is subject to sampling error This introduces uncertainty in the inferred bulk ODF However this same error also reflects the variability of fabric properties on on the scale of thin sections hundreds of grains without assuming that grains from different regions are drawn from different distributions Therefore one may expect deformation to randomly vary over the same small length scales even if the ODF is stationary across space The true distribution of grain orientations may also be non-stationary in space due to differences in material properties This can result in inaccuracies as a sample from a thin section may not be drawn from the same distribution as the bulk fabric Therefore due to sampling error and possible spatial non-stationarity thin-section samples do not perfectly capture the larger-scale bulk-fabric ODF Several different methods have been developed to measure c-axes in thin sections The Rigsby Stage technique 51 was the first method for c-axis determination in thin sections using extinction angles of polarized light This is a manual technique which gives pergrain measurements of c-axes In recent years automatic fabric analysers 83 and electronbackscatter diffraction EBSD 46 have become popular These techniques yield highresolution images of grain orientations with c-axes measured per-pixel rather than per-grain Typically there are many more pixels than grains It may initially seem that the sampling error would be nearly eliminated due to the very large number of pixels However in Appendix A1 we show this is not the case because nearby pixels are usually highly correlated We will also show that intragrain variability of c-axis orientations may be neglected when estimating sampling error from thin sections From these two results we show that sampling error of per-pixel measurements is similar to that of per-grain 26 In this section we assume that all grains from a thin section are drawn from the same underlying bulk distribution This is distinct from the situation where there are actual differences in distribution across the thin section for example if a thin section crosses a summer-winter boundary or if vertical thin section includes a thin layer of high impurity content By examining how much sampling error can be expected from thin sections it is possible to infer whether variability among thin sections is real or just an artifact of small sample size We are treating a collection of measurements from a thin section as a realization of a spatially-correlated sample from the underlying ODF The empirical ODF of each thin section sample itself is completely deterministic except for measurement error However here we are interested in the bulk ODF of the surrounding ice not the crystal orientations of a particular slice of ice Thus it makes sense for example to consider correlations of c-axis measurements by looking at how they would be related under repeated thin-section samples taken from the same ODF To get an intuitive idea of how spatial correlation works suppose that we have a perfectly isotropic fabric We choose a single point in this fabric and look at its orientation We previously had the least information possible about the orientation of this point because it is an isotropic fabric Once we select a sample of a single point we know the orientation of that point perfectly Now suppose we select a second point within the same grain The c-axis orientation of this second point will be very close to the first Therefore we can predict the orientation of the second point very accurately Thus while they are both take from the same isotropic ODF they are dependent on each other because they are not independent samples from the ODF of the In Appendix A we derive estimates of the sampling error of the estimate A bulk second order orientation tensor A appropriate for both per-pixel and per-grain c-axis measurments From Equation 7 the variance of this sampling error can be estimated by Var A ij Aijij Aij Aij s2n 2 5 with no sum in i or j Here s2n is the sum of squared grain areas when the area of a 27 thin section is normalized to unity It reaches a minimum when all grains have equal sizes and reaches a maximum when a single grain has a a normalized area approaching unity It tends to be smaller for thin sections with more grains reflecting the fact that having more data reduces uncertainty This estimate applies whether the data are collected per-grain as with manual fabric measurements or per-pixel We show in the appendix that intragranular misorientations can be ignored when estimating sampling error thus per-pixel measurements can be averaged out for each grain When per-pixel measurements are averaged within each grain it is the same as if the data were collected on a per-grain basis in the first place In Appendix A1 we also derive error estimates for fabric eigenvalues and eigenvectors from Equation 7 under the assumption that formulas for first-order eigenvalue and eigenvector perturbations are approximately valid 2 3 1 Bootstrap estimates of sampling error We now explore the use of bootstrap resampling for estimating fabric sampling error Bootstrapping 29 is based on the idea that the empirical distribution of the observed data can be used as an approximation to the unknown true distribution This requires that the data are approximately independent and are drawn from the same distribution We can approximate the distribution of a statistic of interest that depends on the data such as A ij by first resampling the empirical distribution many times with replacement The statistic is calculated for each resample thus approximating the distribution of the statistic In the case of per-grain c-axis measurements this is straightforward assuming that orientations of different grains are approximately independent Bootstrapping is not valid for resampling per-pixel measurements with many pixels per grain because of the high correlation of the orientations of nearby points within the same grain The general idea of bootstrapping is that it is supposed to approximate repeated draws from the underlying distribution by resampling from the original sample However this does not work when the data are dependent as is the case with per-pixel c-axis measurements The data depend on one another in that if we observe a pixel with a particular orientation 28 many other nearby pixels are likely to have the same orientation conditioned on the first pixel They are not sampled independently from the ODF Simply resampling all data from a thin section ignores spatial correlation of the data leading to a large underestimate of variance Instead we suggest a technique known as block bootstrapping 43 Block bootstrapping resamples blocks of data at a time rather than individual datums The goal is that the larger blocks are approximately uncorrelated There is a tradeoff involved in choosing block sizes: larger blocks have less correlation with each other which helps avoid underestimating variance However using blocks that are too large causes overestimation of the variance by making the effective sample size too small Ideally the variance within each block should be as small as possible while maintaining approximate independence between blocks An obvious choice for thin sections is to take individual grains as blocks: Within-block variance is small since c-axes within a grain are not misoriented by more than several degrees Likewise the orientations between different grains are approximately independent from each other By taking individual grains as blocks block bootstrapping per-pixel c-axis measurements is identical to ordinary bootstrapping of per-grain c-axis measurements 2 3 2 Sampling-error estimates for WAIS Divide We now derive error estimates for the WAIS Divide core using both the analytical method developed in the appendix and bootstrapping The c-axis measurements were collected on a per-grain basis 30 We compare the derived sampling distribution of fabric eigenvalues from both approaches in Figure 2 3 To assess uncertainty in fabric principal directions we also compare the sampling distributions of the fabric Euler angles in Figure 2 4 The two methods match very closely for both eigenvalue and Euler angle sampling distributions The 95% central intervals of the area-weighted bootstrapped sampling distributions of Aii no sum are plotted in Figure 2 2 For the WAIS core the observed variability of the fabric eigenvalues over short length scales in depth seems to be primarily explained by sampling error For the most part it is not necessary to assume actual differences in the bulk ODF to 29 explain these differences The exception to this is near the bed where there exists layers of recrystallized and non-recrystallized fabric 30 The sampling error in this core tends to be more sensitive to fabric distribution than it is to sample size The variance Aijij Aij Aij s2n no sum tends to zero as fabric strength increases towards a maximum eigenvalue of unity In this limiting case Aijij Aij Aij no sum and the eigenvalue variance is zero Thus sampled fabric eigenvalues and fabric eigenvectors have smaller variances for strong fabrics compared to weaker fabrics For example the fabric eigenvalues of the thin-section with weak fabric at 180m has similar variance than those of the strong fabric at 3265m thin-section This is despite the fact that the 180m thin-section has nearly three times as many sampled grains as the 3265m thin section 2 3 3 Sampling error in enhancement factor Sampling error in fabric can lead to large uncertainties in flow characteristics The Schmid factor is a measure of the proportion of compressive stress resolved on a c-axis basal plane It is given by Sg cos sin where is the angle between the c-axis and the stress axis Azuma 9 found that the scalar enhancement factor for ice flow under uniaxial compression depends on the fourth power of the Schmid factor averaged among grains This assumption is also used for the CAFFE flow model 67 The dependence on the fourth power indicates that smaller variations in c-axis fabric can induce much larger changes in deformation rates In Figure 2 5 we used bootstrap resampling to estimate the sample distribution of the enhancement factor under simple shear for each thin section in the WAIS core This is given by the fourth power of the average Schmid factor scaled by the average Schmid factor of an isotropic polycrystal which is 1 3 The enhancement factor can vary by 100% or more The power-law viscosity of ice will tend to make smaller differences in fabric correspond to much larger differences in strain rate 30 Figure 2 2: Estimates of the diagonal elements Aii no sum of the second-order orientation tensor Aij from fabric thin sections from the WAIS Divide core The error bars are the 95% bootstrap confidence intervals of the observed area-weighted thin section Aii 1 0 Key Aii A11 A22 A33 0 5 0 0 0 1 2 Depth km 3 4 31 Figure 2 3: Bootstrap resampling and analytical estimates of the sample distributions of the eigenvalues of the thin section fabric at 140m The analytical dashed lines and resampled bootstrap estimates solid lines match closely Because the fabric is rather weak there is still a moderate amount of uncertainty despite this sample having 1405 grains 80 Density 60 40 20 0 0 0 0 1 0 2 0 3 Sample eigenvalue 0 4 0 5 32 Figure 2 4: Bootstrap resampling and analytical estimates of the sample distributions of the error in fabric Euler angles of the thin section fabric at 140m The analytical and resampled bootstrap estimates match closely The smallest eigenvalue has a wide distribution in the associated Euler angle because the other two eigenvalues are close 15 Density 10 5 0 -3 -2 -1 0 1 2 Fabric Euler angle error rad 3 33 Figure 2 5: Bootstrap 95% confidence intervals for enhancement factor for the 83 WAIS thin sections Due to the dependence on the fourth power of the average Schmid factor the confidence intervals are wide 4 5 Enhancement factor 4 0 3 5 3 0 2 5 2 0 1 5 1 0 0 5 0 0 0 500 1000 1500 2000 Ice depth m 2500 3000 3500 34 2 4 Conclusions We compared PODFs with their log-likelihoods for different observed thin sections This is a standard technique to fit probability distributions The Bingham distribution Equation 2 3 and the Dinh-Armstrong distribution Equation 2 4 perform nearly equally for the WAIS and Siple Dome ice-core thin sections Lliboutry s Fisherian distribution Equation 2 1 did not fit the thin sections as well This is chiefly because the Fisherian distribution assumes axial symmetry Axial symmetry which is an assumption used by many previously proposed PODFs is not capable of accurately approximating ODFs with three distinct fabric eigenvalues Ice fabric in most realistic situations has three distinct eigenvalues However the ideal parameterized ODF may not be the same in all situations Inferring larger-scale bulk fabric from limited thin section samples is subject to sampling error We showed analytical estimates of eigenvalue and eigenvector sampling error Eigenvalue and eigenvector sampling error depends strongly on fabric strength with singlemaximum fabrics having smaller eigenvalue and eigenvector variances than diffuse fabrics for the same sample size Thus to achieve the same certainty in fabric ODF larger sample sizes are needed for diffuse fabrics We also examined bootstrapping of per-pixel EBSD or automatic fabric analyzer measurements of thin section data It is necessary to use block bootstrapping for per-pixel data rather than ordinary bootstrapping Ordinary bootstrapping neglects covariances between nearby pixels which causes sampling error to be severely underestimated Sampling error estimates are sensitive to the grain size distribution Often thin sections are dominated by a few large grains with many smaller ones This results in much larger sampling uncertainties than even grain-size distributions The estimates of sampling error distributions for the WAIS core show that fabric eigenvalues are very poorly constrained for some thin sections Sonic fabric measurements are a promising way of overcoming this inaccuracy e g Diez and Eisen 19 Maurel et al 57 These results indicate that fabric variability is likely important for small-scale flow As ice experiences power-law creep relatively small variations in fabric strength can have a large 35 impact on flow Volumes of several hundred to several thousand grains can be expected to display a fairly large amount of fabric variability indicating that ice flow characteristics are unpredictable at those length scales We may also expect regions of ice with larger grain-sizes to experience significant fabric variability from sampling effects over larger length scales than regions with small grain sizes as a doubling of average grain radius will roughly double the length over which sampling variability is important Sampling variability may provide an impetus for layer overturning or boudinage on small length scales Acknowledgements We thank Joan Fitzpatrick and Don Voigt for the WAIS thin-section data We also thank Maurine Montagnat and Ilka Weikusat for helpful discussions on thin-section uncertainty This work was supported by the National Science Foundation grant 1246045 36 Chapter 3 ICE FABRIC INFERENCE WITH THIN-SECTION MEASUREMENTS AND SONIC VELOCITIES WITH APPLICATION TO THE NEEM ICE CORE This manuscript will be submitted to The Cryosphere Discussions soon with co-authors Erin Pettit Ed Waddington Dan Kluskiewicz and Maurine Montagnat Dan Kluskiewicz Erin Pettit and others collected the sonic-velocity data Maurine Montagnat gave us the fabric eigenvalues I developed the model and wrote this manuscript Abstract: We explore methods of inferring crystal orientation fabric using sound waves in ice-core boreholes in tandem with velocity data from ice-core thin sections We pay particular attention to sonic-velocity data collected from the NEEM ice core Thin-section fabric measurements have been the predominant way of inferring crystal fabric from boreholes However thin-section measurements suffer from sampling error and do not provide a spatially continuous record of fabric Sonic-velocity measurements in boreholes allow for spatially-continuous measurements of fabric and largely eliminate sampling error Unfortunately fabric inference from sonic-velocity measurements suffer from error associated with the use of an imperfect sonic-velocity model model error In addition the sonic tool used at NEEM suffered from error due to poor tool centering in the borehole It also collected only P-wave velocities which are sensitive only to the largest fabric eigenvalue To address these difficulties we introduce a method to combine sonic-velocity measurements with fabric measurements We show that this new method suffers from significantly less sampling error than thin-section measurements alone while greatly reducing model error and the effects of poor tool centering In addition this method provides a spatially-continuous record of all three fabric eigenvalues even if only P-wave data are available We apply this method to 37 fabric thin-section data and sonic-velocity data collected at NEEM to produce a spatially continuous and accurate record of fabric 3 1 Introduction Ice is a highly viscoplastically anisotropic material deforming most easily in shear parallel to the basal plane orthogonal to the crystallographic c-axis The distribution of c-axis orientations in a polycrystal is known as the orientation distribution function ODF The bulk strain rate of a polycrystal can vary by an order of magnitude depending on the ODF 76 The ODF is an antipodally-symmetric probability distribution on the sphere giving the density of c-axes by orientation across the sphere Commonly ODFs are summarized by the second-order orientation tensor which is the second moment A of the ODF That is it is the average of the outer product of the c-axis with itself c c taken over the ODF Equivalently the second-order orientation tensor is the covariance matrix of c-axis directions An estimate of the second-order orientation tensor can be found from a thin-section sample as A A X i i ci ci 3 1 where there are N grains ci in the sample with i 1 N Also i is the area of grain i where the areas are normalized such that the total area of the thin section is unity The eigenvalues i of this tensor provide a measure of fabric concentration in each of the three corresponding eigenvectors or fabric principal-directions The largest eigenvalue 3 is associated with the direction of the greatest c-axis concentration The smallest 1 is associated with the direction of least concentration The middle eigenvalue 2 is associated with the direction orthogonal to the other two The eigenvalues sum to unity by construction If 3 2 1 the fabric is isotropic If 3 2 1 the ODF exhibits a single-maximum fabric with a large concentration in one direction If 3 2 1 then the concentration lies along a great circle orthogonal to the direction associated with 1 This is known as a girdle fabric 38 If c-axis directions of a polycrystal are distributed uniformly across the sphere the polycrystal has bulk isotropic viscosity However ice undergoing deformation develops a nonuniform ODF C-axes tend to rotate towards the directions of principal compression due to lattice rotation during deformation 5 This induces bulk anisotropic flow In ice sheets ice crystals are usually somewhat randomly oriented at deposition although preferred orientations have been observed in the firn column close to the surface Placidi et al 67 Durand et al 27 Vertical compression causes c-axes to rotate towards the vertical direction Likewise shear on horizontal planes develops vertical-maximum fabrics due to the combined pure shear and rotation Near divides horizontal extension in one direction and compression along the other two axes often causes vertical girdle fabrics to develop 5 In addition to strongly affecting ice flow the ODF seems to be sensitive to climate at the time of deposition Initial perturbations in fabric due to climate can persist into deep layers 49 In thin sections from the NEEM core 61 there is an abrupt change in fabric corresponding to the Holocene boundary Orientation distribution functions are commonly estimated from ice thin sections taken from ice cores typically consisting of several hundred grains This provides a direct sample of the ODF from the section of ice but suffers from sampling error This sampling error can be especially severe due to the typically highly non-uniform distribution of grain sizes Polycrystal properties are best weighted by area in the thin section 34 if several large grains cover much of the thin-section area the effective sample size can be much smaller than the number of sampled grains In addition to sampling error thin-section samples have very limited spatial coverage usually on the order of 100 cm2 Thin-section samples are labor intensive and consume core ice Due to this thin-section samples are typically taken only on the order of every tens of meters Therefore thin-section samples cannot capture fabric variability at shorter length scales In addition if one is interested in fabric characteristics averaged over several cubic meters rather than a single thin section short length-scale fabric variability on the scale of decimeters introduces another source of error 39 Bentley 12 first proposed sonic logging as a method of fabric measurement to ameliorate some of the difficulties of thin-section fabric measurements In addition to being viscously anisotropic ice is elastically anisotropic Therefore sonic velocities of individual ice crystals are dependent on grain orientation The stiffness tensor of a polycrystal is dependent on the orientation of the constituent grains Sonic velocity measurements holds several advantages over thin-section fabric measurements Sonic logging tools can sample on the order of 3m3 of ice 50 which nearly eliminates sampling error and can reduce the influence of small-scale variability in fabric Unfortunately inference of fabric from sonic velocities is not straightforward Model error can be an issue First sonic velocity in ice is affected by pressure and temperature P-wave velocity in ice changes by around 2 5m s 1 K 1 to 2 8m s 1 K 1 which is a significant issue in polythermal ice e g Helgerud et al 44 Vogt et al 79 This can cause differences in velocity on the order of 100m s 1 in ice sheets 42 Effects of temperature and pressure can be corrected but significant uncertainties may still remain Recently Maurel et al 57 developed analytical expressions for the elasticity tensors and sonic velocities of ice for several ODF types These included single-maximum fabrics with c-axis density distributed uniformly within a given zenith angle from vertical In addition they found solutions for idealized thick girdle and partial girdle fabrics These relations have since been applied by Smith et al 71 to infer crystal fabric in the Rutford ice stream using shear-wave splitting of seismic signals In this paper we outline a statistical model to infer fabric from sonic velocities using the Google Tensorflow automatic differentiation library 1 In contrast to Maurel et al 57 we model sonic velocities numerically using a flexible discrete ODF This trades analyticity for greater accuracy in ODF approximation We apply this technique to combine pseudo P-wave and thin-section measurements taken from the NEEM ice core to find spatially continuous and more accurate fabric estimates Unfortunately the data collected from the NEEM core suffers from large velocity drift due to poor tool centering in the borehole In addition model error may be significant To correct 40 these errors we incorporate thin-section measurements While thin-section measurements lack spatial coverage and have significant sampling error they are unbiased although correlated samples of the actual crystal fabric If the systematic velocity error due to bias or model error varies on length scales significantly larger than the spacing of the thin-section measurements then the thin-section measurements can be used to estimate this error In this way we can combine the relative strengths of thin-section measurements unbiasedness and sonic-velocity measurements spatial coverage little sampling error while reducing their weaknesses We also test this technique on synthetic fabric data and sonic measurements and show that it can effectively correct velocity drift and model error 3 2 Velocity model for sound waves in ice We now outline the forward velocity model used to estimate sonic velocity from ice fabric Ice crystals exhibit anisotropic stiffness dependent on c-axis direction Bulk stiffness of ice anisotropic polycrystals is therefore anisotropic dependent on the orientation of individual grains The bulk stiffness can be estimated using a volume-weighted average of the stiffness tensor across the polycrystal C ijkl Z c Cijkl c 3 2 S2 where is the ODF giving the density of c-axes at orientation c and Cijkl c is the stiffness tensor of an individual ice grain with c-axis aligned to c in the bulk coordinate system Estimating bulk stiffness through volume-weighted stiffness assumes uniform strain throughout the polycrystal The other end-member instead takes the harmonic mean of the stiffness tensor which corresponds to a homogeneous-stress assumption The truth is somewhere in between these two 45 although both produce similar predictions Here we assume uniform strain throughout the polycrystal because it avoids numerical difficulties that occur with small elements of the stiffness tensor under the harmonic mean Sonic velocities can be derived from plane-wave solutions to the elastodynamic wave 41 equation with zero forcing d2 d2 1 ij 2 Ciklj uj 0 dt dxk dxl 3 3 where ui is the material velocity of the polycrystal induced by the waves Plane waves are waves of the form ui f ki xi t u i where ki is the propagation direction u i is the polarization direction and is the phase velocity The function f is a scalar function of one scalar argument It may be a sine or cosine function for example Plugging the expression for a plane wave into the above equation the function f cancels out and it can be seen that admissible plane wave solutions are those where u i and 2 are eigenvalue eigenvector pairs of the Christoffel matrix 4 whose components are given by Mij 1 Ckijl kk kl 3 4 The Christoffel matrix is symmetric because the stiffness tensor posesses symmetries such that Ckijl Cjlki Cljik The square roots of the three eigenvalues give the pseudo P-wave velocity vp the fastest and the two pseudo-shear wave velocities vsh the slowest and vsv intermediate speed Unlike waves in isotropic media the pseudo P-wave polarization is not necessarily aligned with the propagation direction and the shear waves are not necessarily polarized orthogonal to the propagation direction However the polarizations are orthogonal to one another because the Christoffel matrix is symmetric Most observed fabrics in ice sheets have a principal direction associated with the highest c-axis concentration which is approximately vertical Therefore the pseudo P-wave velocity is typically polarized nearly vertical As an alternative to stiffness averaging and solving the resulting Christoffel equations many authors have averaged the harmonic mean of sonic velocities or the mean of the slowness across the ODF instead of the stiffness tensor While simple and intuitive this approach ignores mode conversion between P and S waves at grain boundaries 56 We implemented this velocity model numerically by assuming that ice fabrics follow a discrete ODF where the support the domain where probability density is nonzero of the 42 distribution is confined to 900 minimum energy points cmep 70 which are approximately i uniformly distributed over the sphere Since the ODF is antipodally symmetric we consider only the points on the upper hemisphere The distribution is parameterized by unconstrained weights for each point wi In order for the distribution to add up to unity the probability measure at each point is given by exp wi cmep P i j exp wj 3 5 This is known as softmax normalization e g Bouchard 14 This distribution which in this paper we will refer to as the discrete approximating distribution has many more parameters than a typical PODF However over-fitting can be avoided by introducing a quadratic regularization penalty similar to Tikhonov regularization This is a very convenient distribution to fit fabric eigenvalues and sonic velocities The vast majority of PODFs do not have analytical solutions for sonic velocities or eigenvalues in terms of their parameters Thus these quantities usually need to be calculated by quadrature on the sphere With this distribution we are cutting out the middleman by assuming beforehand that the distribution is supported only on the quadrature points To find the bulk stiffness we rotate the stiffness tensor Equation 3 2 such that the vertical axis of the transformed coordinate system is aligned with the c-axis of the quadrature point point cmep This rotation is non-unique since we assume that stiffness is invariant under i rotations about the c-axis in other words we are not attempting to measure a-axes We choose to rotate about the unique axis orthogonal to both cmep and the vertical direction in i the global reference frame Then the bulk stiffness tensor is constructed by taking the sum of the stiffness tensors for each point cmep weighted by the discrete approximating distribution i Equation 3 5 3 3 Fabric inference model Fabric thin-sections provide a limited sample from the fabric ODF from where the sample was taken As discussed above inference of the larger-scale ODF can have substantial error 43 from both sampling error and spatial nonstationarity of the ODF Sonic measurements on the other hand sample a large volume of ice leading to extremely small sampling error In addition the effects of sub-meter-scale spatial variability are significantly reduced In the NEEM core only P-wave velocities were collected which are not sensitive to azimuthal fabric concentrations In addition the sonic data for the NEEM ice core have substantial error varying slowly over longer length-scales which we will refer to as drift This contrasts to the thin-section error which is predominantly white noise stemming from sampling error or short length-scale variability in the ODF The thin-section measurements have less total error when smoothing measurements over sufficiently long length-scales but substantial error over short length scales In this section we develop a model to combine thin-section and sonic-log estimates of fabric eigenvalues while correcting for velocity drift and model error that varies smoothly with depth We do this by fitting the discrete approximating distribution Equation 3 5 at each depth such that the modeled velocities derived from the discrete approximating fabric distribution fit the thin-section data and the observed velocities as closely as possible This procedure requires several steps which can be summarized as follows: First we use kriging 17 to fit the observed thin-section data Next at each depth we fit the discrete approximating distribution Equation 3 5 to the thin-section eigenvalues Then sonic velocities can be generated using the discrete approximating distribution fitted to the thinsection eigenvalues This yields modeled sonic velocities from the thin-section data alone If significant velocity drift or smooth model error are present there will be large low-frequency mismatches between the modeled velocity and observed velocities This mismatch is distinct from the higher-frequency mismatch due to thin-section sampling error or small-scale fabric variability The smooth velocity mismatch is then regressed out using kriging to yield corrected velocities Finally the discrete approximating distribution is fitted to the corrected velocities and the thin-section eigenvalues simultaneously This then yields eigenvalue estimates incorporating information from both sonic velocity and thin-section data To start with we will use Gaussian-process regression 68 or kriging to fit the observed 44 thin-section data A Gaussian process is a random function f whose values yi f xi at any finite number of points xi follow a multivariate normal distribution The covariance matrix between sets of points X and X is K X X where K is a positive-definite covariance function or kernel giving the covariance between two points as a function of their location This induces a spatial structure in the Gaussian process For example a squared-exponential or Gaussian kernel is often used Here K is set to K X X k exp b X X 2 where b is a constant giving the bandwidth of the Gaussian and k is a scaling parameter This favors smooth functions because the correlation of nearby points is unity to first order Gaussian white noise is also a Gaussian process whose covariance function is K x x a if x x and zero otherwise This indicates that the values at different points are uncorrelated but the value at a given point follows a univariate normal distribution Rather than working with eigenvalues directly we instead fit the i : i logit i log i log 3 3 6 While the fabric eigenvalues are constrained to sum to unity the logit eigenvalues i can take on any value This makes the logits much easier to work with because the sum constraint is removed The corresponding inverse softmax transformation squashes the logits back such that they sum to unity: exp i i softmax i P j exp j 3 7 We assume that each of the observed logit-transformed eigenvalues i are drawn from a realization of a Gaussian process whose prior covariance is given by the sum of an exponential covariance function exp a xi xj and a white noise covariance function The exponential kernel allows for discontinuous functions because the nearby points are not perfectly correlated to first order as is the case with the squared-exponential kernel This is a more realistic covariance function than the squared-exponential covariance function since observed fabric eigenvalues do seem to change abruptly with depth From this the predictive mean of the logit eigenvalues at a depth d0 conditioned on the observed logit eigenvalues ts 45 at depths dts is given by ts i d0 K d0 d0 K 1 dts dts its 3 8 The predictive variance of the the estimated logit eigenvalue i at depth d0 is Var d0 K d0 K d0 dts K 1 dts dts K dts d0 3 9 This mean and variance defines a normal distribution for the logit eigenvalues i at each depth From this at each depth d0 we can fit the discrete approximating distribution Equation 3 5 to these eigenvalues This is done by minimizing the squared error between the predicted mean of i at depth d0 given by Equation 3 8 and the calculated fabric eigenvalues from the discrete approximating distribution Equation 3 5 This is given by the of the discrete approximating eigenvalues of the estimated second-order orientation tensor A distribution Equation 3 5 : A X ccT c 3 10 c M where M is the set of minimum-energy points If we assume that the fabric has a principal direction oriented nearly vertical then the estimated eigenvalues i are given by the diagonal elements A ii no sum to first order From this at each depth we have fitted the discrete approximating distribution to the observed thin-section data but not the observed velocities We then calculate modeled sonic velocities given the thin-section data The calculated sonic velocities do not suffer from the drift of the observed sonic velocities and are approximately correct on longer length scales unlike the observed sonic velocities However due to the usually low spatial coverage of thin sections the calculated sonic velocities do not detect the meter-scale features of fabric that the sonic-velocity measurements can since the velocity measurements are taken nearly continuously with depth We approximately correct this mismatch by using Gaussianprocess regression to estimate the mismatch under the assumption that it is smooth This will not remove the non-smooth higher-frequency components of the velocity mismatch which can instead be expected to correspond to actual short length-scale fabric variability 46 which is not captured by thin-section measurements For each velocity vi either vsh vsv or vp the mismatch at a depth d0 is i d0 vits d0 viobs d0 3 11 where viobs d0 is the observed velocity at depth d0 and vits d0 is the modeled velocity from the thin-section data Here we take the covariance function to be a sum of a squared-exponential covariance function and white noise This is given by K i d d0 k i exp a i d d0 2 2i I d d0 3 12 where k i and 2i are scaling parameters and a i is the bandwidth I is a function where I 0 1 and I z 0 for z 6 0 This covariance produces smooth predictions encoding a belief that the velocity drift is smooth Similar to the Gaussian-process regression of the logit-transformed eigenvalues the predicted mean of the the velocity mismatch is ts ts ts i d0 K i d0 dts K 1 i d d i 3 13 The modeled velocity is found from Equation 3 4 This then gives us the corrected veloci0 ties with mean v icorr viobs vel i Finally at each depth d we simultaneously fit the discrete approximating distribution to the corrected velocities Equation 3 13 and the inferred thinsection logit-transformed eigenvalues i d0 Equation 3 8 This is done by minimizing the following quantity with respect to the weights w of the discrete approximating distribution at each depth of interest 2 2 corr 2 corr 2 vsv w vsv J w sh vsh w vsh sv p 2 vp w vpcorr 2 2 1 w 1 2 1 2 2 w 2 2 2 3 w 3 2 w 2 2 3 3 14 2 Here sh is the variance of the velocity estimation given by the sum of the variance of the velocity-correction term and the variance of the sonic-velocity measurements The quantities sv and p are defined similarly The quantity 2i is the variance of the posterior Gaussian 47 process estimation of the logit-transformed fabric eigenvalue i given by Equation 3 9 The last term w 2 is a regularization term equivalent to putting a zero-mean Gaussian prior on the weights w This regularization term serves only to ensure that a unique minimum exists for the objective function 3 14 rather than representing any kind of prior knowledge The term is small enough that any fabric eigenvalues can be fit almost exactly We minimized J with respect to w using Adagrad gradient descent 23 with the gradients derived using the Google Tensorflow automatic differentiation package 1 Note that the objective function 3 14 is optimized independently at each depth of interest We do not assume any kind of prior knowledge of smoothness with depth for this objective function Sonic data collected from sonic tools are best averaged over a length-scale similar to the distance between the two sonic receivers This accounts for short length-scale spatial correlations There is no reason to assume a that fabric over longer length-scales is significantly correlated since fabrics do indeed vary significantly over short length-scales Assuming smoothness over longer length-scales would not allow for such short length-scale variability 3 4 Eigenvalue inference on synthetic data We now evaluate the statistical model developed in the previous section on synthetic fabric data We generated true fabric eigenvalues for a 3000m deep borehole by assuming that the logit-transformed eigenvalues are sampled from a Gaussian process with an exponential covariance function to yield eigenvalues that are discontinuous with depth We then generate true vp vsh and vsv velocities from these eigenvalues We then add a smooth velocity corruption to these velocities corresponding to model error and velocity drift to yield synthetic corrupted velocities The velocity corruption is the same absolute value for vsh vsv and vp However we do not use this knowledge in fitting the model Instead we fit a separate correction for each velocity Synthetic thin-section samples were generated every 30m by adding noise averaging 0 2 to the logit-transformed eigenvalues at each depth with 100 thin sections in total 48 1 0 True 1 True 2 True 3 Modeled 1 Modeled 2 Modeled 3 Thin section 1 Thin section 2 Thin section 3 0 8 Eigenvalue 0 6 0 4 0 2 0 0 0 500 1000 1500 Depth m 2000 2500 3000 Figure 3 1: Application of the statistical model to synthetically generated fabric Thinsection eigenvalues with 30m spacing are generated by adding noise to the true eigenvalues The modeled eigenvalues are close to the true eigenvalues over the majority of the depth Error is primarily due to error in the velocity-correction term 49 The results are plotted in Figure 3 1 Over the majority of the core the true fabric eigenvalues are approximated accurately In a few spots larger errors occur due to misestimation of the velocity corruption The estimated velocity corrections and the true velocity corruption are plotted in Figure 3 2 Typical errors are on the order of 10ms 1 Note that we do not add white noise to the synthetic velocity data which would correspond to sonic velocity measurement error uncorrelated with depth We expect that uncertainties in arrival times are the primary cause of non depth-correlated velocity errors With velocities averaged over several runs and smoothed over a few meters this error would typically be small in comparison to the depth-correlated errors of model error and velocity drift This is a challenging synthetic dataset with large high-frequency spatial variability in eigenvalues With only 100 noisy thin-section measurements it can be difficult to separate the effects of the velocity corruption from actual variability in fabric eigenvalues More thin sections or less fabric variability can reduce this substantially 3 5 Application to sonic measurements at NEEM In this section we apply the statistical model to P-wave velocity data and thin-section data collected at NEEM 61 Unlike the case with synthetic data only P-wave velocities were collected The P-wave velocity constrains only the concentration of c-axes in the vertical direction associated with the largest fabric eigenvalue 3 However due to the sum constraint of eigenvalues this still provides information on the sum of 1 and 2 The data were collected with a Mount Sopris CLP-4877 sonic-logging tool modified to have a larger receiver spacing The tool emits a monopole impulse source which travels through the borehole fluid through the ice and back through the borehole fluid to two recievers spaced at 90cm and 303 5cm from the source Pulses are emitted every 2 s Three separate sonic logs were completed with several sonic measurements taken every meter Since the tool itself is roughly 3m long spatial variability in sonic velocities shorter than 3m are difficult to interpret Thus in our analysis we take 3m moving averages of the 50 20 True velocity drift Est vsh drift Est vsh drift Est vp drift 40 Velocity m s 60 80 100 120 140 0 500 1000 1500 Depth m 2000 2500 3000 Figure 3 2: Velocity corruption dashed and estimated velocity corrections solid lines for vp vsh and vsv Estimation of the velocity corruption depends on the thin-section eigenvalues Due to the large degree of spatial variability of the fabric and the noise in the thin sections inaccuracies on the order of 10m s occur More thin-section samples and more accurate samples can reduce this error substantially 51 data This also serves to significantly reduce uncorrelated measurement error reducing error in measured vp due to uncertainties in arrival times to the order of 1mi s 1 over multiple runs 50 As discussed previously large velocity drift occurs due to poor tool centralization in the borehole This can differ between runs of the logging tool However short length-scale features are consistent between between runs We use the thin-section data from Montagnat et al 61 There are 271 thin sections taken from 34m to 2461m At some depths multiple thin sections are taken This gives a rough indicaton of the sampling error of the thin sections at those depths We apply the model only below 250m Above this depth the velocity model becomes increasingly inaccurate We expect this is due to a higher concentrations of air bubbles in the ice In Figure 3 3 we plot the modeled P-wave velocities from NEEM thin sections and the collected P-wave velocities There is a significant mismatch with the collected P-wave data typically being on the order of 100m s 1 less than the modeled P-wave velocities The lowerfrequency part of this mismatch is due to some combination of model error and velocity drift We expect both to be smooth as the assumptions of the statistical model require In addition to these smooth errors the velocities derived from thin sections have significant uncertainties due to sampling error In Figure 3 4 we plot the eigenvalues derived from thin sections along with eigenvalues estimated using both thin-section data and the collected P-wave velocity The largest eignvalue 3 increases almost linearly in the first 1300m of the core Below about 2000m the modeled eigenvalues begin to display large high-frequency spikes This may be due to differing amounts of recrystallization between layers Layers experiencing greater amounts of recrystallization tend to have weaker fabrics These fabric contrasts may also help initiate flow disturbances near the bed Applied to the NEEM ice-core data we believe this model produces very accurate predictions of the largest eigenvalue 3 Other eigenvalues are not informed by the P-wave velocity except due to the eigenvalue sum constraint While the P-wave data provide information on 52 4100 Measured P-wave velocities Modeled P-wave vel at thin sections 4050 P-wave velocity m s 4000 3950 3900 3850 3800 0 500 1000 Depth m 1500 2000 2500 Figure 3 3: P-wave velocities modeled from thin sections dots and observed P-wave velocities line The observed P-wave velocities are smoothed over 3m and are averaged over multiple runs Due to a combination of model error and velocity drift the observed velocities are on the order of 100m s 1 less than the modeled velocities the sum of 1 and 2 it does not inform the difference between the two There are more thin sections and much less large spatial variability in the NEEM core compared to the test on synthetic fabric Thus we expect the estimation of the velocitycorrection term in the model to be more accurate resulting in more accurate predictions of the largest eigenvalue 3 compared to the results for the synthetic data Error in thin sections in estimating the eigenvalues of the bulk fabric in volumes sampled by the sonic tool is on the order of 0 1 over most of the core increasing in the recrystallized deep layers These errors correspond to larger uncertainties in ice viscosity due to the power-law rheology of ice 3 6 Conclusions We showed P-wave velocity data collected from the NEEM ice core with a borehole soniclogging tool The collected P-wave velocities provide a high-quality continuous record of 53 1 0 Modeled 1 Modeled 2 Modeled 3 Thin section 1 Thin section 2 Thin section 3 0 8 0 6 0 4 0 2 0 0 0 500 1000 1500 2000 2500 Figure 3 4: Eigenvalues derived from thin sections at NEEM dots 61 together with spatially-continuous estimates from the assimilation procedure The variability of eigenvalues over shorter length scales in the upper core appears to be due to sampling error The large variations seen in the thin sections in the deep ice are confirmed by the sonic velocity data fabric over depth at scales longer than 2m However they are subject to smoothly-varying errors We derived a method of incorporating thin-section data and sonic-velocity data in order to gain a more accurate and spatially continuous picture of the ODF This is especially important for understanding stratigraphic disruption that occurs near the bed of NEEM and other cores The inferred fabric from the NEEM core shows variability in fabric on the order of several meters This may trigger or enhance stratigraphic disruption Fabric variability on these length scales is impossible to observe with thin sections taken only every several meters with large sampling error This work demonstrates the utility of combining different methods of ODF measurements Future work measuring S-wave velocities will greatly enhance the capabilities of sonic-velocity measurements in ODF determination Improved sonic tools could reduce velocity measurement error and bias However we still expect that thin-section measurements 54 are a useful adjunct to provide a mostly unbiased ground-truth for ice-sheet fabric to correct velocity-model error 55 Chapter 4 THE RESPONSE OF ICE-CRYSTAL ORIENTATION FABRIC TO VELOCITY-GRADIENT PERTURBATIONS This chapter is under review at the Journal of Glaciology Ed Waddington is a co-author I developed the analytical and numerical models and wrote this manuscript Abstract: The distribution of crystal orientations of ice grains the crystal fabric of a polycrystal has a strong influence on the flow of polycrystalline ice due to the plastic anisotropy of the individual grains The fabric is in turn affected by ice flow Flow on ice-sheet flanks is dominated by shear on horizontal planes and divide flow is dominated by longitudinal extension However other velocity gradient components may also exist due to bed topography variability in fabric or grain size or other factors This can in turn result in a fabric that differs from the fabric that would occur without any such flow disturbances Indeed disturbed stratigraphy is commonly observed near the bed of ice sheets In this paper we treat these flow disturbances as random but correlated in time and determine their effects on crystal fabric These small deviations in velocity gradient from pure shear or simple shear can induce the development of single-maximum fabrics with off-vertical directions of maximum c-axis concentration In turn this has the potential to induce stratigraphic distortion 4 1 Introduction An individual ice crystal deforms most easily in shear parallel to the crystal basal plane orthogonal to the crystallographic c-axis Deformation on planes in other orientations is on the order of 10 to 100 times harder Plastic deformation of an ice polycrystal depends on the orientations of its constituent grains e g Azuma 8 which is described by the c-axis 56 Table 4 1: List of symbols Symbol Definition qi Component of a tensor in index notation q Same tensor in vector notation c Ice-crystal c-axis vector c Ice-crystal orientation dist func qi Expected value of qi under aij Component of the structure-tensor ci cj Aij Comp of the 2th order orient tensor aij Aijkl Comp of the 4th order orient tensor aij akl k A fabric eigenvalue of A Matrix of eigenvectors of A V Vorticity or spin tensor D Strain-rate tensor ij Kronecker delta symbol S Stress tensor A small parameter v Vector magnitude of v vT v orientation distribution function ODF The ODF is a probability distribution of c-axis density often defined on the upper hemisphere because a c-axis vector c is indistinguishable from c In this paper we will instead treat the ODF as an even function defined on the entire sphere for mathematical convenience A polycrystal with an isotropic ODF will have a bulk isotropic response to applied stress However polycrystals develop an anisotropic ODF in response to applied strain The development of a preferred orientation is guided primarily by intracrystalline slip There is a tendency for the c-axes to rotate away from the directions of principal extensional 57 strain due to lattice rotation 10 ODFs are often summarized using orientation or moment tensors e g Svendsem and Hutter 73 where the nth order moment tensor is the nth order moment of the ODF Throughout this paper the indices 1 2 and 3 will be associated with the x- y- and z-directions respectively Fabric is usually described using only the second-order orientation tensor A The component of the second-order orientation tensor Aij is the expectation ci cj where i j 1 2 3 The mean of the ODF or the first-order orientation tensor in this terminology ci is always zero because of antipodal symmetry and likewise for any odd-order tensor Therefore Aij is also a component of the covariance tensor of the distribution: Cov ci cj ci ci cj cj ci 0 cj 0 Aij 4 1 The diagonal elements A11 A22 and A33 give a measure of the c-axis concentration on the x y and z axes respectively Similar to the second-order orientation tensor the fourth-order tensor is the expected value Aijkl ci cj ck cl Since the second-order orientation tensor is symmetric it is diagonal in the coordinate system defined by its eigenvectors or fabric principal directions The diagonal elements are the fabric eigenvalues i The eigenvalues sum to unity by construction The three fabric principal directions denote the directions of greatest density corresponding to the largest eigenvalue smallest density the smallest eigenvalue and a direction orthogonal to the other two An isotropic fabric has three equal eigenvalues A girdle fabric in which there is a band of high concentration along a great circle has two nearly equal eigenvalues and one small eigenvalue A single-maximum fabric has one large eigenvalue and two small eigenvalues If the evolution of the ODF is given by a partial differential equation PDE over the sphere it is possible to derive an ordinary differential equation ODE for the evolution of Aij This is much easier than solving the PDE whose solution at any given time is 58 a function defined on the sphere rather than just the six unique elements of the secondorder orientation tensor This substantially reduces computational difficulties With this approach Gillet-Chaulet et al 38 used a Jefferys-type equation for Aij valid when the caxes move by basal slip only Their model works for arbitrary vorticity tensors and velocity gradients G odert 40 developed a similar model incorporating rotary diffusion into the evolution equation for Aij In this paper we take a similar approach to Gillet-Chaulet et al 38 Fabric development during ice flow is likely a physically deterministic process However at any given site there are uncertainties in strain history impurity content initial conditions at deposition and other factors We examine how these uncertainties may affect uncertainties in ice flow Flow inhomogenities can result from numerous sources On small scales random variations in fabric strength can in turn induce spatial differences in flow Near the bottom of the West Antarctic Ice Sheet WAIS divide core some layers have experienced recrystallization and have a weaker fabric compared to others that have not recrystallized 30 Durand et al 25 found an abrupt transition in the ice fabric at EPICA Dome C corresponding to Termination II suggesting that climate at the time of initial deposition can play a prominent role in in the subsequent development ice fabric Alley et al 7 found evidence of striping in the GISP2 core in which elongated areas of grains possessed offvertical c-axes In horizontal extension under divide flow these stripes localize shear within them and offset layers in the hard surrounding ice This induces flow disturbances around stripes as well as overturning stratigraphic layers Jansen et al 47 produced bands similar to observed stripes in strong single-maximum fabrics using the two-dimensional ELLE microstructure model Regions where the fabric was tilted away from the bulk lattice-preferred orientation toward the direction of shear seeded the formation of the bands On larger scales flow disturbances can arise due to basal topography and transient flow basal-ice accretion 11 or various other sources Thorsteinsson and Waddington 76 examined the development of low-angle wrinkles in stratigraphic layers in ice sheets Under simple shear low-angle wrinkles will steepen 59 Figure 4 1: The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with pure shear and a strain perturbation whose components average 2% of the background pure shear and 1 The central 95% of realizations are shaded Significant deviations of A13 and A23 occur These correspond to tilted cone fabrics whose direction of greatest concentration differs on the order of 5 from vertical 1 0 A11 1 0 A22 1 0 0 8 0 8 0 8 0 6 0 6 0 6 0 4 0 4 0 4 0 2 0 2 0 2 0 0 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A23 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A13 0 4 0 4 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 4 0 4 0 4 1 2 3 4 5 6 7 8 9 10 Total strain 1 2 3 4 5 6 7 8 9 10 Total strain A12 0 4 1 2 3 4 5 6 7 8 9 10 Total strain A33 1 2 3 4 5 6 7 8 9 10 Total strain 60 eventually producing overturned folds Pure shear or vertical uniaxial compression produce the opposite effect flattening out wrinkles Near ice divides simple shear is less prominent compared to pure shear However vertical single-maximum fabrics develop under both vertical compression and simple shear These fabrics make the ice harder under vertical compression and soft under horizontal simple shear This may greatly aid the development of stratigraphic disruption in simple shear because steepening of incipient folds is enhanced while flattening is reduced In this paper we analyze how small amounts of variability in the velocity gradient can affect crystal fabric By variability we mean small components of the velocity gradient distinct from the dominant background flow e g simple shear in flank flow The goal is to see whether it is possible to develop large excursions in the ODF in response to small velocity-gradient perturbations If as a result of small excursions in the velocity gradient large spatially non-homogeneous differences in fabric can develop they may seed further velocity gradient disturbances and stratigraphic disruption We do not examine sources of such flow disturbances Instead we make the approximation that they are random but correlated in time That is the perturbation at a certain time will be highly correlated to perturbations at sufficiently nearby times This paper is split into two main parts In the first section we develop a first-order approximation of the effects of a velocity-gradient perturbation on concentrated vertical single-maximum fabrics in flank flow horizontal simple shear and divide flow pure shear We show that in both cases small perturbations of the velocity gradient can cause the fabric principal directions to rotate significantly generating a fabric that would induce a vertical velocity perturbation in both flow situations In the second section we expand on the analytical result by numerically solving the Jeffery s-type equation for the evolution of Aij see next section perturbed by a small random velocity gradient We generate confidence intervals of the six unique components of Aij by computing several thousand realizations The results numerically confirm the analytical observations in the first section 61 4 1 1 Fabric evolution The most important process governing the development of crystal fabrics is deformationinduced grain rotation If grain deformation is due solely to basal glide the rate of change of the c-axis orientation is the sum of bulk rotation and viscoplastic spin From Meyssonnier and Philip 58 the evolution of c-axis orientation in response to strain can be described by a modified Jeffery s equation 48 : g g c i Vij cj Dij cj ci cj ck Djk 4 2 g are where ci is the unit vector in the direction of the c-axis The quantities Vij and Dij components of the rotation-rate tensor and local strain-rate tensor of the grain respectively The first term gives the rotation rate due to the bulk rotation of the polycrystal while the second term gives the rotation rate due to viscoplastic spin Thus for example the c-axis of a grain experiencing uniaxial compression will rotate towards the compressive direction The last term of Jeffery s equation 5 2 ensures that the motion of grain orientation is tangent to the unit sphere at c which is necessary due to the convention that the c-axis vector is of unit length This can be seen by noting that the Vij cj term does not affect the magnitude of ci leaving only the Dij cj term Assume that at time t 0 the c-axis is given by c0 After a short length of time t the magnitude of the new c-axis c t is without the final term in Equation 5 2 c t c0 tDc 4 3 c0 cT0 Dc0 t 4 4 1 cT0 Dc0 t 4 5 to first order in t Thus for the c-axis to maintain unit length we must add the quantity cT Dc t projected onto c by multiplying by c This then gives the last term of Equation 5 2 Rather than compute the rotation rate for each grain individually we instead seek an evolution equation for the second-order orientation tensor whose components are given by 62 Aij ci cj Differentiating with respect to time we have dAij c i cj ci c j dt 4 6 This introduces the problem of homogenization We must average out the quantity in the brackets over the entire ODF However c ki for some individual grain k depends on the strainrate tensor of that particular grain as can be seen in Equation 5 2 Thus we need a tractable method for relating the bulk stress and strain to that of individual grains The stress and strain of each individual grain should ideally be consistent with the bulk stress and strain rate The two possible end-members are the Taylor-Bishop-Hill model 74 assuming homogeneous strain among grains and the Sachs model 69 which assumes homogeneous stress among grains Visco-plastic self-consistent VPSC homogenization methods 52 have been used for anisotropic ice-flow constitutive relations e g Castelnau et al 15 Gillet-Chaulet et al 38 VPSC schemes treat each individual grain as an ellipsoidal inclusion in a medium with the average properties of the polycrystal This can provide a more accurate distribution of stress and strain within the polycrystal with stress and strain both dependent on the orientation of a grain Grain rotation due to lattice rotation can also be directly incorporated into VPSC schemes However VPSC schemes are typically computed iteratively over finite samples of grains and are difficult to directly incorporate into Eq 4 6 As a compromise Gillet-Chaulet et al 37 took the strain on an individual grain as a weighted average between the homogeneous stress and homogeneous strain assumption In g this case Dij in Eq 5 2 is g ij Sij Dij 1 D 4 7 2 ij is a component of the bulk strain-rate tensor S ij is a component of the bulk stress where D tensor and is the fluidity for shear parallel to the basal plane The weighting between homogeneous stress and homogeneous strain is given by the interaction parameter Setting 0 gives the homogeneous strain rate assumption while 1 gives homogeneous stress This parameter may be tuned to fit a VPSC model In Gillet-Chaulet et al 38 they used a value of 0 06 Throughout this paper we use the homogeneous strain assumption 63 with 0 The homogeneous strain assumption for grain rotation produces fairly realistic predictions for fiber orientation even though the homogeneous strain assumption produces rather poor predictions of ice flow Given that Gillet-Chaulet et al 38 found the best results with 0 06 we are not too far off by setting 0 Note that setting 6 0 to yield a local grain strain rate equal to Gij produces the same predictions as assuming ij Gij For vertical single-maximum homogeneous strain and setting the bulk strain D fabrics forced with simple shear or pure shear as in this paper Dij and Sij are proportional with dimensions of viscosity With this assumption the derivative of the second-order orientation tensor A becomes dAij Vik Akj Aik Vkj Dik Akj Aik Dkj dt 4 8 2Aijkl Dkl The presence of the fourth-order orientation tensor Aijkl in Eq 5 7 introduces the closure problem In general Aijkl cannot be found from A If we used an additional evolution equation for Aijkl then the six-order orientation tensor would appear in that equation and so on Thus we need some way of approximating Aijkl in terms of A In this paper we use the popular and simple quadratic closure where Aijkl Aij Akl 3 This closure is exact in the case of perfectly concentrated single-maximum fabrics where Aij i3 j3 It is quite accurate whenever 3 0 8 or so In this paper we are primarily intersted in the response of strong fabrics to velocity-gradient perturbations so this is a good approximation for our purposes 4 2 First-order perturbations to strong single-maximum fabrics We now examine the analytic sensitivity of strong vertical-maximum fabrics to velocitygradient perturbations We show that fabrics are susceptible to developing tilted cone fabrics in which the direction of greatest concentration is not vertical in both horizontal pure shear and simple shear Here we add a small perturbation A ij to the component of has zero trace and is small Then the second-order orientation tensor Aij The tensor A 64 Figure 4 2: The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with pure shear and a strain perturbation whose components average 5% of the background pure shear with 1 the central 95% of realizations are shaded Larger deviations of A13 and A23 occur than under 2% average perturbations These correspond to tilted cone fabrics tilted on the order of 10 from vertical The background pure shear is very effective at restraining perturbations of other components of A 1 0 A11 1 0 A22 1 0 0 8 0 8 0 8 0 6 0 6 0 6 0 4 0 4 0 4 0 2 0 2 0 2 0 0 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A23 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A13 0 4 0 4 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 4 0 4 0 4 1 2 3 4 5 6 7 8 9 10 Total strain 1 2 3 4 5 6 7 8 9 10 Total strain A12 0 4 1 2 3 4 5 6 7 8 9 10 Total strain A33 1 2 3 4 5 6 7 8 9 10 Total strain components of the perturbed second-order orientation tensor are given by A ij Aij A ij Next we also assume that the vorticity and strain rate are perturbed by small quantities respectively Then we can substitute these quantities into Eq 5 7 and discard V and D quantities of O 2 and higher This then gives us a first-order equation for the perturbed 65 As with the case of pure shear the only components that are directly affected by velocitygradient perturbations to first order are A 13 and A 23 The growth of the perturbation A 13 13 and V 13 it may be restrained or to A13 is affected by A 22 Depending on the signs of D reinforced by A 22 Similarly other components depend on each other to first order For example A11 depends negatively on A13 However we may expect that A 13 and A 23 will in magnitude As long as their magnitudes are generally be the largest components of A 66 Figure 4 3: The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with simple shear and a strain perturbation whose components average 2% of the background pure shear with 1 The central 95% of realizations are shaded Smaller perturbations develop than with pure shear However they still may be enough to seed further fabric and flow disturbances 1 0 A11 1 0 A22 1 0 0 8 0 8 0 8 0 6 0 6 0 6 0 4 0 4 0 4 0 2 0 2 0 2 0 0 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A23 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A13 0 4 0 4 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 4 0 4 0 4 1 2 3 4 5 6 7 8 9 10 Total strain 1 2 3 4 5 6 7 8 9 10 Total strain A12 0 4 1 2 3 4 5 6 7 8 9 10 Total strain A33 1 2 3 4 5 6 7 8 9 10 Total strain 67 generally less than the applied velocity-gradient perturbations perturbations to other components will grow more slowly For example if 2A 13 the growth rate of the perturbation to A11 is less than A 22 D13 W13 the growth rate of A 13 we can expect A 13 to grow faster than A 11 This intuition is confirmed numerically in the next section 4 3 Monte-Carlo analysis of stress perturbations We now expand on the sensitivity analysis of the previous section by considering numerical solutions to the Jeffery s equation 5 7 forced with background simple shear or pure shear in addition to a small random velocity gradient This gives us an idea of the magnitude of fabric perturbations that we may expect in response to velocity-gradient perturbations It also allows us to look at the effects of velocity-gradient perturbations away from equilibrium In the previous section we showed that background pure shear or simple shear is not effective at restraining perturbations of the A13 and A23 components of the second-order orientation tensor Integrating the Jefferys equation 5 7 through time we can expect the effects of velocity-gradient perturbations to be magnified as integration acts as a low-pass filter First we must have some way of generating velocity-gradient perturbations It is reasonable to assume that a velocity-gradient perturbation at time t will be highly correlated to perturbations at t if is small enough To account for this we construct the velocitygradient perturbations using realizations of a Gaussian process A Gaussian process is a random process or function X t for which any finite sample Xt1 Xt2 Xtk from the process has a joint Gaussian distribution determined by a covariance function C t0 t1 which gives the covariance Cov Xt0 Xt1 C t0 t1 Let U ijt be a component of a realization of the perturbed velocity gradient at time t To generate U ijt we first sample a realization Gtijk from the Gaussian process for each discretized time tk Since the time is taken at a discrete number of points this is just a sample from an ordinary multivariate normal distribution with a mean of zero whose covariance tensor has components given by Kij C ti tj We assume that Gtij has a squared-exponential covariance function C t t0 2 exp t 68 Figure 4 4: The six unique components of A for 3000 realizations of the Jeffery s-type equation 5 7 forced with simple shear and a strain perturbation whose components average 5% of the background pure shear using 1 The central 95% of realizations are shaded Large deviations in A13 and A23 occur than with 2% average velocity-gradient perturbations corresponding to tilted cone fabrics deviating on the order of 5 from vertical Smaller deviations occur in other components 1 0 A11 1 0 A22 1 0 0 8 0 8 0 8 0 6 0 6 0 6 0 4 0 4 0 4 0 2 0 2 0 2 0 0 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A23 1 2 3 4 5 6 7 8 9 10 Total strain 0 0 A13 0 4 0 4 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 4 0 4 0 4 1 2 3 4 5 6 7 8 9 10 Total strain 1 2 3 4 5 6 7 8 9 10 Total strain A12 0 4 1 2 3 4 5 6 7 8 9 10 Total strain A33 1 2 3 4 5 6 7 8 9 10 Total strain 69 t0 2 The parameter where 0 controls how closely nearby points are correlated A small value of means that two different points are more highly correlated Smaller values of will tend to promote larger fabric perturbations since the higher degree of correlation over time will help prevent fabric perturbations from being cancelled out The quantity 2 gives the variance of the perturbation at a single point The tensor with components Gtij does not satisfy incompressibility Incompressibility is recovered by subtracting one third of the trace from each component of the diagonal yielding the velocity-gradient perturbation U ijt We plot the central 95% interval of the six independent elements of the tensor A for 3000 realizations of velocity-gradient perturbations under pure shear for perturbations averaging 2% and 5% of background strain in Figures 4 1 and 4 2 respectively The model is run until reaching a total strain of 10 excluding the velocity-gradient perturbations Time is nondimensionalized by the strain rate such that the strain rate is unity We set 1 which means that velocity-gradient perturbations occuring at nondimensional times seperated by more than 2 are nearly uncorrelated The initial fabric is taken to be isotropic with A11 A22 A33 1 3 Consistent with the analytical results from the previous section A13 and A23 have much greater differences between their 2 5% and 97 5% quantiles than other components This corresponds to the development of a tilted cone fabric with A13 being the Euler angle of rotation about the x-axis to first order Similarly A23 is the Euler angle rotation of the fabric about the y-axis to first order In Figures 4 3 and 4 4 we plot the same results for simple shear under 2% and 5% average velocity-gradient perturbations respectively Just like the case with pure shear A13 and A23 have relatively large spreads between the 2 5% and 97 5% quantiles Other components are perturbed to a lesser extent but to a much greater degree than in the case of pure shear This is most likely because the background simple shear does not restrain the growth of perturbations in any component to first order 70 4 4 Conclusions Stratigraphic disruption in basal ice is a significant problem for the interpretation of ice-core records The strong viscous anisotropy of ice may play a significant role in the development of stratigraphic disturbances e g Azuma and Goto-Azuma 10 Thorsteinsson and Waddington 76 We showed that ice-crystal orientation fabric is sensitive to velocitygradient perturbations In particular even small velocity-gradient perturbations are capable of producing single-maximum fabrics whose axes of maximum c-axis concentration deviate significantly from vertical Background pure shear or simple shear is not effective at restraining these perturbations Such fabrics are capable of inducing layer overturning in response to pure shear divide flow or simple shear flank flow There may be numerous sources for stratigraphic disruption in basal ice The dynamics of basal ice can become very complicated in some settings due to basal freeze-on recrystallization and sliding However c-axis orientation fabric must always play a role because any flow which can induce stratigraphic disruption will also affect fabric We did not consider the coupling of flow and fabric evolution in this paper Perturbations to fabric cause perturbations to flow possibly inducing further fabric disturbances Therefore this analysis is only appropriate to help understand the onset of disturbances to crystal fabric in response to a velocity-gradient perturbation More work is needed to understand the coupling of fabric development to ice flow and other physical processes of basal ice 71 Chapter 5 PERTURBATIONS OF FABRIC EVOLUTION AND FLOW OF ANISOTROPIC ICE This chapter will be submitted to the Cryosphere Discussions soon I wrote this manuscript and developed the model Ed Waddington helped edit the manuscript Abstract: The distribution of crystal orientations of ice grains the crystal fabric of a polycrystal has a strong influence on polycrystalline ice-flow due to the plastic anisotropy of the individual grains In turn crystal-orientation fabric evolution is guided primarily by deformation This suggests that the coupled dynamics of flow and fabric may produce significantly different behavior than if they were uncoupled We develop an analytical firstorder perturbation model of coupled linear flow of anisotropic ice and fabric evolution We analyze the development of several types of perturbations in different flow scenarios The results show that fabric development coupled to flow of anisotropic ice is dynamically unstable in many flow scenarios These instabilities may lead to the development of shear bands boudinage and other stratigraphic disturbances seen in ice sheets 5 1 Introduction An individual ice crystal has an anisotropic creep response deforming most easily in shear parallel to the crystal basal-plane orthogonal to the crystallographic c-axis Plastic deformation of an ice polycrystal depends on the orientations of its constituent grains e g Azuma 8 which is described by the c-axis orientation distribution function ODF The ODF is a probability distribution of c-axis density often defined on the upper hemisphere because a c-axis vector c is indistinguishable from c In this paper we will instead treat the ODF as being defined on the entire sphere for mathematical convenience A polycrystal with an 72 isotropic ODF will have a bulk isotropic response to applied stress However polycrystals develop an anisotropic ODF in response to applied strain Grains tend to rotate towards the axes of principal compression This produces a bulk anisotropic response to stress In flank flow in ice sheets c-axes typically cluster near vertical This puts the basal plane in close alignment with applied shear stress producing ice that can be several times softer under shear than isotropic ice Vertical-maximum fabric also develops under vertical compression Unlike with simple shear however the ice becomes harder to the applied vertical compression with stronger single-maximum fabrics Given that fabric has such a strong effect on flow and vice-versa it is therefore important to understand it as a coupled system rather than treating flow and fabric separately Many or perhaps most complex coupled dynamical systems of physical interest exhibit instability Examples include the gravitational n-body problem which has unstable solutions or Earth s weather There are indications that coupled flow of anisotropic ice has instabilities as well Thorsteinsson and Waddington 76 studied the development of low-angle stratigraphic wrinkles near ice divides They concluded that single-maximum fabrics typical near ice divides enhance the ability of low-angle incipient wrinkles to steepen and eventually overturn The singlemaximum fabrics near ice divides promote horizontal shear which steepens incipient wrinkles and hinder vertical compression which flattens them Fudge et al 32 found evidence of boudinage in electrical conductivity measurements in the West Antarctic Ice Sheet Divide core Boudinage effectively removes layers from the record and additionally could act as a source of incipient stratigraphic wrinkles in the surrounding layers Alley et al 7 found striping in the GISP2 core These stripes were composed of elongated regions of grains possessing aligned off-vertical c-axes in a medium of vertical single-maximum fabric In horizontal extension under divide flow these stripes localize shear within them and displace layers in the hard surrounding ice Jansen et al 47 produced bands similar to observed stripes in strong single-maximum fabrics using microstructure modeling These were identified as shear bands Regions where the fabric was tilted away 73 from the lattice preferred orientation towards the direction of shear seeded the formation of the bands These small-scale disturbances which have been found hundreds of meters off the bed cannot be related to basal topography They must arise from inhomogeneities in the ice itself Montgomery-Smith 62 developed a coupled perturbation model for the orientations of slender fibers immersed in Stokes flow It was shown that instabilities of fiber orientations can develop which would not occur in uncoupled flow Coupled ice flow and fabric are mathematically related to the case of fibers immersed in Stokes flow In this paper we derive a full-Stokes coupled anisotropic-flow and fabric-perturbation model to study the stability of the coupled flow and fabric system similarly to Montgomery-Smith 62 We show that dynamical instability of fabric coupled to ice flow can seed such disturbances 5 1 1 Background Preferred c-axis orientations in ice develop primarily due to intracrystalline slip This causes c-axes to rotate away from the directions of principal extensional strain 10 ODFs are often summarized using orientation or moment tensors e g Svendsem and Hutter 73 The second-order orientation tensor Aij is the expectation ci cj where i j 1 2 3 The mean of the ODF ci is always zero because of antipodal symmetry Therefore Aij is also the covariance matrix of the distribution by definition of covariance as Cov ci cj ci ci cj cj 5 1 The diagonal elements A11 A22 and A33 give a measure of the c-axis concentration on the x y and z axes respectively Throughout this paper the indices 1 2 and 3 will be associated with the x- y- and z-directions respectively Similar to the second-order orientation tensor the fourth-order tensor is the expected value Aijkl ci cj ck cl Since ODFs over the sphere are antipodally symmetric odd-order tensors are zero The second-order tensor may be eigendecomposed The eigenvalues 1 2 3 sum to unity by construction The eigenvectors or fabric principal-directions denote the directions of greatest density corre- 74 Table 5 1: List of symbols Symbol Definition qi Tensor quantity in index notation q Same tensor in vector notation ci ice-crystal c-axis for i 1 2 3 in x y z directions c Ice-crystal orientation dist func qi Expected value of qi under Aij Second-order orientation tensor ci cj aij Aijkl Fourth-order orientation tensor ci cj ck cl i Fabric eigenvalue of Aij Jij Jacobian matrix of the perturbed fabric system i Eigenvalues or growth rates of Jij Vij Vorticity or spin tensor Dij Strain-rate tensor Angle of rotation about the y-axis Angle of rotation about the x-axis ij Kronecker delta symbol S2 unit sphere Rijkl viscosity tensor A standard deviation Sij Stress tensor A small parameter i Three-dimensional wavevector y An unperturbed quantity y The Fourier coefficient of a perturbation to y 75 sponding to the largest eigenvalue 3 smallest density the smallest eigenvalue 1 and a direction orthogonal to the other two corresponding to 2 An isotropic fabric has three equal eigenvalues A girdle fabric in which there is a band of high concentration along a great circle has two nearly equal eigenvalues and one small eigenvalue A single-maximum fabric has one large eigenvalue and two small ones If the evolution of the ODF is given by a PDE over the sphere one may integrate Aij to derive a ODE for the evolution of Aij Gillet-Chaulet et al 38 used a Jeffery s-type equation for Aij valid when the c-axes move by basal slip only Their model works for arbitrary flow conditions G odert 40 developed a similar model incorporating spherical diffusion into the evolution equation for Aij In general linear anisotropic viscosity must be a fourth order 3 3 3 3 tensor Rijkl This is because it relates stress and strain rate two second-order tensors Rijkl is a function of the ODF and also the strain rate if it is a nonlinear constitutive relation With no simplifications this is too computationally and analytically difficult for most applications However numerous constitutive relations have been developed to account for anisotropy of ice in a more tractable way The most popular and simple method is to use a scalar enhancement factor as a multiplier of fluidity in Glen s flow law to adjust for anisotropy or other factors 53 This method is mainly useful under flank flow using the shallow ice approximation Since only horizontal shear stresses are significant other stresses and their corresponding viscosity components may be ignored The enhancement factor is usually chosen empirically However the enhancement factor method is not valid if the ODF does not have a vertical axis of symmetry In this case true anisotropic flow laws predict the development of larger normal stresses This makes the assumption of a scalar enhancement factor invalid in these situations 66 A number of anisotropic constitutive relations attempt to predict the flow response of a polycrystal from the properties and orientations of individual grains This brings the problem of homogenization: it is necessary to relate the bulk stress and strain of the entire polycrystal to that experienced by individual grains in a consistent way There are two 76 possible end members Homogeneous stress or the Taylor-Bishop-Hill model 74 assumes that strain but not stress is identical in all grains This has the advantage of maintaining spatial compatibility among grains It is a good approximation for materials with several easily-activated slip systems The homogeneous-strain assumption is an upper bound on the viscous dissipation of the polycrystal: For a given applied bulk strain the hardestoriented grains receive the same strain as the easiest-oriented grains Hard-oriented grains produce more dissipation for the same strain compared to soft-oriented grains At the other end the homogeneous stress or Sachs model 69 assumes that stress but not strain is identical between grains This is the lower bound on dissipation The key disadvantage of the Sachs bound is that spatial compatibility between grains is not maintained Apart from these the Visco-Plastic Self-Consistent VPSC homogenization scheme 52 attempts to more accurately treat homogenization by assuming that each individual grain is an ellipsoidal inclusion in a continuum that has the average properties of the polycrystal rather than explicitly treating nearest-neighbor interactions This scheme allows for consistent stress and strain homogenization intermediate between the homogeneous stress and homogeneous strain assumptions However the VPSC scheme does not have analytical solutions in general requiring iterative numerical schemes In this paper we use the homogeneous stress assumption for ice deformation due to its simplicity While strain compatibility is violated the homogeneous stress assumption produces more accurate predictions of rheological properties than homogeneous strain in the case of ice 77 This is due to basal slip being by far the most active slip system with other slip systems accounting for far less strain Materials with several active slip systems can be more accurately modeled with the homogeneous strain bound The homogeneous stress assumption is a lower bound on the strength of anisotropy Therefore we can intuitively expect it to underestimate the strength of the coupling between fabric and flow 77 5 2 Fabric Model The most important process governing the development of crystal fabrics is deformationinduced grain rotation If grain deformation is due solely to basal glide the rate of change of the c-axis orientation is the sum of bulk rotation and viscoplastic spin From Meyssonnier and Philip 58 the evolution of c-axis orientation in response to strain can be described by a modified Jeffery s equation 48 : c i Vij cj Dij cj ci cj ck Djk 5 2 where ci is the unit vector in the direction of the c-axis The tensors Vij and Dij are the vorticity tensor and local strain-rate tensor of the grain respectively The first term gives the rotation rate due to the bulk rotation of the polycrystal while the second term gives the rotation rate due to viscoplastic spin Thus for example the c-axis of a grain experiencing uniaxial compression will rotate towards the compressive direction The last term of Jeffery s equation 5 2 ensures that the motion of grain orientation is tangent to the unit sphere at c which is necessary due to the convention that the c-axis vector is of unit length This can be seen by noting that the Vij cj term does not affect the magnitude of ci leaving only the Dij cj term Assume that at time t 0 the c-axis is given by c0 After a short length of time t the magnitude of the new c-axis c t is without the final term in Eq 5 2 c t c0 t Dc 5 3 c0 cT0 Dc0 t 5 4 1 cT0 Dc0 t 5 5 to first order in t Thus for the c-axis to maintain unit length we must add the quantity cT Dc t projected onto c This then gives the last term of 5 2 The above equation gives the evolution of a single grain in response to the applied velocity gradient It is not practical to integrate this equation for each grain in a polycrystal Instead we may instead derive an equation for the second-order orientation tensor Aij ci cj by 78 integrating the material derivative of the structure tensor ci cj over the ODF: dAij c i cj ci c j dt 5 6 Expressing the material derivative in spatial coordinates yields Aij Aij uk Vik Akj Aik Vkj Dik Akj Aik Dkj 2Aijkl Dkl t xk 5 7 where Dij is the strain-rate tensor Wij is the vorticity tensor and Aijkl is the fourth-order orientation tensor ci cj ck cl Unfortunately the presence of Aijkl introduces the closure problem The fourth-order orientation tensor cannot in general be determined from Aij An ODE for Aijkl may be derived however it in turn depends on the sixth-order orientation tensor and so on Therefore some kind of an approximation of Aijkl in terms of Aij must be taken Here we use the popular and simple quadratic closure 3 where Aijkl Aij Akl This closure is accurate whenever the largest eigenvalue 3 0 8 It is exact for perfect single-maximum fabrics where 3 1 Deeper layers of ice sheets typically have strong single-maximum fabrics so this is a good approximation for our purposes 5 3 Flow Model We now outline the constitutive relation and physical equations of our flow model We use the constitutive relation for an orthotropic material with linear transversely isotropic components from Gillet-Chaulet et al 37 Let be the viscosity of shear in the basal plane Also let be the ratio of viscosity for shear parallel to the basal plane to that in the basal plane and be the viscosity in response to normal stress along the c-axis to that in the basal plane We assume 1 because ease of deformation by compression is approximately the same in the c-axis direction as along the basal plane We set 10 2 and 1 The inverse form of the constitutive relation is given by Dij Sij 1 Aijkl Skl 2 Sik Akj Aik Skj 3 Akl Skl ij 2 5 8 where 1 2 2 1 4 1 2 1 1 1 3 1 2 2 3 5 9 79 The standard form of the constitutive relation with stress as a function of strain rate is then found by inverting this relation The fluidity R 1 ijkl of the consitutive relation given by Eq 5 8 is a fourth-order tensor formed found from the coefficient of Sij from adding up the terms of Eq 5 8 with appropriate representation of each term as a fourth-order tensor coefficient of Sij The viscosity in Eq 5 8 is also a fourth-order tensor Rijkl given by the inverse of R 1 ijkl It is often useful to write anisotropic constitutive relations in terms of Voigt notation 80 in which symmetric fourth-order tensors are represented as matrices and symmetric second-order tensors are represented as vectors The viscosity Rijkl may be represented as a 6 6 symmetric matrix Rij Likewise the symmetric stress tensor may be represented as a six-vector si where si Sii for i 1 2 3 s4 S23 s5 S13 and s6 S12 The case for Dij is identical Then the constitutive relation is just si Rij dj where di is the Voigt form of Dij Along with the constitutive relation Stokes flow is governed by stress balance and incompressibility p Sij 0 xj xi ui 0 xi 5 10 5 11 The stress Sij in 5 10 is given by the inverse of 5 8 5 4 Perturbation approximation Now we derive an analytical coupled first-order perturbation model from the equations 5 7 5 8 5 10 5 11 We seek seek to see how a small perturbation to background fabric can grow or disappear under this system homogeneous in all three dimensional First assume a background velocity gradient of U space We may assume that the velocity vanishes at the origin With this background velocity may be found from 5 7 given initial conditions Likewise the gradient the unperturbed A may also be found unperturbed stress S 80 Figure 5 1: Cartoon of the form of a sinusoidal perturbation in space with spatial wavevector The shading represents the sign and magnitude of cos x for a perturbation of the form v cos x where v is the Fourier coefficient of the perturbation The sinusoidal perturbation extends throughout three-dimensional space The plane of the perturbation is given by the plane which is normal to the wavevector In this diagram the positive x-axis extends outwards from the page z 1 y 81 The unperturbed quantities above are all homogeneous throughout space Suppose there is now a perturbation of fabric with a single Fourier wavevector The wavevector is a vector rather than a wavenumber because it is for three-dimensional space This gives sinusoidal perturbations where the normal to the plane of the perturbation is the wavevector See Fig 5 1 for a cartoon The perturbation to the second-order orientation tensor is given A cos x The parameter is small enough that we may neglect 2 and by A A is the Fourier coefficient of the perturbation Other quantities higher powers The tensor A with hats and bars are defined similarly We emphasize that the only spatial variability of this perturbation is due to the cosine term The perturbations themselves are deformed by flow over time therefore is not constant is a Fourier coefficient which is constant throughout space From in time The quantity A Montgomery-Smith 62 to satisfy Jeffery s equation must have the form A u A cos x cos x O 2 t t 5 12 Simplifying this equation and discarding terms of 2 and higher the first-order equation for the evolution of the wavenumber is T U t 5 13 is the unperturbed velocity gradient The solution for an initial wavevector where again U T 0 0 and a constant velocity gradient is t exp tU Now we seek to derive an approximate evolution equation for the fabric perturbation A under the assumption that 2 0 to see how it grows or shrinks Since fabric evolution is dependent on flow we first see how the fabric perturbation affects the flow equations 5 8 5 10 and 5 11 We will solve these flow equations to get perturbations of velocity and pressure and from that substitute the perturbed velocity gradient back into Eq 5 7 while discarding higher-order terms To first order there are no other spatial Fourier components to any of the other perturbed quantities other than that given by the wavevector This is because any interaction of 82 different wavevectors would be O 2 or higher which is negligibly small Therefore we make the following replacements u u u sin x 5 14 S cos x S S 5 15 D cos x D D 5 16 p p p sin x 5 17 R cos x R R 5 18 5 19 Now we substitute these perturbed quantities into the flow equations and neglect terms of 1 is found by substituting O 2 and higher The perturbed fluidity in Voigt notation R D cos x into Eq 5 8 then subtracting out the unperturbed fluidity and removing D terms of O 2 and higher The spatially-variable cos x appears in every term and can be cancelled out This removes any dependence on the spatial location x Then it can be shown that to first order the Fourier component of the perturbation of viscosity is ij R ik R 1 R lj We can then use this to find Fourier component of the stress given by R kl perturbation S ij if one knows the pertubations to stress and strain: 1 u u U x cos x 1 U U D 2 1 T W U U 2 d R d s R 5 20 5 21 5 22 5 23 where s and d are respectively the stress and strain tensors represented in Voigt notation Force balance and incompressibility perturbations by substituting the perturbed stress S and pressure cos x S p sin x p into the flow equations 5 10 and 5 11 After 83 cancelling out the spatially-variable sin x from each equation this yields S p 0 5 24 u 0 5 25 we Knowing the Fourier coefficient of the perturbed second-order orientation tensor A can now use Eq 5 24 and Eq 5 25 to analytically solve for the perturbed u and p and W In both Eqs 5 24 and 5 25 cos x appears in each term and in turn D as the only spatially variable component and can thus be cancelled out This produces a spatially-homogeneous algebraic system We can now write our equation for the evolution as of A dA A D W Q A dt V A A V A V D A D A A D A D V A A D A A D A A D 2 A 5 26 and This is a linear system of ordinary differential equations Note that the perturbed D depend on A through the previous flow equations Next we linearize this equation in W being represented by a six-vector a Voigt notation with A This then gets us the Jacobian of the system given by q D W J 0 A a a 0 5 27 where q is Q in Voigt notation The eigenvalues i of J give the stability of the system as a function of the unperturbed fabric velocity gradient and wavevector of the perturbation If there is an eigenvalue with a positive real part the system is unstable about the equilibrium 0 A small nudge in the direction of the corresponding eigenvector will grow Note that A in in Voigt notation or A the eigenvectors of this system are characteristic perturbations of a standard notation The corresponding eigenvalues give the growth rates of the corresponding Thus they may be thought of as eigenmatrices In characteristic perturbation of A 84 the next section we examine the stability of this system for different flow regimes and perturbation wavevectors 5 5 Results We now present results for layered perturbations in pure shear and horizontal simple shear at different angles to flow To do this we forced the perturbation model with wavevectors rotated about the x- and y-axes at different angles from vertical This corresponds to having layered perturbations whose planes are rotated from horizontal by the same angles We plot the real part of the largest eigenvalue of the linearized system for each flow scenario This gives the perturbation of A with the fastest growth rate Note that a perturbation eigenvalue may be interpreted as a growth rate of the paired perturbation eigenvector of A We examine only the real parts of the eigenvalues which are complex in general because the imaginary part corresponds to spinning about the fixed point of the perturbation where a 0 and is not as relevant to stability In addition the complex eigenvalues come in conjugate pairs associated with complex conjugate-pair eigenvectors which are not physical A perturbation with a real growth rate equal to the real part of the complex eigenvalues can be formed by taking a linear combination of the complex-conjugate pair Everywhere we take the unperturbed fabric to be a vertical single-maximum where the two smallest eigenvalues are equal and the largest eigenvalue 3 ranges from 0 8 to unity 5 5 1 Layered perturbations in simple shear First we take the background flow to be simple shear with the unperturbed component of the velocity-gradient tensor U 12 1 and other components set to zero We examine layered perturbations where the plane of perturbation is rotated around by several angles about the x-axis and y-axis For perturbations rotated about either axis there is an axis of symmetry for the largest eigenvalue about the rotation angle of 4 This means that for example a layer angled at 7 will have the same growth rate as one angled at 7 7 This reduces the range of angles we must plot This symmetry does not hold for general rotations 85 Figure 5 2: The largest real part of the eigenvalues of the Jacobian matrix 5 27 under simple shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the y-axis 60 0 max Re 50 100 40 50 30 25 20 10 10 3 8 0 0 80 0 85 0 90 0 95 1 00 Largest fabric eigenvalue Figure 5 3: The largest real part of the eigenvalues of the Jacobian matrix 5 27 under pure shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the x-axis max Re 150 0 100 100 50 25 50 10 3 8 0 0 80 0 85 0 90 Largest fabric eigenvalue 0 95 1 00 86 Figure 5 4: The largest real part of the eigenvalues of the Jacobian matrix 5 27 under pure shear as a function of the largest fabric eigenvalue 3 Each curve is a perturbation whose wavevector has been rotated by a different angle about the y-axis 80 0 max Re 60 100 50 40 25 20 10 3 8 0 0 80 0 85 0 90 0 95 1 00 Largest fabric eigenvalue We first discuss the case where the wavevector is rotated about the y-axis by an angle shown in Fig 5 2 This corresponds to a layered perturbation whose plane which is tilted in the y-direction When the plane of the perturbations is horizontal 0 with a vertical wavevector the fabric is stable In this case the real part of the largest eigenvalue is identically zero across the entire range of fabric eigenvalues plotted However instabilities occur when the wavenumber and plane of perturbations is rotated from vertical about the x-axis For strong fabrics with 3 0 9 perturbation planes with shallow dips or dips near vertical have the highest growth rates Perturbations with dip angles closer to 2 become small or negative for strong fabrics whose largest fabric eigenvalues are more than about 0 9 In all cases the velocity perturbation is confined to the y direction as can be seen in Table 5 2 This is because the wavevector is orthogonal to this direction Interestingly the growth rates of perturbations whose wavevectors are rotated about the y-axis are very close to those rotated about the x-axis This can be seen in Table 2 For perturbations whose wavevectors are rotated about the y-axis the velocity Fourier coefficient in the x direction u 1 is of equal and opposite sign to the velocity component in the y direction 87 of the perturbation with the wavenumber tilted by the same angle about the y axis The situation is somewhat different if the wavenumber is rotated by about both the xaxis and the y-axis see Table 5 2 In this case nonzero velocity perturbations may occur in the x and z directions as well This is important because stratigraphic folding requires a vertical velocity component to develop Therefore in the context of this model stratigraphic disruption is a three-dimensional phenomenon in simple shear and cannot be captured in two dimensions Table 5 2: Fourier coefficients u i of the perturbed velocity and the highest perturbation growth rate max Re for perturbations whose planes of perturbation are rotated from horizontal by a rotation of about the y-axis and then a rotation of about the x-axis The unperturbed background flow is simple shear The largest fabric eigenvalue is 0 8 max Re u 1 u 2 u 3 0 0 0 0 0 0 100 0 0 79 0 1 84 0 3 8 0 2 02 0 5 96 0 0 3 8 2 36 5 96 0 0 0 100 0 43 1 84 0 0 8 3 8 6 69 5 5 2 0 15 4 37 5 1 Layered perturbations in pure shear We now examine the case of pure shear in the xz-plane as commonly seen near ice divides We first look at the case where the planes of perturbation are rotated about the y-axis but with no rotation about the x-axis The results are shown in Fig 5 4 Horizontal layers are again completely stable the growth rates of perturbations are negative There is no associated velocity perturbation However again layers with shallow dips are unstable with high growth rates Growth rates are higher for strong single-maximum fabrics for perturbations with shallow dips Layers with steeper dips have lower growth rates and 88 Table 5 3: Fourier coefficients u i of the perturbed velocity and the highest perturbation growth rate max Re for perturbations whose planes of perturbation are rotated from horizontal by a rotation of about the x-axis and then a rotation of about the x-axis The unperturbed background flow is pure shear The largest fabric eigenvalue is 0 8 max Re u 1 u 2 u 3 0 0 -0 4 0 0 0 100 0 1 08 0 0 53 0 17 3 8 0 3 13 0 0 794 1 92 0 100 5 13 2 36 0 0 07 0 3 8 15 81 3 53 0 8 54 8 3 8 13 82 3 54 0 83 7 66 become stable for strong single-maximum fabrics When the wavenumber is rotated about the x-axis as well fabrics become generally less stable The highest growth rates for perturbations whose wavevectors are rotated about the xaxis are shown in Fig 5 3 The results are similar to the case where the wavevector is rotated about the x-axis Figure 5 4 except the growth rates are generally higher The growth rates for more steeply-dipped perturbations are near zero for strong fabrics but do not become strongly negative In Table 5 3 the Fourier coefficients of velocity perturbations and maximum growth rates are listed for perturbations whose wavevectors are rotated from vertical by several combinations of angles about the y-axis and about the x-axis This table illustrates that the wavevector must have a nonzero component in both x- and y-directions in order to produce a nonzero velocity perturbation in all three directions 5 5 3 Discussion In the flow scenarios considered dynamic instability seems to be the rule rather than the exception An important constraint to the flow perturbations is that the perturbed velocity 89 must be orthogonal to the wavevector and parallel to the plane of the perturbations This can be seen from the incompressibility constraint 5 25 in the perturbation model u 0 Since the velocity perturbation is u cos x this means that the velocity perturbation must be orthogonal to the wavevector Thus if the wavevector is vertical then there cannot be a vertical component to the velocity perturbation The perturbed velocity gradient must consist solely of shear orthogonal to the wavevector To overturn stratigraphic layers in ice sheets there must be a vertical velocity component This means that perturbations of horizontal layers can never generate vertical movement since the velocity perturbation is confined to the plane of perturbation However a layer needs to be tilted only a small amount to produce a vertical-velocity perturbation and fabric perturbations on layers with shallow but nonzero dips tend to have higher growth rates This corresponds to buckling Depending on the sign of cos x this perturbation moves some ice upwards and other ice downwards In flank flow the perturbation must have a tilt in both x and y to generate vertical motion Growth rates of perturbations in this model can be very high However it is important to keep in mind some of the limitations of this model It is applicable only to perturbations with thicknesses sufficiently smaller than the ice sheet For thick layers the effects of the ice-sheet boundaries become more important violating the assumptions of this model The scale of perturbations must also be large enough that the ice can be treated as a continuum In addition it is a first-order model valid for small perturbations As perturbations become larger higher-order effects which this model does not capture become important However the stability of perturbations in this model can show in which situations perturbations can develop in the first place Even with a high growth rate a sufficiently-small initial perturbation could take quite some time to grow large For this reason we do not expect large perturbations to develop in upper layers of ice sheets However perturbations may have enough time to develop in the lower layers of ice sheets This may be especially true for flank flow where simple shear dominates The high shear stress near the bed would accelerate the growth of the perturbations 90 It is possible that the effects of coupled flow on perturbations studied in this paper may reinforce the development of perturbations from other sources Disturbed layering is ubiquitous in deeper layers of ice sheets and any flow disruption will also have a corresponding effect on fabric Disturbances due to basal topography spatially-variable recrystallization or basal freeze-on may provide additional means of seeding fabric perturbations 5 6 Conclusions Due to the strong viscous anisotropy of ice as a function of c-axis orientation fabric it is important to understand flow of anisotropic ice as a coupled system To this end we developed a first-order coupled perturbation model of fabric evolution and flow of anisotropic ice We examined the stability of the system under various perturbations and flow scenarios Under this model coupled ice flow and fabric evolution is unstable across a wide range of flow and fabric conditions Fabric perturbations are capable of causing vertical-velocity gradients for both simple shear and pure shear This is a potential mechanism for stratigraphic disruption in ice The instabilities would not occur in fabric that is uncoupled to flow These types of perturbations may help explain the small-scale stratigraphic disturbances seen far above the bed in ice sheets In addition it provides a means of growth for fabric perturbations from other sources Further numerical simulations of macroscopic coupled flow and fabric would shed more light on the development of perturbations The numerical model of coupled fabric and plane flow in Gillet-Chaulet et al 38 seems to show large fabric perturbations developing in response to basal topography Additional numerical simulations especially three-dimensional ones in different flow scenarios and with different initial fabric perturbations would be useful The results from this analytical model suggest that two-dimensional flow models are not capable of capturing the growth of perturbations in simple shear This reinforces the fact that flow of anisotropic ice and fabric development is a fundamentally three-dimensional problem which cannot be represented as plane flow 91 Chapter 6 CONCLUSIONS 6 1 Summary Chapter 2 develops novel analytical and bootstrap estimates of the sampling error of fabric eigenvalues and fabric eigenvectors I showed that typically very uneven grain-size distributions produce much larger uncertainties in area-weighted estimates of fabric properties I also applied bootstrapping to estimate the confidence intervals of the inferred strain enhancement factor in simple shear Due to the power-law rheology of ice I showed that the enhancement factor is very poorly constrained by thin sections I also introduced a new parameterized orientation distribution function the Bingham distribution to glacioogy I compared the performance of this distribution to the Dinh-Armstrong distribution and the Fisherian distribution proposed by Lliboutry I showed that the Dinh-Armstrong distribution and the Bingham distribution produce much better fits than the Fisherian distribution This underscores the shortcomings of axially-symmetric distributions for representing most realistic fabrics seen in ice cores Chapter 3 explores the use of sonic velocity measurements to infer ice fabric in boreholes with application to P-wave data taken from NEEM I developed a model which estimates eigenvalues in boreholes using both thin-section measurements and P Sv and Sh sonic velocities This model helps combine the relative strengths of the two measurement methods while reducing their relative weaknesses Thin-section samples provide unbiased although possibly dependent measurements of thin-section samples but they have typically large sampling error Sonic velocity measurements on the other hand nearly eliminate sampling error due to the large amount of ice sampled by the sound waves However model error can be significant In addition poor tool centering was a problem at NEEM which produced 92 large but fairly smooth biases in the measured velocity The method uses thin-section derived eigenvalues to correct for this bias producing continuous more accurate estimation of fabric eigenvalues The next two chapters move from examining error in measurement of fabric characteristics to looking at stability of ice crystal fabrics in response to flow or fabric perturbations The fourth chapter examined the response of fabrics to small flow perturbations I showed that under random velocity gradient perturbations tilted-cone fabrics where the largest concentration is not vertical can develop in simple shear and pure shear This can produce deformation in components other than the applied stress and potentially induce stratigraphic disruption The fifth chapter develops a first-order coupled model of anisotropic ice-flow and fabric evolution It is informative to treat fabric evolution and anisotropic flow as a coupled system since fabric greatly affects flow and vice-versa I applied this model to examine the stability of spatially heterogeneous fabric perturbations in both simple shear and pure shear I showed that single-maximum fabrics in this coupled system are unstable This has important implications for the development of stratigraphic disruption in ice sheets All unstable perturbations in this model cause vertical offset in layers which can invert stratigraphic layers 6 2 Implications This thesis reinforces the utility of sonic measurements of fabric to avoid the severe sampling error and spatial discontinuities of thin-section fabric measurements Future work incorporating S-waves will expand the usefulness of sonic method by allowing inference of information on azimuthal c-axis concentration However despite their inaccuracy thin-section fabric measurements can be effectively used in combination with sonic measurements This work underscores the difficulty of predicting ice-core fabrics and anisotropic ice-flow My work indicates that basal ice flow and fabric development may be nearly impossible to predict accurately on smaller length scales at high strains due to the instabilities of coupled 93 ice flow and fabric evolution Further numerical investigations of coupled anisotropic ice-flow and fabric evolution would be useful to expand on the analytical treatment in Chapter 5 In particular larger-scale perturbations which interact with the ice boundaries or temporal flow perturbations could be investigated This thesis also lends support to the idea that fabric anisotropy may aid the development of stratigraphic disturbances in basal ice Stratigraphic disturbances are very commonly seen in ice cores e g Fuchs and Leuenberger 31 Alley et al 7 Steeply dipping disturbed basal layers are also a leading candidate for the cause of the abrupt loss of radar returns in echofree zones in Greenland and Antarctica 22 Irregular bed topography alone cannot explain stratigraphic disturbances Temporal variations in flow over an irregular bed or significant basal freeze-on can cause stratigraphic disruption However I speculate that interactions of fabric with ice flow sometimes in concert with temporal flow and bed topography are a better explanation of the seeming ubiquitousness of disturbed basal ice Unlike temporal flow or basal freeze-on fabric exerts a strong influence on ice flow everywhere which is not necessarily true of these other processes 94 1 Appendix A: Derivation of analytical estimates of sampling error We now derive analytical estimates for sampling error from estimating the bulk second-order orientation tensor from ice core thin sections First we focus on the case of per-pixel EBSD or automatic fabric analyzer measurements which typically yield many measurements per grain We take into account correlations between different measurements It is important to take depedendence between measurements into account in this case Samples taken from the same grain will be highly correlated since intragranular misorientations are typically no more than a few degrees In this section upper indices represent spatial locations and lower indices are indices for tensor quantities at one location For example cki is the i component of the c-axis tensor at P spatial location k Let A ij k akij N be the sample estimate of Aij where akij cki ckj no sum in k is a component of the structure tensor for an individual c-axis measurement and N is the total number of measurements We assume that each measurement is equally weighted for simplicity of presentation Extending these results to the case where measurements are not equally weighted is fairly simple Suppose that we can determine a covariance tensor giving the covariance between the ij component of the structure tensors at spatial locations k and l This is given by Cijkl Cov akij alij 1 Now we wish to determine the variance of the sample estimate A ij First note that Var akij N Var akij N 2 Also the variance of a sum of random variables X1 Xn is Var X i Xi X i j Cov Xi Xj 2 95 P Since A ij k akij N we have Var A ij Var X k l X akij k kl Cij N2 N 3 4 where Cijkl is the covariance between the structure tensor akij at site k and alij at site l and N is the total number of measurements in the thin section From the previous equation we can see that if each structure-tensor measurement is strongly correlated with m other measurements then the variance of A ij would be approximately m times larger than if it were uncorrelated In a high-resolution per-pixel thin-section measurement a single pixel can be expected to be highly correlated with many other pixels The structure tensor akij for measurement k can be written as the sum akij Aij gijk hkij 5 Here gijk is a random component accounting for intergrain variance in akij constant across M each grain Let the site k be in grain M Then gijk aM ij Aij where the mean aij is the expectation of alij taken over all measurements l in grain M Likewise hkij is a random component which can be identified with intragrain variability By rearranging terms hkij akij Aij gijk We assume that gijk and hkij are independent Note that we separate out the mean of Aij which is the mean of akij for all k taken over the ODF Furthermore we are also separating out the mean of each individual grain as well This decomposition separates out the components of the structure tensor that vary on different length scales: global Aij per grain gijk and intragrain hkij This will allow us look at the relative contributions of these components and their effect on sampling error Suppose akij and alij were taken from the same grain Let Gkl ij be the covariance between gijk and gijl From Equation 5 gijk gijl This also implies that every entry of the covariance k l k tensor of gijk Gkl ij is equal to Cov gij gij Var gij no sum for all k l taken from the 96 same grain Due to independence between gijk and hkij we can write the covariance as the l k kl sum Cijkl Hijkl Gkl ij where Hij is the covariance between hij and hij Correlation between adjacent grains is usually small unless there is active polygonization 26 Correlation between distant grains is always small even if two distant grains happen to have similar orientations Therefore we are justified in neglecting covariances between kl points in different grains This means that we can take Gkl ij 0 and Hij 0 whenever observations k and l are not from the same grain We now show that the intragrain variability hkij may be ignored under some light assumptions The covariance Hijkl is non-negligible only where points k and l lie not only within the same grain otherwise it is zero by assumption but sufficiently close together This is because intragraular misorientations for example due to the formation of subgrain boundaries occur on lengths smaller than the grain Because of this Hijkl is negligible for may more combinations of k and l than Gkl ij is In addition intragranular c-axis misorientations are usually not more than a few degrees so the covariance as opposed to correlation Hijkl is likely small for even highly correlated nearby pairs of c-axis measurements k l Given this we may approximate the total covariance Cijkl Gkl ij k k k This implies that Cijkl Cijpq Gkl ij Var gij Var ci cj whenever k l p q lie in the same grain and zero otherwise From this we can write the variance of the sum of all akij m m taken from a grain m as nm Var cm i ci where n is the number of observations from the grain m with index m Finally due to independence between different grains Var cm i cj Var ci cj is the same for all grains since by these assumptions they are drawn independently from the same ODF Now we have an expression for the variance of individual grains in terms of Var ci cj Then we can write Var A ij as a sum of the variances of individual grains in turn This is given by Var A ij X wm 2 Var ci cj s2n Var ci cj 6 m where wm nm N is a weighting coefficient corresponding to the fraction of observations 97 lying in grain m of a total number of observations N The coefficient s2n is the sum of the squared weights If we have many observations per grain Equation 6 substantially simplifies treatment of uncertainty compared to Equation 3 By only considering data on a per-grain basis and ignoring intragrain c-axis variability we are also able to use the same analysis for thin-section data collected per-grain as in the Rigsby Stage method or per-pixel as with EBSD or automatic fabric analyzers Note that in the case of c-axis measurements given per-grain rather than per-pixel weighting the measurements by grain area is physically preferred to equal weighting 35 Area weighting also yields similar variance estimates to per-pixel measurements if the number of per-pixel measurements in each grain is proportional to the area We now derive analytical estimates of the distribution of the sample estimate A ij using Equation 6 For a large-enough sample A ij will have principal directions and eigenvalues close to those of Aij For a large enough number of grains we can apply the central limit theorem to estimate the sampling distribution of Aij As the number of sampled grains n becomes large A ij converges in distribution to the normal distribution with mean Aij and variance Var ci cj s2n Variance is the mean of the square minus the square of the mean From this Var ci cj ci cj ci cj ci cj 2 Aijij Aij Aij Then the variance of the sample estimate of A ij is given by Var A ij Aijij Aij Aij s2n ijij A ij A ij s2 A n 7 8 with no sum in i or j The preceding gives us an expression for variance of the sample estimate A ij of Aij Note that s2n is at a minimum when all area weights are equal corresponding to equal grain weighting In that case the sum of squared weights is s2n n 1 This is the minimum s2n for any choice of positive weightings that sum to unity Therefore equal weighting of grains always underestimates sampling error For simplicity we choose to work in the reference frame defined by the three true fabric 98 eigenvectors In this case Aij is a diagonal matrix of the fabric eigenvalues i and the components of ci are uncorrelated For a large enough number of grains A ij Aij ij where ij is small We can then estimate the sampled fabric eigenvalues and eigenvectors as a first-order perturbation of the original eigenvalues and eigenvectors In this case let Aij have i i i eigenvalues i Aii no sum Also let the fabric sample have eigenvalues Then to first order i ii no sum 78 i is then given by Var A ii no sum It follows that the variance of sample eigenvalues i no sum This is most easily found by calculating Var c2 where ci is expressed since A ii i in the reference frame defined by the principal directions and has zero empirical mean In the case of analytical orientation distribution functions the second- and fourth-order orientation tensors which correspond to the second and fourth moments of the distribution can be used directly From this it can be seen that samples from more diffuse orientation distribution functions will have larger variance of sample eigenvalues and concentrated fabrics will have less variance Now that we have an estimate for the sample variance of eigenvalue estimates from thin sections we examine sampling error of the fabric eigenvectors or principal directions Similarly to the eigenvalues we use a first-order approximation of the eigenvalue perturbations 78 If we are in the reference frame defined by the true fabric eigenvectors then the sam will be be close to being diagonal with small off-diagonal elements The ple estimate A of the A are then eigenvalues V V 1 21 A 1 2 31 A 1 3 12 A 2 1 1 13 A 3 1 23 A 3 2 12 A 2 3 1 9 is then also an infinitesimal to first-order accuracy in A ij The perturbed eigenvalue matrix V rotation matrix which is a first-order approximation for rotation matrices valid for small rotation angles This defines the approximate reference frame formed by the perturbed eigenvectors The three elements above the diagonal are the Euler angles of this infinitesimal 99 rotation with V 23 V 13 and V 12 being the rotation angles around the z-axis y-axis and x-axis respectively As before the sample-based estimate A ij of the component of the second-order orientation tensor Aij is approximately normally distributed for a large enough sample of grains with variance Aijij Aij Aij s2n no sum Thus is approximately normally distributed with variance 2 1 2 Var A 12 and a mean of zero The cases for and are similar From this variance of the Euler angle about an axis is inversely proportional to the difference in the fabric eigenvalues associated with the other two axes This means that the variance becomes large if the other two eigenvalues are very close together It is not defined if the eigenvalues are identical This is because if there are two identical eigenvalues then there are two corresponding orthogonal eigenvectors and any vector in the plane formed by those eigenvectors is an eigenvector Therefore there is not a unique reference frame which makes A diagonal in this case Grain-size distribution also has an important influence on sampling error of eigenvalue and eigenvector estimates Uneven distributions in which a small number of large grains account for most of the volume 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    • Sophia Amador, Elena - Ph.D. Dissertation
      Characterizing Habitable Environments on Mars Using Infrared Spectroscopy from Orbit 2017, Sophia Amador,Elena ,Elena Sophia Amador Copyright 2017 Elena Sophia Amador Characterizing Habitable Environments on Mars Using Infrared Spectroscopy from Orbit Elena Sophia Amador A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: Joshua L Bandfield Chair David C Catling Victoria S Meadows Program Authorized to Offer Degree: Earth and Space Sciences University of Washington Abstract Characterizing Habitable Environments on Mars using Infrared Spectroscopy from Orbit Elena Sophia Amador Chair of the Supervisory Committee: Dr Joshua L Bandfield Department of Earth and Space Sciences Until recently the search for habitable environments on Mars has mostly been driven by the motto follow the water as water is thought to be one of the fundamental requirements for life Over the last several decades there has been abundant geomorphic and mineralogical evidence for surface and near-surface liquid water early in Mars history increasing the potential for past habitable environments However it has becoming progressively clear that there are several more requirements in addition to liquid water that make an environment habitable including a source of energy for biochemical processes major and trace elements to form macromolecules e g CHNOPS as well as clement physicochemical conditions e g pH salinity temperature The search for habitable environments on Mars has now become more refined searching for locales that show evidence for not only liquid water but these other important constraints This dissertation first focuses on the Nili Fossae region of Mars an area that shows extensive evidence for aqueous alteration with a diverse range of hydrated minerals This work views the region through the lens of both bulk surface composition and secondary alteration minerals in particular with respect to minerals that would indicate not only liquid water but an energy source and a means for creating organic materials such as with serpentinization The study ultimately uses what is learned in Nili Fossae to better understand the global distribution of mineralogical evidence for serpentinizing systems detectable from available orbital data The studies presented here rely on near-infrared 1 0-3 0 m reflectance and thermal-infrared 550 m emissivity measurements of both the martian surface and terrestrial analog materials to best describe the composition of surfaces exposed in Nili Fossae Chapter Two uses a complementary approach for looking at near- and thermal-infrared measurements of the surfaces in Nili Fossae to identify elevated bulk-silica exposures that imply increased aqueous alteration of a capping unit that was previously considered unaltered This extends aqueous alteration to all three major stratigraphic units in the area Chapter Three uses near- and thermal-infrared laboratory measurements of rocks from the Lost City Hydrothermal Field on Earth to better constrain the geochemical and astrobiological environment that formed similar minerals in Nili Fossae Mars This work identified a suite of spectral types and minerals serpentine Mg-carbonate and talc saponite associated with low-temperature serpentinizing systems on Earth and compared them to what was observed in Nili Fossae This resulted in an additional identification of serpentine within the region and additional evidence for a sustained habitable serpentinizing system in Nili Fossae This framework was used to search for similar sites across Mars in Chapter Four This produced a global map of the distribution of spectral types associated with low-temperature serpentinizing systems This study resulted in new identifications of serpentine across the southern highlands predominately in isolated exposures in crater and valley walls crater ejecta and ancient knobby terrains Additionally it found that serpentine was much more pervasive in the Nili Fossae region than previously thought making it an increasingly compelling site for future detailed surface investigations with respect to habitability TABLE OF CONTENTS List of Figures v List of Tables xi Chapter 1 Introduction 16 1 1 Organization of Dissertation 16 1 2 Motivation 16 Chapter 2 Elevated bulk-silica exposures and evidence for multiple aqueous alteration episodes in Nili Fossae Mars 19 2 1 2 1 1 2 2 Introduction 19 Geologic Setting 20 Data and methods 23 2 2 1 Thermal Emission Imaging System THEMIS 23 2 2 2 Compact Reconnaissance Imaging Spectrometer for Mars CRISM 28 2 2 3 Context Camera CTX 29 2 3 Results 30 2 3 1 TIR Spectral Results 30 2 3 2 NIR Spectral Analysis 36 2 3 3 Unit Textures 41 2 4 Discussion 43 2 4 1 Compositions 43 2 4 2 Stratigraphic Relationships 47 2 4 3 Localized Alteration of the Capping Unit 49 i 2 5 Summary and Conclusions 52 Chapter 3 The Lost City Hydrothermal Field: A spectrcopic and astrobiologial analog for Nili Fossae Mars 54 3 1 Introduction 54 3 1 1 Serpentinization 55 3 1 2 The Lost City Hydrothermal Field 57 3 1 3 Nili Fossae Mars 60 3 2 Approach 61 3 2 1 Laboratory Spectral Measurements 64 3 2 2 Mars Dataset from the Compact Reconnaissance Imaging Spectrometer for Mars CRISM 68 3 3 Measurements and Observations 69 3 3 1 Lost City Hydrothermal Field Measurements 69 3 3 2 Mars Observations 81 3 4 Discussion 86 3 4 1 Laboratory Measurements 86 3 4 2 Mars Observations 90 3 4 3 Spectral Differences between Measurements from the Lost City Hydrothermal Field and Nili Fossae Mars 92 3 4 4 3 5 Implications for Serpentinization in Nili Fossae Mars 94 Conclusions 98 Chapter 4 A search for minerals associated with serpentinization across Mars using CRISM spectral data 100 ii 4 1 Introduction 100 4 2 Background 104 4 2 1 Serpentinization and its Astrobiological Implications 104 4 2 2 Identifying serpentine from remote sensing datasets 105 4 2 3 Serpentine on Mars 105 4 3 Data and Methods 107 4 3 1 Approach 107 4 3 2 Compact Reconnaissance Imaging Spectrometer for Mars CRISM 108 4 3 3 Factor Analysis 109 4 4 Results 113 4 4 1 Target Transformation Fits 113 4 4 2 Global Distributions 122 4 5 4 5 1 Discussion 129 Usefulness of Factor Analysis and Target Transformation in Searching for phases Associated with Serpentinization 129 4 5 2 Global Distributions Spatial Correlations between Phases and Regions of Interest 131 4 5 3 Implications for global serpentinization processes on Mars and searching for regions with the highest potential for containing once habitable environments 143 4 6 Summary and Conclusions 145 Chapter 5 Conclusions 148 5 1 Summary of work 149 5 2 Future Work 152 iii Bibliography 153 Supplementary Material 171 iv LIST OF FIGURES Figure 2 1 Nilo-Syrtis Major colorized elevation map with THEMIS Global Day IR mosaic used for shading Solid white box indicates initial THEMIS image search area Dashed white box indicates area covered by Figure 2 10 Image is centered around 77 02 E and 21 86 N 21 Figure 2 2 3-panel decorrelation stretch DCS for THEMIS image I37499019 Arrow points to elevated bulk-silica surface identifiable by its color combination across all three stretches 26 Figure 2 3 Depiction of the calculation for the weighted absorption center WAC value for a given THEMIS spectrum bands 3-9 27 Figure 2 4 Panels A and B show the four TIR defined spectral units Panel A THEMIS image I18532009 shows the Purple Unit and the Yellow Amber Unit arrows Panel B THEMIS image I01570009 over THEMIS day IR shows the Fuchsia Orange Unit Panel A is centered around 76 53 E and 23 38 N Panel B is centered around 80 23 E and 21 74 N 31 Figure 2 5 THEMIS WAC index maps and associated CTX images covering regions with exposures of the Purple and Yellow Amber Units and phyllosilicate-bearing terrain Low WAC values indicate surfaces with high bulk-silica compositions White arrows point to Yellow Amber Unit exposures dashed white polygon indicate phyllosilicate-bearing surface Purple Unit exposures are light-toned and have variable texture at the decameterscale Yellow Amber Unit exposures are dark-toned and smooth and have a sharp contact with the bright Purple Unit THEMIS and CTX images are a-b I18532009 and P13_006211_2038_XN_23N283W c I36613020 and G18_025225_2058_XN_25N_283W and d I02007009 and F06_037963_XI_23N_282W respectively 33 Figure 2 6 THEMIS emissivity data for bands 3 7 93 m through 9 12 57 m A Spectral data for the four TIR defined spectral units found in the Nili Fossae region including the subtly different Yellow and Amber spectra of the Yellow Amber Unit B Comparison of the Yellow Amber Unit spectra to other Mars spectral endmembers Surface Type 2 v spectrum acquired by TES and convolved to THEMIS spectral sampling Line and sampling for THEMIS spectra can be found in Supplementary Table 5 10 35 Figure 2 7 A CRISM MSP BD1900 hydration index map using individually stretched images across Nili Fossae White box indicates location of Panel B Hydrated phases span across most of the region and predominately indicate the presence of phyllosilicate-phases B Dashed polygons indicate the location of Yellow Amber Unit exposures identified by TIR data that show hydrated signatures in NIR MSP data White arrows indicate exposures of phyllosilicate-bearing surfaces identified by D2300 index and inspection of spectral ratios Panel A is centered near 78 54 E and 21 76 N See Supplementary Table 5 12 for MSP image IDs 37 Figure 2 8 Comparison of phyllosilicate-bearing surfaces high 2300 index values MSP0000366C_01 and elevated bulk-silica surfaces low WAC index values THEMIS I18532009 Panels A and B cover the same spatial region Solid white polygons indicate location of Yellow Amber Unit exposure and dashed white polygons indicate phyllosilicatebearing surfaces index maps shaded by CTX image data Image is centered near 77 83 E and 23 37 N 38 Figure 2 9 CRISM MSP spectra for the TIR defined spectral types except typical terrain and a phyllosilicate-bearing exposure 5km from a Yellow Amber Unit exposure Yellow Amber Unit spectrum is an average of 8 Yellow Amber Unit spectra taken from MSP0000366C_01 see Supplementary Table 5 13 and Supplementary Table 5 14 for all pixel locations for spectra presented here Yellow Amber Unit spectra show a weak broad short-wavelength absorption consistent with olivine and a weak 1 9 m absorption consistent with bound H2O 39 Figure 2 10 CTX mosaic centered around 76 93 E and 23 45 N Inset solid boxes indicate locations for Panels A-D in Figure 2 5 42 Figure 2 11 A Representative exposure of typical terrain dark-toned cratered and rough in texture CTX P13_006211_2038_XN_23N_283W B Representative exposure of the Fuchsia Orange Unit dark barchanoid-shaped dunes with lighter-toned scalloped terrain underneath CTX P17_007_648_2015_XN_21N_279W 43 vi Figure 2 12 Eastern Nili Fossae stratigraphy in terms of bulk-rock composition and alteration products Spatial scaling is not represented in this visualization The top capping unit can be broken down into an unaltered olivine-poor basalt and separately an altered capping unit with an elevated bulk-silica composition that is sometimes hydrated 48 Figure 3 1 Nilo-Syrtis Major colorized elevation map with THEMIS Global Day IR mosaic used for shading centered around 76 6 E 22 4 N Inset image shows typical Nili Fossae stratigraphy in CTX image DO1_027691_2025_XN_22N_282W 60 Figure 3 2 Photographs of the Lost City Hydrothermal Field samples used for this study 62 Figure 3 3 Thermal-infrared emissivity measurement for carbonate and pelagic top-layer samples compared to end-member library spectra for calcite and aragonite Carbonate measurements match best with library calcite spectra while pelagic top-layer measurements match best with library aragonite spectra 70 Figure 3 4 Deconvolution results for non- serpentinite Lost City samples Any mineral group with abundances calculated to less than 5% have been grayed out 72 Figure 3 5 Deconvolution results for serpentinite Lost City samples Serpentinite emissivity measurements showed the greatest spectral variability and were therefore broken-down into five Spectral Types A-E Any mineral group abundances calculated to less than 5% have been grayed out 73 Figure 3 6 Near-infrared reflectance measurements for Lost City rock samples 78 Figure 3 7 Near-infrared library spectra for serpentine tremolite amphibole talc and saponite Serpentine can be uniquely identified by an absorption 2 1 m Amphibole talc and saponite are difficult to distinguish spectrally in this wavelength region 80 Figure 3 8 Alteration mineral distribution map for Nili Fossae on THEMIS Global Day IR mosaic background centered around 75 7 E 20 8 N CRISM stamp colors indicate the identification of one or multiple alteration phases of interest within that given CRISM image Identifications made by this study and Ehlmann et al 2009 Viviano et al 2013 and Thomas and Bandfield 2016 82 Figure 3 9 CRISM ratioed I F spectral measurements for the spectral suite associated with lowtemperature serpentinization found in Nili Fossae Olivine and Mg-carbonate spectra from CRISM FRT00003E12_07 Ehlmann et al 2008 Mg-serpentine spectrum from CRISM vii image FRT0000ABCB_07 Ehlmann et al 2009 and talc saponite spectrum from CRISM image FRT0000A053_07 Viviano et al 2013 See Supplementary Table 5 19 for pixel locations 83 Figure 3 10 CRISM image FRS0002AE17_01 with new detections of serpentine carbonate and talc - saponite and amphibole in association with the olivine-rich basalt unit See Supplementary Table 5 19 for CRISM pixel locations for displayed spectra False-color IR image projects CRISM wavelengths 2 53 m 1 50 m and 1 08 m as red green and blue respectively 85 Figure 3 11 Near-infrared reflectance and thermal-infrared emissivity spectra for the three Mgrich serpentine polymorphs The polymorphs have nearly indistinguishable spectral absorptions in the near-infrared while having unique spectral shapes and contrast in the thermal-infrared 87 Figure 4 1 Near-infrared reflectance library spectra for minerals associated with serpentinization reactions See Supplementary Table 5 20 for references 102 Figure 4 2 Three examples of excellent target transformation fits for serpentine Panels A-C show examples of CRISM images where serpentine has previously been identified Panel A Ehlmann et al 2010 where serpentine has been speculated Panel B Michalski and Niles 2010 and a new image outside of Nili Fossae with a clear fit for serpentine Panel C CRISM image FRT0000634B_07 shows the best spectral match for serpentine in both ratioed I F spectra Ehlmann et al 2010 and via target transformation using independent eigenvectors 115 Figure 4 3 Target transformation fit for Mg-carbonate in CRISM image HRL000095C7_07 in Chia Crater The presence of Mg-carbonate can be independently verified by viewing ratioed I F spectra and by displaying the BD2500 Mg-carbonate index map 116 Figure 4 4 Target transformation fits for talc saponite spectral type Panels A and B show fits to talc and saponite respectively for one image in Her Desher Vallis Fit can be independently verified using ratioed I F spectra and D2300 colorized index map Panel C 117 Figure 4 5 Representative target transformation fits for all spectral types in Nili Fossae from CRISM image FRT000028BA_07 Target transformation fits for serpentine exhibit viii diagnostic 2 12 m absorption and an additional minor absorption near 2 4 m similar to talc and saponite implying variable alteration of serpentine to a talc saponite phase 119 Figure 4 6 CTX mosaic of Leighton Crater with outlines of all overlapping CRISM images Green stamps indicate images with fits for serpentine magenta stamp and magenta circles indicate images with fits for Mg-carbonate gray stamps indicate images with no fits for investigated phases Spectra come from CRISM image FRT0000A546_07 starred Fits are strong for all investigated phases and an Al-phyllosilicate phase consistent with montmorillonite 121 Figure 4 7 Viking MDIM 2 1 mosaic of the Mawrth Vallis region with all overlapping CRISM images Small black squares indicate CRISM images with no fits for investigated phases Green stamps indicate images with fits for serpentine magenta stamps indicate fits for Mgcarbonate and blue stamp indicates fit for talc saponite Representative target transformation fits shown to the right Mg-carbonate and serpentine fits are clear talc saponite fits appear more consistent with talc Additionally target transformation techniques clearly identify a Fe Mg-phyllosilicate phase consistent with nontronite and an Al-phyllosilicate phase consistent with montmorillonite 122 Figure 4 8 Global distribution of target transformation fits for serpentine green squares Mgcarbonate magenta squares and talc saponite blue squares over MOLA shaded relief map Results from this study are shown with serpentine detections from 125 Figure 4 9 Global distribution of target transformation fits for investigated spectral types over colorized OMEGA dust map As expected and consistent with other studies searching for secondary alteration minerals our detections are associated with relatively low dust covered areas This low dust coverage provides an orbital window to interpret the mineralogy of exposed surfaces 133 Figure 4 10 Colorized MOLA over THEMIS Day-IR mosaic of Nili Fossae centered around 76 09 E 19 98 N White inset shows area described in Figure 4 11 Colored stamps and circles indicate CRISM images with target transformation fits for investigated spectral types Green indicates serpentine magenta indicates Mg-carbonate and blue indicates talc saponite The three starred CRISM images FRT0000ABCB_07 FRS0002AE17_01 ix and HRL0000B8C2_07 are where previous studies have detected serpentine previously 138 Figure 4 11 Colorized MOLA over THEMIS Day-IR mosaic Most serpentine detections are concentrated in this region east of the main Nili Fosse troughs Black insets indicate areas shown in detail in Figure 4 12 139 Figure 4 12 Colorized MOLA over THEMIS Day-IR mosaic Panel A shows proposed Mars2020 landing site Carbonate Plains Panel B shows proposed Mars2020 landing site NE Syrtis Both landing sites would put a rover near the spectral types of interest 140 Figure 4 13 Colorized MOLA topography over THEMIS Day-IR mosaic with 200 m contour lines Color stamps indicate CRISM image with target transformations fits for serpentine green Mg-carbonate magenta and talc saponite blue The highest concentration of the mineral suite of interest is found at lower elevations relative to Nili Fossae possibly along a hydrologic flow gradient from the higher Nili Fossae plateau towards Isidis Basin 142 x LIST OF TABLES Table 2 1 THEMIS Spectral Bands 25 Table 2 2 TIR-defined Unit Descriptions 34 Table 3 3 Lost City Hydrothermal Field Samples with descriptions Reference ID is used across studies by others working with these samples Sample Number is used for this study only 63 Table 4 4 Regions of Interest 108 Table 4 5 Imagine line sample bands used for factor analysis 111 Table 4 6 Description of Images with Serpentine Detections 125 Table 4 7 Detections for investigate spectral types 129 Table 5 8 Initial THEMIS Day IR DCS 8-7-5 images visually inspected for compositional variability and Purple 171 Table 5 9 Down-selected high quality THEMIS images with Purple and Yellow Amber Units in regional proximity These THEMIS images were atmospherically correct and used for all further TIR analyses 173 Table 5 10 THEMIS line and sample numbers used for spectra in Figure 2 6 174 Table 5 11 CRISM Multispectral Product images IDs listed below were visually inspected for 8 phase and or hydration index maps A qualitative and subjective characterization of yes or no was assigned to each index if high index values were or were not present in a structurally coherent formation 175 Table 5 12 CRISM Multispectral Image IDS used in Figure 2 7 Images were cropped between 19 0 and 25 0 N 176 Table 5 13 CRISM MSP sample and line numbers for spectra used in Figure 2 9 177 Table 5 14 CRISM MSP sample and line numbers used for Yellow Amber Unit spectrum in Figure 2 9 178 Table 5 15 Spectral end-member library used for thermal-infrared deconvolution modeling Unless otherwise noted spectra come from the ASU Spectral Library speclib asu edu 179 xi Table 5 16 CRISM images taken after 2011 these images were not looked at by previous studies and were searched for this study 183 Table 5 17 Thermal-infrared deconvolution model results for the non-carbonate rocks used for this study Rows highlighted in green indicate abundances well within the detection limits for this study Rows highlighted in red fall within known limits of the technique and can be noted but should not be used quantitatively 184 Table 5 18 New CRISM detections of Mg-carbonate Talc and or saponite and serpentine in Nili Fossae from this study Images correspond to stamps mapped in Figure 3 8 188 Table 5 19 CRISM sample and line numbers for spectra shown in Figure 3 9 and Figure 3 10 190 Table 5 20 Reference Spectra for Library Spectrum for Figure 4 1 191 xii ACKNOWLEDGEMENTS It really does take a village to make a planetary scientist so I will do my best to thank all those who have helped me along this journey First I want to express my deepest gratitude to Josh Bandfield for taking me on as a graduate student and teaching me how to think critically about spacecraft data and planetary science in general I would not have been able to finish my dissertation without your patient guidance and support Thank you to my committee Victoria Meadows David Catling and Darlene Zabowski Thank you for always having your doors open especially as the planetary remote sensing group was shrinking at UW Additionally there were several others who aided in the scientific content of this dissertation: Billy Brazelton and Deborah Kelley for providing Lost City Hydrothermal Field samples and teaching me about terrestrial serpentinization and of course Bernard Evans for explaining all the mineralogical details involved in serpentinization I also must thank those who encouraged me to pursue planetary science when I was an undergraduate student Dr Janice Bishop at the SETI Institute introduced me to CRISM data and near-infrared spectroscopy Thank you to Dr Carl Allen and Dr Dorothy Oeheler at NASA Johnson Space Center for an incredible undergraduate research experience and project Thank you to the UC Santa Cruz Earth and Planetary Science faculty who first introduced me to planetary geology in particular professors Francis Nimmo and Erik Asphaug There were several others who encouraged me at a young age to pursue planetary exploration: Jim Erickson Bonnie Buratti and Eleanor Basilio at the Jet Propulsion Laboratory Thank you to the Department of Earth and Space Sciences for providing funding for my graduate studies and an inclusive atmosphere over the years I d like to especially thank those who worked behind the scenes to keep this department running so smoothly: Eunice Yang Kathy Gabriel Lauren McOwen Wood No ll Bernard-Kingsley Nathan Briley Ed Mulligan Dave McDougall Sue Bernhardt and I ve probably missed others but you ve made this process as painless as possible Thank you to the UW Astrobiology Program This program has kept me sane during my graduate career The opportunities given to me because of UW Astrobiology are unmatched at any other xiii university I ve been from Iceland to Hawaii to the Rio Tinto in Spain thanks to the AB program Woody Sullivan told us that when we left this program we would be able to a sit through and comprehend any seminar related to astrobiology from microbiology all the way to astrophysics and b that we would have a unique perspective and look at planetary problems in a whole new way Well he was right and only a program like this could have accomplished that Additionally I have to specifically call out Victoria Meadows for being our fearless director Thank you Vikki for guiding this program and creating an environment that we the graduate students could really take ownership of You ve treated us as colleagues rather than students and we will remember that when we are mentors to future students Special shout out to my FELDSPAR Iceland colleagues We were a rag-tag group of early-career scientists who just wouldn t quit Thank you for the wonderful science and most importantly all the laughs Thank you to all my friends I ve made over the years at UW and in Seattle We have had a lot of fun and I will miss the community that we have built I d especially like to thank Topher French and Marty McFly for the nonstop adventures love and kindness I cannot wait to see what California has in store for us in particular sunshine and burritos Last but certainly not least thank you to my incredible family Thank you to my beautiful sister Sarah for jaws being incredibly patient with me always letting me talk first and last and always being there for me when I need you Thank you to my intelligent mother Bego a for teaching me to be tough and stand my ground how to manage a budget and always being available to talk on the phone when I m waiting at a bus-stop Thank you to my inspiring father Arthur for teaching me about the Universe The three of you have encouraged and supported me my entire life and we ve been mostly laughing the whole way xiv DEDICATION To my sister Sarah and my parents Bego a and Arthur xv 16 Chapter 1 INTRODUCTION 1 1 ORGANIZATION OF DISSERTATION This introductory chapter contains a brief overview of the motivation for my dissertation work Chapters 2 through 4 of the dissertation have been written as stand-alone papers as such each chapter contains a detailed introduction with a thorough literature review The second chapter Elevated bulk-silica exposures and evidence for multiple aqueous alteration episodes in Nili Fossae Mars was published in the journal Icarus in the spring of 2016 The third chapter The Lost City Hydrothermal Field: A spectroscopic and astrobiological analog for Nili Fossae Mars was submitted to the journal Astrobiology in October 2016 and was returned with minor revisions in December 2016 and a revised manuscript will be submitted to the editor in February 2017 The fourth chapter A search for minerals associated with serpentinization across Mars using CRISM spectral data will be submitted to the journal Icarus during Winter Quarter 2017 A bibliography of all references within all chapters can be found at the end of the dissertation 1 2 MOTIVATION One of the main motivations driving planetary exploration today is to understand the range of geologic and geochemical environments found across our Solar System throughout its history The underlying questions behind this motivation are: Under which geologic conditions did life evolve on Earth Did other planetary bodies experience similar geologic constraints And ultimately could or did life ever arise outside of the Earth Scientific attention has been particularly placed on constraining the evolution of Mars for several reasons including its similarity in geologic features to Earth its strong evidence for past surface liquid water e g Poulet et al 2005 Hynek et al 2010 and its proximity to the Earth aiding in the timely exploration and turn-around time between exploration missions 17 Geomorphic and mineralogical observations of the martian surface over the last several decades have taught scientists that Mars has undergone a series of transient or potentially sustained periods of surface and near-surface liquid water e g Ehlmann and Edwards 2014 And though as a whole the martian surface is primarily composed of unaltered basalt it is becoming clear from the increasing return of data from planetary exploration missions that at the regional and local scale the martian surface can have a wide range of primary and secondary alteration minerals Ehlmann and Edwards 2014 implying more sustained and localized aqueous environments These sites that show evidence for sustained aqueous alteration are compelling for the study of astrobiology as they may preserve evidence for putative martian life or conversely they may provide important clues for why life may not have formed on Mars The study of martian surface mineralogy and rock composition can be extremely powerful tools for understanding the environmental geochemical and global conditions on Mars as many minerals are diagnostic of specific conditions Even more illuminating is the variation of mineralogical alteration suites across the planet and their association to the surrounding unaltered source rock The ability to place the alteration products in the context of bulk surface composition is a powerful means of constraining the duration intensity and type of aqueous alteration of the surface and subsurface while revealing specific chemical pathways available as an energy source for potential microbial life in Mars past This dissertation work focused on studying Mars from the perspective of surface composition and mineralogy specifically as it related to habitability The work was predominantly concentrated in the Nili Fossae region of Mars an area that has been studied extensively because of its unique and rich mineralogical diversity detailed description of the geologic setting in Section 2 1 1 However the work presented here used newly applied data analysis techniques and 18 viewed the region through the lens of terrestrial sites of astrobiological importance Additionally this work sought to use what was learned about the past habitability and mineralogy in Nili Fossae to better understand the potential for similar sites across the planet Finally a major component of each chapter presented in this dissertation was using acquired spectroscopic measurements of either Mars or terrestrial field samples in new and often more comprehensive ways This allowed the problem or question being asked to be approached in a different way often more completely In Chapter 2 we created weighted absorption center index maps from thermal-infrared THEMIS Thermal Emission Imaging System multispectral data to visually display the relative bulk-silica content across the Nili Fossae By doing this we could identify elevated bulk-silica units that would have otherwise gone undetected using traditional analysis techniques In this chapter we also systematically compared thermal- and near-infrared spectroscopic datasets that provide complementary but different information about the surface Similarly by using the two datasets collaboratively we could make mineralogical interpretations that would have been missed by any one dataset use alone In Chapter 3 we measured the thermal-infrared emissivity and near-infrared reflectance of terrestrial rock samples from a serpentinizing system These specific measurement techniques were used to not only assess the mineralogical composition and variability found in these samples but to do so with techniques comparable to those on past current and future spacecraft Lastly in Chapter 4 we applied factor analysis and target transformation techniques to CRISM Compact Reconnaissance Imaging Spectrometer for Mars near-infrared spectral data to search for spectral evidence for serpentinization across Mars This approach allowed us to look through 10 000 CRISM images in a timely and quantitative manner and search for the subtle and weak spectral absorptions associated with serpentine that can be missed with traditional analysis techniques 19 Chapter 2 ELEVATED BULK-SILICA EXPOSURES AND EVIDENCE FOR MULTIPLE AQUEOUS ALTERATION EPISODES IN NILI FOSSAE MARS Originally published in the journal Icarus Elena S Amador and Joshua L Bandfield 2016 Elevated bulk-silica exposures and evidence for multiple episodes of aqueous alteration in Nili Fossae Mars Icarus 276 39-51 doi:10 1016 j icarus 2016 04 015 2 1 INTRODUCTION Spectrometers on orbital spacecraft around Mars inform our understanding of the mineral composition of the upper few microns to tens of microns of the martian surface This mineralogy provides a record of the geochemical conditions present during the time of formation and allows past environmental conditions to be ascertained especially when local mineralogies are investigated with respect to regional compositions and geologic context Orbital spectroscopy has been used extensively to identify regional surface mineralogy on Mars and given that specific wavelength regions are sensitive to different phases a combined analysis can lead to a more comprehensive view of the surface This study focuses predominately on spectral data acquired by the 2001 Mars Odyssey Thermal Emission Imaging System THEMIS Christensen et al 2004 and the Compact Reconnaissance Imaging Spectrometer for Mars CRISM Murchie et al 2007 on the Mars Reconnaissance Orbiter MRO The combined wavelength coverage from CRISM and THEMIS allows for the characterization of both bulk surface compositions and the identification of secondary alteration products 20 This study has two goals: 1 To introduce a detailed and systematic approach to analyzing near-infrared CRISM and thermalinfrared THEMIS spectral datasets in a complementary fashion including the applicability of using a new index map the weighted absorption center as a tool for the reconnaissance of THEMIS images with elevated bulk-silica compositions We use Nili Fossae as the test locale for this approach given its high mineralogical diversity 2 To document the presence of elevated bulk-silica exposures in the Nili Fossae region These newly observed exposures are associated with local olivine-rich basalts and phyllosilicate-bearing basalts but are not spatially co-located with either unit The units likely represent a period of aqueous activity in Nili Fossae separate from that which formed the previously identified phyllosilicates 2 1 1 Geologic Setting The Nili Fossae are a set of concentric graben surrounding the north-west rim of the Isidis impact basin Schultz and Frey 1990 and likely formed due to mass unloading and flexure associated with the Isidis impact event that occurred approximately 4 Ga Wichman and Schultz 1989 Figure 2 1 Apart from the early Hesperian-aged flood basalts from Syrtis Major that inundate the floor of the Nili Fossae trough Hiesinger and Head 2004 the fossae provide a rare glimpse into Mars geologic and geochemical past with extensive exposures of Noachian crustal materials The fractures themselves local impact craters as well as the relatively low dust cover Ruff and Christensen 2002 reveal compositionally heterogeneous exposures that can be spatially resolved from orbit The diverse surface compositions and alteration products found in Nili Fossae imply unique igneous activity during the region s history in addition to multiple phases of aqueous alteration e g Hoefen et al 2003 Hamilton and Christensen 2005 Poulet et al 2005 Bibring et al 2006 Mangold et al 2007 Mustard et al 2007 2009 Ehlmann et al 2008 2009 21 2010 Tornabene et al 2008 Brown et al 2010 Viviano et al 2013 Edwards and Ehlmann 2015 The basement rock in the region is described as a massive to brecciated basalt with localized signatures of Fe Mg-smectite likely due to subsurface aqueous alteration prior to the Isidis impact event e g Poulet et al 2005 Bibring et al 2006 Mangold et al 2007 Mustard et al 2007 Ehlmann et al 2009 Alternatively the Fe Mg-smectites may have formed syn- postIsidis impact from ground water circulation Viviano et al 2013 An olivine-rich basalt unit is primarily exposed in the eastern portion of the Nili Fossae troughs stratigraphically above the Figure 2 1 Nilo-Syrtis Major colorized elevation map with THEMIS Global Day IR mosaic used for shading Solid white box indicates initial THEMIS image search area Dashed white box indicates area covered by Figure 2 10 Image is centered around 77 02 E and 21 86 N 22 Noachian basement unit Hoefen et al 2003 Hamilton and Christensen 2005 Mustard et al 2007 Tornabene et al 2008 Quantitative deconvolution analyses of emission spectra from the Mars Global Surveyor MGS Thermal Emission Spectrometer TES have shown that this basalt contains between 20 and 30 wt% olivine with olivine compositions ranging from Fo68-75 Hamilton and Christensen 2005 Koeppen and Hamilton 2008 Edwards and Ehlmann 2015 The olivinerich unit appears to drape pre-existing topography and may have formed as a post-Isidis impact melt sheet Mustard et al 2009 or post-Isidis volcanic lava flows Hamilton and Christensen 2005 Tornabene et al 2008 Isolated locations of the olivine-rich basalt have subsequently been variably altered to Fe Mg-carbonates Ehlmann et al 2008 2009 Edwards and Ehlmann 2015 Mg-serpentine Ehlmann et al 2009 2010 and talc and or saponite Brown et al 2010 Viviano et al 2013 The presence of these mineral phases has been attributed to localized hydrothermal alteration of both the underlying Fe Mg-smectites and the olivine-bearing basalt during the emplacement of Hesperian aged lava flows e g Viviano et al 2013 Both the northeastern and northwestern portions of Nili Fossae are capped by an olivinepoor basalt e g Tornabene et al 2008 Mustard et al 2009 The source of this basalt is still debated though Mustard et al 2009 hypothesize that it may represent the upper less dense portion of the impact melt sheet that formed the olivine-rich basalt unit More recently Edwards and Ehlmann 2015 proposed that the capping unit may be an eroded volcanic ash based on Hapke modeling of single scattering albedo from CRISM data and low thermal-inertia values derived from THEMIS observations in addition to observed composition and morphology This is similar to work presented by Bandfield et al 2013a who argued that much of Mars older surfaces are composed of relatively friable volcanic ash of a basaltic composition The region also shows evidence for reworking by late Noachian early Hesperian fluvial activity based on the presence of 23 channel networks e g Ehlmann et al 2009 The fluvial activity likely led to the transport and re-emplacement of Fe Mg-smectites into fan deposits e g Ehlmann et al 2009 2 2 DATA AND METHODS To determine the surface composition of exposures of interest in Nili Fossae we incorporated both near-infrared NIR defined here as 1 0 3 0 m and thermal-infrared TIR 5 0 50 0 m spectral datasets that provide highly complementary information based on their specific sensitivities When present as coarse particulates TIR spectral measurements are sensitive to the major phases present and the bulk-rock compositions e g Thomson and Salisbury 1993 Ramsey and Christensen 1998 Smith et al 2013 NIR spectral measurements are sensitive to hydrated and Fe-bearing phases e g Hunt 1977 This property allows for the detection of specific phases even when present only as minor constituents although it can be difficult to retrieve quantitative mineral abundance information from the NIR spectra e g Hunt 1977 Indepth examination of both NIR and TIR wavelength regions can reveal details that might be otherwise missed by the investigation of either dataset alone Here we present an updated TIR data analysis technique and a new approach to comparing the two wavelength regions in a complementary fashion 2 2 1 Thermal Emission Imaging System THEMIS THEMIS multispectral thermal-infrared data can be used to understand the bulk mineralogy of martian surfaces e g Huang et al 2013 Edwards and Ehlmann 2015 We applied several analysis techniques to the THEMIS data Decorrelation stretch image products were first used as a preliminary survey tool to obtain a broad understanding of the variability in rock composition within the region e g Bandfield et al 2004a Similarly colorized index images mapping the weighted absorption center WAC or center of gravity e g Smith et al 2013 of THEMIS emissivity spectra were produced and used to infer the variability in bulk-silica 24 abundance Smith et al 2013 Based on the regions of interest identified from the broad survey products a more detailed analysis of emissivity spectra from individual locations was conducted using the atmospherically corrected images 2 2 1 1 Introduction to data and atmospheric corrections THEMIS is a multi-spectral visible near-infrared and thermal-infrared imager on the 2001 Mars Odyssey spacecraft The imager has 10 thermal-infrared spectral channels spaced between 6 5 and 15 m Table 2 1 with a spatial sampling of 100 meters pixel and a swath width of 32 km collected from the orbital height of 420 km The thermal-infrared component of THEMIS consists of an uncooled 320 by 240 element microbolometer array that produces calibrated radiance images using an internal calibration flag and instrument response functions determined from pre-launch data Further description regarding calibration and data processing procedures and errors are detailed by Bandfield et al 2004b Christensen et al 2004 and Edwards et al 2011 For this study only THEMIS day-time infrared images with average surface temperatures of greater than 250 K and water-ice and dust opacities of less than 0 15 were examined THEMIS data were corrected for atmospheric effects using the techniques described by Bandfield et al 2004b Briefly this correction is performed in two steps: First a spectrally uniform region with a range of surface temperatures e g shaded and sunlit slopes is isolated in the THEMIS image This set of spectra is then used to isolate and remove the additive contributions of atmospheric emission and scattering Second surface emissivity derived from Thermal Emission Spectrometer TES data coincident with a portion of the THEMIS image is isolated the surface emissivity from this area is then used to provide the multiplicative contributions for atmospheric attenuation in each THEMIS spectral band The multiplicative terms are then applied pixel by pixel at the full spatial resolution of THEMIS to retrieve atmospherically corrected 25 emissivity spectra across the full THEMIS image Bandfield et al 2004b This method assumes that the atmosphere is constant across the THEMIS scene which is generally the case in images with small variations in elevation and low water-ice opacity For this study elevation varies by up to 1 8 km over the surfaces analyzed Assuming an atmospheric scale height of 12 km and wellmixed atmospheric dust this results in a maximum 9 m opacity difference of 250K and dust and water-ice opacities 250 C with brucite when rates of MgFe diffusion in olivine are orders of magnitude faster than in the low-temperature systems such as in mantle fore-arc wedges Evans 2004 2010 These increased reaction rates limit the amount of magnetite and H2 produced Evans 2004 We observe modeled antigorite in several serpentinite spectral types in the Lost City samples however they are never the predominant serpentine polymorph and this lack of antigorite has been described by others who have studied these rocks previously e g Fr h-Green et al 2004 Additionally it is common to observe naturallyoccurring inter-growths of all three polymorphs Rinaudo et al 2003 89 3 4 1 3 Observed Phases Compared to Theoretical Serpentinization Reactions Our deconvolution results of TIR emissivity measurements are generally in agreement with expected mineral phases from theoretical serpentinization reactions Reactions 1-3 However notably missing from our derived mineralogy are brucite Mg-hydroxide and magnetite Feoxide Both phases were included in our end-member spectral library but neither was modeled in the deconvolution results There are several reasons why those phases might not be reflected in the modeled mineralogy Magnetite has high emissivity values in the thermal-infrared with shallow absorptions near 600 and 300 cm-1 As such it is difficult to detect magnetite using this technique Conversely brucite has distinct spectral absorptions in the thermal-infrared however brucite is typically described in previous studies as being found within the carbonate-bearing rocks Ludwig et al 2006 but we were unable to use the deconvolution model to determine mineral abundances for these samples due to textural effects Brucite has been shown to be present within those samples from past studies Ludwig et al 2006 and its presence as detected by others is consistent with the generalized serpentinization reactions Reaction 3 Deconvolution models of the Lost City rock samples indicate significant amounts of talc Though not a direct product of serpentinization talc-rich rocks are commonly found in association with serpentinites and have been shown to be present within the Lost City rock assemblages e g Fr h-Green et al 2004 On Earth the most abundant occurrence of talc is in metamorphosed ultramafic rocks such as those at the Lost City Evans and Guggenheim 1988 Talc is expected to form as a product of the alteration of serpentine by dissolved silica e g Moore and Rymer 2007 and tends to breakdown at 800 C Evans and Guggenheim 1988 90 3 4 1 4 Near-infrared Spectral Ambiguity A notable difference between the near- and thermal-infrared measurements is their ability to distinguish between the different rock types and the spectral variability within a given rock type For example the serpentinite rock types show five different spectral types in the thermalinfrared Figure 3 5 all consistent with a serpentine-rich rock but with notable variability The five serpentinite rocks measured in the near-infrared have consistent spectral absorptions with limited variability Figure 3 6 The three Mg-serpentine polymorphs that make up the serpentinite rocks are distinguishable and identifiable in the thermal-infrared but are spectrally ambiguous in the near-infrared portion of the spectrum This indicates the importance of having both measurements to properly characterize the suite of minerals within this set of samples Similarly the talc-rich fault rock amphibole-rich fault rock and the gabbro have nearly identical spectral characteristics in the near-infrared portion of the spectrum Talc and amphibole are known to contain similar deep spectral absorptions in the near-infrared portion of the spectrum Figure 3 7 In the case of the gabbro the observed absorptions are likely due to the 35 vol% amphibole and serpentine phases modeled in the rock composition Supplementary Table 5 17 The thermal-infrared emissivity measurements were used to determine the specific composition for these three rock types and the near-infrared measurements indicate the presence of H2O OH- and OH- stretch and Mg-OH- bending modes e g in Mg-phyllosilicates or from hydroxyl in amphiboles 3 4 2 Mars Observations 3 4 2 1 Compositions as Described by CRISM As presented by past studies the mineral assemblages observed in Nili Fossae are consistent with low-temperature hydrothermal alteration of an ultramafic protolith e g Viviano et al 2013 In particular the spectral detection of phases consistent with serpentine and magnesite 91 are unambiguous and clearly indicate their presence within the rock record in Nili Fossae The detection of a phase with absorptions at 1 4 1 9 2 3 and 2 4 m Figure 3 9 and Figure 3 10 has been attributed to the Mg-rich smectite saponite e g Ehlmann et al 2009 Brown et al 2010 and to talc e g Brown et al 2010 Viviano et al 2013 As we have shown in earlier sections talc saponite hydroxylated hydrated amphibole are spectrally ambiguous in the near-infrared portion of the spectrum Figure 3 7 Viviano et al 2013 argue that talc and saponite are not spectrally ambiguous and that it is possible to differentiate the two phases based on the shape and spectral contrast of the 2 3 2 4 m absorptions and they argue that the surfaces in question in Nili Fossae are talc-bearing Viviano et al 2013 also argue that the presence of talc is consistent within the greater mineralogical context of the region in that it can form through the carbonation of serpentine to form talc and magnesite e g Viviano et al 2013 Despite this spectral conundrum the spectral ambiguities observed in Nili Fossae are like those we observe in the Lost City rocks Mg-rich saponite typically forms via the hydrothermal alteration of basalt Evans and Guggenheim 1988 Given that there is abundant olivine-poor basalt in the Nili Fossae region e g Amador and Bandfield 2016 within the same stratigraphic column as the observed talc saponite exposures it is possible that saponite formation could occur In addition talc and saponite have been shown to grow within mixed-layered structures at submarine hydrothermal sites on Earth Cuadros et al 2008 Michalski et al 2015 making their spectral disambiguation even more difficult and showing that the two phases do form together Similarly we have shown with our Lost City rock samples that talc and saponite can both be significant constituents of rocks that form in serpentinizing systems as is the case with the talcrich fault rock Supplementary Table 5 17 So while the distinction of whether this spectral signature in Nili Fossae is due to talc or saponite has specific implications for the alteration 92 trajectory of these rocks we have shown that these phases are not mutually exclusive and are both well represented within low-temperature serpentinizing systems on Earth Lastly it is important to note that with the CRISM NIR data alone it is not possible to determine if the ambiguous 1 4 1 9 2 3 2 4 m spectral signature is due to amphibole phases like tremolite or actinolite As we have shown with the Lost City rock samples the talc-rich fault rock and amphibole-rich fault rock look nearly identical in near-infrared measurements Amphiboles have been detected in martian meteorites e g Williams et al 2014 and are possibly present on the surface of Mars They are potentially present as spectral mixtures of saponite and hornblende Carter et al 2013 but otherwise have not been discussed extensively in the martian literature In the case of Nili Fossae Viviano et al 2013 note the spectral ambiguity between talc and actinolite but argue that the presence of amphibole within the context of the mineral assemblage observed in the region is unlikely While we agree that talc and or talc saponite are likely at least partially for the ambiguous spectral signature in Nili Fossae given the nearby presence of magnesite it is important to note that amphibole does fit into the common assemblage of minerals formed during serpentinization as shown by the Lost City rock samples 3 4 3 Spectral Differences between Measurements from the Lost City Hydrothermal Field and Nili Fossae Mars There are some clear differences between the spectral characteristics and therefore mineralogy of the Lost City terrestrial rock samples and the surface exposures in Nili Fossae Mars First the Nili Fossae assemblage has abundant olivine still present within the stratigraphic section Interestingly numerous reactants and products of serpentinization-associated reactions are still present The fact that abundant olivine remains unaltered to serpentine or magnesite indicates that the serpentinization reactions in the area never went to completion perhaps indicating a limited period of alteration and or volume of water Comparatively the Lost City 93 serpentinites and associated rocks used for this study no longer show signs of their unaltered protolith and the most mafic rock in the group acquired is a still an extensively altered metagabbro This in-part is likely a sampling bias for the Lost City rock samples as the rocks acquired by the DSV Alvin were most often pulled from surface outcrops However cores drilled from the southern wall of the Atlantis Massif during the 2016 IODP Expedition 357 show evidence for variable serpentinization with depth Fr h-Green et al 2016 Another mineralogical difference between the Lost City rocks and Nili Fossae surface exposures is the presence of different major-metal cations in their respective carbonates The Lost City carbonates are dominated by either Ca-rich calcite or aragonite depending on whether the rock was formed via the accumulation of pelagic material pelagic top-layer rocks dominated by calcite or via the precipitation of aragonite as high-pH hydrothermal fluids encounter seawater carbonates dominated by aragonite though it should be noted that the aragonite-rich chimney rocks revert to calcite over-time Ludwig et al 2006 The Nili Fossae carbonate-bearing exposures are Mg-rich and spectrally consistent with magnesite There are several potential scenarios for the formation of the martian carbonate in Nili Fossae one is via the direct alteration of the Mg-rich olivine in the area by near-surface water Ehlmann et al 2008 Another potential formation mechanism is the carbonation of the serpentine-bearing rocks Viviano et al 2013 This process would not only produce the Mg-rich magnesite but also produce talc which is also observed near the Mg-carbonates in the region The carbonates in Nili Fossae and the Lost City Hydrothermal Field were likely produced and controlled by separate processes The Lost City carbonates used for this study were buffered and controlled by the seawater present at the seafloor ocean-water interface while the carbonates produced in Nili Fossae Mars were likely controlled by the continued subsurface hydrothermal alteration of the bedrock This is one clear 94 example of where the environmental analog between the Lost City and Nili Fossae is not as strong given the evidence currently at hand 3 4 4 Implications for Serpentinization in Nili Fossae Mars 3 4 4 1 Physical Characteristics of Nili Fossae and its Susceptibility to Serpentinization The Nili Fossae region of Mars is only one of several extensive exposures of olivine-rich basalt on the planet e g layers in Valles Marineris Terra Tyrrhena the rim of Argyre Basin Ody et al 2013 However it is the only region that shows spectral evidence for serpentine in association with other mineral phases known to form in a serpentinizing system There are several factors that may have contributed to serpentinization in this area beyond just the necessary olivinerich protolith For example the formation of the Nili Fossae likely occurred in association with the Isidis Basin impact event creating a highly fractured terrain In addition to the large regionalscale fractures that make up the main Nili Fossae troughs the basement phyllosilicate-bearing unit shows abundant local-scale ridges and fractures They are typically hundreds of meters long and tens of meters wide and appear to be the source of the Fe Mg-phyllosilicate spectral signatures Mangold 2007 Mustard 2007 2009 and Ehlmann et al 2009 2010 Work by Saper and Mustard 2013 shows that the orientation of most of the small-scale ridges and fractures line up with the larger orientation of the main Nili Fossae troughs implying that these ridges were emplaced by the same mechanism as the large-scale graben around the same time These local-scale faults fractures and dikes in addition to the regional-scale fossae would have allowed for substantial fluid circulation pathways Additionally there has likely been a longlived heat-source in the region induced by both the Isidis Basin impact event as well as the Syrtis Major volcanic province This early fractured bedrock combined with the olivine-rich protolith would have created an environment suitable for the initiation of serpentinization The 95 serpentinization reactions can be self-sustaining given their exothermic and volume-increasing nature and could produce fresh surface area for continued alteration e g Lowell and Rona 2002 until the protolith olivine is consumed This volume-increasing nature can also seal the rocks from further alteration so a region with a previously fractured lithology makes it particularly prone to sustained serpentinization over time Therefore in addition to the spectral and subsequently the mineralogical evidence for serpentinization occurring in Nili Fossae this region was likely to be uniquely susceptible to these reactions It is important to note however that the extensive remnants of olivine in the region imply that the serpentinization reactions did not go to completion and that water was likely a limiting resource in driving these reactions forward 3 4 4 2 Mineralogical Evidence for Serpentinization The spectra acquired from Nili Fossae are similar to those measurements acquired from rocks collected at the Lost City Hydrothermal Field As noted by McSween et al 2015 rather than looking for a single mineral that might be a smoking gun for a particular geochemical environment the search for specific mineralogical assemblages can provide greater constraints on the environment in question and narrow the search for once habitable environments Furthermore the observation of a suite of minerals indicative of a formation environment provides greater confidence that the environment was indeed present Reliance on the detection of a singular spectral signature indicative of just one mineral phase is not as robust a result since the interpretation can be more easily confounded by spectral ambiguities and data artifacts At both the Lost City Hydrothermal Field and the Nili Fossae analyses conducted in this study document Mg-serpentine phases carbonate-phases and talc saponite and or amphibole Additionally in Nili Fossae abundant olivine has been documented a necessary reactant for the serpentinization process as well as a geologic setting described in the Section 3 4 4 1 that would 96 favor the transport and circulation of hydrothermal fluids Apart from serpentine the other phases documented in Nili Fossae could form under non-serpentinizing conditions For example the Mgcarbonate could be the direct product of near-surface aqueous alteration of the olivine-rich basalt Similarly saponite can form via the hydrothermal alteration of olivine-poor basalt However the presence of all these phases together within the same stratigraphic unit and at times within the same CRISM image likely implies a connected geochemical story This appears most consistent with sustained hydrothermal alteration of an olivine-rich protolith in the eastern portions of the Nili Fossae This alteration triggered serpentinization at the subsurface interface between the olivine-rich basalt and underlying olivine-poor phyllosilicate-bearing basalt The serpentineenriched bedrock was subsequently altered by carbonation to talc and magnesite consistent with their co-spatial occurrence across the eastern region of the Nili Fossae An important consideration is the timing of the serpentinization reactions The alteration must have occurred after the emplacement of the olivine-rich basalt unit approximately 4 Ga Wichman and Schultz 1989 According to the model put forward by Viviano et al 2013 the suite of alteration minerals that we have described here likely formed prior to the emplacement of the Hesperian-aged Syrtis lava flows approximately 3 7 Ga The altered olivine-rich unit has subsequently been eroded by episodic aqueous processes evidenced by channel networks that cut through the Hesperian-aged lava flows and atmospherically-driven processes e g dunes and dust abrasion exposing the suite of alteration minerals today 3 4 4 3 Implications for Habitability of Nili Fossae We have shown that the spectral signatures and mineralogical suites present at the Lost City Hydrothermal Field on Earth are similar to those documented in the Nili Fossae region of Mars This suite of minerals is unique to serpentinization where the reduction of H2O in the 2 presence of Fe 97 generates H2 Molecular hydrogen is particularly interesting from an astrobiological standpoint because it is a strong electron donor that can drive the synthesis of organic molecules in Fischer-Tropsch-type reactions e g Holm and Charlou 2001 McCollom and Seewald 2007 Organic compounds such as various hydrocarbons formate and acetate are present at elevated concentrations in Lost City fluids Proskurowski et al 2008 Lang et al 2010 The abiotic production of organic compounds is significant because they can be used as precursors to important biological polymers and hydrothermal chimneys such as those at Lost City can act as efficient incubators and reaction vessels St eken et al 2013 Kreysing et al 2015 Furthermore H2 is directly used as an electron donor in the metabolism of many chemoautotrophic organisms e g Nealson et al 2005 Schulte et al 2006 St eken et al 2013 For example methanogens which are abundant in Lost City chimneys Schrenk et al 2004 Brazelton et al 2011 use H2 to fix CO2 and produce CH4 and H2O This pathway is thought to be one of the most ancient metabolic strategies Fuchs 2011 and the catalytic cores of enzymes in this pathway resemble minerals found in hydrothermal systems Russell and Martin 2004 These minerals can catalyze some steps of carbon fixation on their own without the scaffolding provided by enzymes suggesting potential links to prebiotic chemistry Cody 2004 St eken et al 2013 Many of the key pieces necessary for life are produced in rock-hosted serpentinizing systems: liquid water energy source reducing power and abiotically-produced hydrocarbons Given the evidence for serpentinization in Nili Fossae it is possible to say that it could have had a habitable subsurface environment present at some point in its history Additionally the fractured nature of the Nili Fossae terrain would have provided local-scale faults and fractures for alteration fluids to concentrate These fluids would likely have been enriched in H2 and low-order organics 98 similar to fluids currently venting from chimneys at the Lost City Hydrothermal Field on Earth The remnants of these fractures and faults would be compelling places to search for potential biosignatures from any hypothetical life that may have been present in the past or simply to better understand the range of abiotically produced organic compounds on Mars It should be acknowledged that it is known that serpentine can form without the production of H2 Reactions 2 and 3 however in a natural setting with non-endmember olivine compositions i e fayalite versus forsterite it is unlikely that only Reactions 2 and 3 would occur without Reaction 1 In particular given the known olivine composition in Nili Fossae Fo68-75 Hoefen et al 2003 Hamilton and Christensen 2005 Koeppen and Hamilton 2008 Edwards and Ehlmann 2015 we expect Reactions 1-3 to take place In order to confirm the occurrence of H2 production during serpentinization future studies should search for the presence of magnetite or other Fe3 phases e g Fe3 -bearing brucite in association with the serpentine as these cannot be detected from current orbital datasets For many geological chemical physical and biological reasons serpentinite-hosted hydrothermal vent systems have been discussed as compelling environments for key steps in the origin of life on Earth before 3 5 Ga e g Russell et al 2010 2014 St eken et al 2013 Sojo et al 2016 The results of this study provide further evidence that similar geochemical systems would have been active on Mars during the same period in our Solar System s evolution 3 5 CONCLUSIONS This work draws mineralogical and geochemical parallels between the Lost City Hydrothermal Field on Earth and the Nili Fossae region on Mars There is abundant evidence for active serpentinization to have occurred in the Nili Fossae region during an important period on our own planet Although it is not possible to determine if life inhabited serpentinizing systems on 99 Mars from the remote sensing data alone habitable environments induced by geochemical processes initiated by abundant geologic constituents were present There are several major geological and geochemical differences between the Lost City and Nili Fossae For example the initial fluid compositions were likely quite different additionally the Lost City Hydrothermal Field is located beneath 800 meters of seawater and 15 km away from a slow-spreading oceanic ridge whereas the serpentinization occurring at Nili Fossae would likely have taken place in the subsurface with a likely limited source of water Regardless the fact that serpentinization reactions require such readily available starting materials and produce biologically accessible byproducts are what make them so compelling as a process for astrobiological study The presence of serpentine in Nili Fossae indicates that fluid-rock reactions took place likely implying that H2 and abiotically-produced organic compounds were produced in the subsurface As such the Nili Fossae specifically where we see the local grouping of the mineralogical suite presented here is a compelling site to search for the evidence of past life on Mars Equally compelling is the opportunity to study a site that parallels in geochemistry and time sites on Earth that likely led to the origin of life Whether or not life inhabited these sites on Mars would have major implications for how and why life evolved on our own planet 100 Chapter 4 A SEARCH FOR MINERALS ASSOCIATED WITH SERPENTINIZATION ACROSS MARS USING CRISM SPECTRAL DATA This chapter is in-preparation for submission to the journal Icarus Co-authored by: Elena S Amador Joshua L Bandfield Nancy H Thomas 4 1 INTRODUCTION Much of Mars research is driven by the search for past habitable environments Research has moved beyond simply follow the water but now is also driven by follow the energy follow the organics and follow the geochemical system Environments prone to serpentinization are of interest because they imply the presence of several of the key elements for life as we know it: liquid water metabolic energy source H2 and abiotic means of forming organics like CH4 through fischer-tropsch type reactions e g Kelley et al 2001 2005 Fr hGreen et al 2004 Russell et al 2010 These reactions are also often discussed and considered relevant for origin-of-life hypotheses for life on Earth Russell et al 2010 2014 St eken et al 2013 Sojo et al 2016 Low- temperature serpentinization reactions on Earth produce a specific suite of minerals providing evidence for the reactions occurrences These reactions result in the presence of serpentine carbonate talc saponite and amphibole e g Frost and Beard 2007 Additionally this suite of minerals can be detected from orbit if they are exposed at the surface due to diagnostic absorptions in the near- and thermal-infrared wavelength regions Figure 4 1 e g Amador et al in revision Chapter 3 Serpentine has been identified in several locations across Mars and much work has gone into specifically describing its occurrence particularly in Nili Fossae Ehlmann et al 2009 2010 Brown et al 2010 Viviano et al 2013 Amador et al in revision Chapter 3 101 The observed serpentine within olivine-rich basaltic exposures in Nili Fossae are associated with both Mg-carbonate and talc saponite phases that likely indicate a sustained low-temperature serpentinizing system making it a compelling site for detailed study by future landed missions to search for potential biosignatures We would like to understand if sites like Nili Fossae are common on Mars and if there are other sites on the planet that once similarly contained these types of habitable environments that could be studied in detail Because serpentinization reactions are favored in environments that are enriched in olivine we might expect to find additional evidence for serpentinization in other regions that are enriched in olivine on Mars like Nili Fossae Initial surveys across Mars have indicated limited exposures of serpentine Ehlmann et al 2010 we hypothesize that its paucity may be due to several factors: First the minor 2 12 m spectral absorption Figure 4 1 that is unique to serpentine can be difficult to detect potentially obscuring our ability to detect its presence with the available remote sensing data Additionally any serpentine that may be exposed on the surface may be occurring in low concentrations or small exposures again precluding our ability to detect the serpentine from orbit Lastly the paucity of observed serpentine may simply be because serpentinization may not have been common on Mars 102 Figure 4 1 Near-infrared reflectance library spectra for minerals associated with serpentinization reactions See Supplementary Table 5 20 for references 103 To gain a comprehensive understanding of the exposures of serpentine across the planet especially in the context of past habitable environments suitable for future exploration we conducted a survey of all Compact Reconnaissance Imaging Spectrometer for Mars CRISM data products between 70 N and 70 S in search for spectral evidence for serpentine We targeted all hyperspectral CRISM image products in regions with elevated abundances of olivine additionally we surveyed a representative sample of the remaining global full-resolution targeted data products outside those targeted regions To look through thousands of images in a timely manner we used semi-automated factor analysis and target transformation techniques Bandfield et al 2000 Thomas and Bandfield 2013 Thomas and Bandfield 2016 in revision to rapidly and quantitatively determine which CRISM images were likely to contain serpentine Mg-carbonate and talc saponite as dominant spectral contributors These techniques are particularly helpful when searching for phases such as serpentine that have subtle spectral absorptions or are widely distributed at low concentrations This study provides a more complete understanding of the spatial distribution of serpentine across the globe and places this distribution into the geologic context in which we observe the phases This constrains the sites on Mars with the highest potential for once containing habitable environments accessible to future landed missions with relevance to astrobiology This study also serves as an example application to provide a more thorough understanding of the strengths and weaknesses of using factor analysis and target transformation for informing global spectroscopic studies 104 4 2 4 2 1 BACKGROUND Serpentinization and its Astrobiological Implications Serpentinization is a geochemical process in which olivine is hydrated to form serpentine magnetite and brucite The oxidation of Fe2 in fayalite Fe-endmember of olivine solid-solution series leads to the production of H2 and can be metabolically exploited by microbial life Additionally H2 is a strong electron donor that can drive the synthesis of organic molecules in Fischer-Tropsch-type reactions e g Holm and Charlou 2001 McCollom and Seewald 2007 Serpentinization is common on Earth in locations where olivine-enriched bedrock is in contact with liquid water typically in tectonically active margins such as at slow-spreading centers e g Lost City Hydrothermal Field off-axis to the Mid-Atlantic Ridge Kelley et al 2001 and obducted ocean-floor sequences e g the Asbestos Ophiolite Complex Greenberger et al 2015 Dense microbial communities have been shown to live in zones of active serpentinization surviving on the products of these reactions in the absence of other energetic inputs like solar or volcanic As an example H2 can be directly used as an electron donor in the metabolism of many chemoautotrophic organisms like the methanogens at the Lost City Hydrothermal Field that use H2 to fix CO2 and produce CH4 and H2O Kelley et al 2001 2005 Furthermore the chemistry and mineralogy that exists in these settings suggest potential links to prebiotic chemistry Cody 2004 St eken et al 2013 and are often discussed as compelling environments for key steps in the origin of life on Earth e g Russell et al 2010 2014 St eken et al 2013 Sojo et al 2016 Because serpentine forms in this setting and typically results in the release of bio-accessible H2 it is considered a unique environmental indicator mineral In this sense the identification of serpentine particularity when found in-situ indicates that serpentinization occurred and that H2 as well as short-chained organics were likely released 105 4 2 2 Identifying serpentine from remote sensing datasets In addition to being an indicator mineral for a specific environment serpentine can also be uniquely identified using readily available remote sensing data such as CRISM on the Mars Reconnaissance Orbiter MRO Near-infrared defined here as 1 0-3 0 m reflectance spectra of serpentine contains a set of five absorptions Figure 4 1 Absorptions near 1 4 and 1 9 m are due to structurally-bound or adsorbed OH- and H2O and are common in hydrated phases e g phyllosilicates Several longer wavelength absorptions are more diagnostic of serpentine: a unique 2 10-2 12 m absorption associated with a sharp asymmetric 2 35 m Mg-OH combination band and a 2 52 m symmetric absorption The presence of the relatively shallow 2 12 m absorption is necessary to confidently identify the presence of serpentine in reflectance spectra as the other absorptions can be found in other hydrated silicate and carbonate phases for example 4 2 3 Serpentine on Mars Ehlmann et al 2009 first described the occurrence of serpentine on Mars in the Nili Fossae region using near-infrared reflectance spectra of the surface collected by CRISM A subsequent study described the global occurrences of serpentine Ehlmann et al 2010 with the data available at the time Ehlmann et al 2010 found that the serpentine observations could be broken down into three geologic settings: 1 m lange terrain 2 southern highland craters 3 Noachian bedrock in stratigraphic section but in general identifications of serpentine were still quite rare across the globe Serpentine exposures outside of Nili Fossae have been identified in several locations across the martian southern highlands These locations include Mawrth Valles Claritas Rise near Baetis Chaos Ehlmann et al 2010 and along the Thaumasia Highlands Viviano-Beck et al 2017 Ehlmann et al 2010 also report additional probable serpentine detections across the southern highlands but given the subtle nature of the diagnostic 2 12 m reflectance absorption it is not 106 clear how reliable these probable detections may be Most of these detections apart from detections made within stratigraphic section likely represent serpentine that did not form in-situ because they are typically associated with impact ejecta e g Chia Crater Ehlmann et al 2010 or in knobby terrain with a diverse range of associated minerals that are inconsistent with any one specific formation environment e g Claritas Rise Ehlmann et al 2010 In other words these phases have now been exposed but likely formed elsewhere either below the surface or more distally and subsequently transported and buried The identification of these occurrences is interesting in that they help confirm the idea that serpentinization is a favorable process on a basaltic planet with likely increasing concentration of olivine at depth However given that they are not found in-place the lack of geologic context makes it difficult to further our understanding of habitable environments on Mars In contrast the identification of serpentine within a well-defined stratigraphic section is particularly interesting because it likely implies that the observed serpentine formed in-situ making that site a compelling place to search for biosignatures or biomarkers For example the serpentine-bearing rocks in Nili Fossae are found within a well-defined olivine-rich basaltic unit with variable concentrations of Mg-carbonate and talc and or saponite e g Amador et al in revision Chapter 3 This olivine-rich unit is of particular interest for serpentinization as both the spectral signatures and the mineralogy observed are consistent with Earth-based sampled from lowtemperature serpentinization environments Amador et al 2016 in revision Chapter 3 It is the observation of this mineralogical suite that makes this site most compelling for in-situ lowtemperature serpentinization and its implications for habitability Rather than the observation of a single mineral e g serpentine that might be a smoking gun for a geochemical environment 107 the observation of this specific mineralogical suite provides greater constraints on the environment and confidence indeed once present 4 3 4 3 1 DATA AND METHODS Approach To gain a more comprehensive understanding for the distribution of serpentine and the serpentinization mineral suite serpentine carbonate talc saponite on Mars and whether they are related to olivine-enriched regions it was necessary to survey a globally representative number of images As of July 2016 there were 13 460 Full Resolution Targeted FRT Full Resolution Short FRS Half Resolution Long HRL and Half Resolution Short HRS CRISM images between 70 N and 70 S available at NASA s Planetary Data System PDS archive Traditional CRISM data analysis techniques involve visual inspection of band depth parameter maps that highlight spectral absorptions and slopes that are indicative of phases of interest and manual analysis of I F equivalent to reflectance ratioed spectra This is a time-consuming process that can take minutes to hours of analysis time for a given image To systematically examine a representative number of CRISM images in a timely manner factor analysis and target transformation techniques were employed to quantitatively describe each image Section 4 3 3 Thomas and Bandfield 2014 Thomas and Bandfield 2016 in revision The CRISM dataset was first separated into seven regions Table 4 4 Five of these include olivine-rich regions: Northern Argyre Nili Fossae Terra Sirenum Tyrhenna Terra Southern Isidis and Valles Marineris e g Ody et al 2013 Claritas Rise was chosen as the sixth regional dataset as this is where Ehlmann et al 2010 found the best spectral example for serpentine to date the seventh region represents all the remaining CRISM images bounded by 70 N and 70 S and exclusive of these six regions 108 Table 4 4 Regions of Interest Region Northern Argyre Claritas Rise Nili Fossae Terra Sirenum Tyrhenna Terra S Isidis Valles Marineris Remaining Latitude Range N -20 to -48 -25 to -42 30 to 15 -20 to -40 8 to -35 Longitude Range E 300 to 336 246 to 264 72 to 80 150 to 207 50 to 107 Number of Images 463 122 229 558 1 306 Images Analyzed 463 122 229 558 1 306 1 to -14 70 to -70 256 to 320 0 to 360 1 092 9 690 1 092 6 854 Each image was run through an automated program that calculated the first 15 eigenvectors and corresponding eigenvalues for the image See Section 4 3 3 for details These eigenvectors describe the independently varying spectral components of the image and therefore can be used as a test for the presence of certain phases of interest within the scene For this study we tested for a set of 12 spectral endmembers from laboratory measurements Section 4 3 3 Using this test CRISM images that showed evidence for the presence of carbonate serpentine and or talc saponite were flagged and subsequently analyzed in detail for the presence or absence of these phases This approach allowed us to examine thousands of CRISM images and interpret the mineralogical information in a timely manner with a high degree of confidence 4 3 2 Compact Reconnaissance Imaging Spectrometer for Mars CRISM CRISM is a hyperspectral visible- and near-infrared imager on the Mars Reconnaissance Orbiter with 544 spectral bands between 0 4 and 4 0 m Murchie et al 2007 CRISM has multiple observation modes with several spectral and spatial samplings For this work we used full-resolution short and targeted FRS and FRT images with a spatial sampling of 20 m pixel and half-resolution short and long HRS and HRL images with a spatial sampling of 40 m pixel CRISM mapping products MSP 200 m pixel sampling with 70 bands between 0 4-4 m exist with near global coverage however these data lack the spatial and spectral sampling necessary to 109 make the measurements we are interested in For example these data products would not be able to spectrally resolve the diagnostic 2 12 m serpentine absorption with a high enough fidelity to confidently identify its presence In addition the spatial sampling of the MSP data products may not be sufficient to identify small-scale exposures CRISM images were first corrected for atmospheric gas absorptions using the scaled volcano-scan method McGuire et al 2009 with additional atmospheric correction techniques adapted from the current CRISM Analysis Tool Version 7 2 1 Spectral index maps were created in a manner like that described by Pelkey et al 2007 and Viviano-Beck et al 2014 Spectral indices map the strength of specific spectral features that are indicative of phases across a CRISM image For example the D2300 index maps the depth of the 2 3 m Fe Mg-OH combination band indicative of Fe Mg-phyllosilicates Areas of interest within a given image were then further investigated by evaluating I F spectra I F is the radiance observed by the CRISM detector divided by the solar irradiance at the top of the martian atmosphere and is equivalent to reflectance and spectral ratios to confirm the presence or absence of the spectral feature s of interest Spectral ratios were created by taking a pixel average of I F values for an area of interest and dividing it by the I F average for a region considered spectrally neutral or spectrally known within the same image columns to reduce the effects of systematic column correlated noise on the spectral ratios as well as to accentuate weak spectral absorptions 4 3 3 Factor Analysis Factor analysis and target transformation Malinowski 1991 enable the search for independently varying spectral components and to test for the presence of individual endmembers within a mixed spectral dataset These methods have previously been applied to laboratory and near- and thermal-infrared spacecraft spectral data Bandfield et al 2000 Christensen et al 2000 Bandfield et al 2002 Hamilton and Ruff 2012 Glotch and Bandfield 2006 Glotch and Rogers 110 2013 Geminale et al 2015 Thomas and Bandfield 2014 Thomas and Bandfield in revision and here we apply these methods at a global scale Factor analysis derives a set of orthogonal eigenvectors and associated eigenvalues from a set of measured spectra The number of significant eigenvectors can be used to estimate the number of independent components present within the mixed system Additionally the significant eigenvectors can be used to reconstruct spectral endmembers even if those endmembers do not exist in the original data in a pure unmixed state Therefore the eigenvectors can be used to test for the presence of independent spectral components like serpentine or carbonate that may be present in the system This test is done by using target transformation a least squares fit of the significant eigenvectors to a laboratory spectral endmember If the endmember can be closely matched then it is likely a component of the system In cases where the match is good but not perfect the resulting fit spectrum typically represents a more accurate endmember than the test spectrum and can be used to identify spectral variations like those due to cation content e g Mg Fe- or Ca-carbonates Bandfield 2000 This technique allows for the identification of specific endmembers from an image without having to first identify regions containing high and low concentrations of the endmember of interest Because it is sensitive to the independently variable component anywhere within an image no spectral ratioing is required to identify the endmember For the CRISM dataset we follow methods like those developed by Thomas and Bandfield 2014 Thomas and Bandfield in revision and calculate the significant eigenvectors from a range of 133 spectral bands between 1 7 and 2 6 m CRISM bands 197 through 330 where spectral features of interest are located This spectral range includes features due to structurally-bound or adsorbed H2O phyllosilicates smectites and carbonate phases Eigenvectors and eigenvalues are calculated from CRISM images after removal of atmospheric gas absorptions The images are 111 cropped to remove null edge values as well as right-edge pixels that typically contain significant noise that can interfere with calculations Table 4 5 To reduce processing time the eigenvectors are calculated from every 5th pixel of every 5th line of a given CRISM image which is sufficient to reconstruct the weak spectral absorptions associated with serpentine and still capture the dominant spectral components of the image Table 4 5 Imagine line sample bands used for factor analysis CRISM Data Product Full-Resolution Short FRS Full-Resolution Targeted FRT Half-Resolution Short HRS Half-Resolution Long HRL Column Samples Use 10:592 Row Samples Used 2:179 Spectral Bands Used 197:330 10:592 2:389 197:330 7:283 2:224 197:330 7:283 2:419 197:330 Lastly the eigenvectors were used to test the image for potential spectral endmembers using target transformation If the reconstructed spectrum produced a good fit to the laboratory endmemeber spectrum this indicated a high likelihood that the endmember spectrum was an independent spectral constituent of the image It is possible to calculate the root mean square difference between the reconstructed spectra and the spectral endmember and use this to quantitatively identify matches by goodness-of-fit Malinowski 1991 however we found that the RMS value and therefore the quantitative measure of goodness-of-fit can be confounded by noisy data especially around 2 0 m where residual atmospheric CO2 features are common in the data even when the spectra fit well at the particular wavelengths that would indicate the presence of the endmember phase Therefore for this study we relied on the visual inspection of the target 112 transformation fits for each CRISM image processed Compared to traditional CRISM data analysis techniques this still reduced analysis time to several seconds per image compared to the minutes to hours that were previously required Future work will aim to understand how to place more stringent quantitative measures for goodness-of-fit to eliminate by-hand and visual inspection of the target transformation fits and fully automate this process The inspection of target transformation fits for all the CRISM images were then used to create a database of images with excellent fits for the mineral suite of interest: serpentine magnesite and talc saponite in addition to nine other phases that were documented for completeness calcite siderite hydrated silica gypsum rozenite kieserite kaolinite nontronite and illite Excellent fits indicated that the endmember phases of interest were a spectrally dominant constituent of the given image cube However this target transformation fit does not indicate where in the image the phases occur and subsequent parameter map and spectral ratios were necessary to identify outcrops containing phases of interest This can be particularly tricky in the case of serpentine as the unique and diagnostic absorption at 2 12 m has a relatively shallow spectral contrast compared to the other dominant absorptions at 1 9 2 3 and 2 5 m Figure 4 1 Several attempts at producing a serpentine 2 12 band depth index have been unsuccessful at identifying pixels where known serpentine spectral characteristics exist such as in CRISM image FRS0002AE17_01 Amador et al in revision Chapter 3 in Nili Fossae We attribute this inability to map pixels containing serpentine to several factors: 1 the weak spectral contrast of this absorption relative to the typical noise level within a given CRISM image and 2 the fact that this absorption is just long of any absorption due to residual atmospheric CO2 at 2 0 m Because of this as a first order confidence check that our method was indeed sensitive to serpentine we 113 confirmed our independent serpentine detection with CRISM images where Ehlmann et al 2010 reported serpentine Additionally to ensure that no obvious false-positive detections were made and provide additional confidence in our method all images that were flagged were first visually inspected to ensure that it was reasonable for the flagged phase to be present within the image For example an image that was flagged to contain serpentine needed to have a clear exposure s highlighted by the D2300 index indicative of a negative spectral slope or drop-off at 2 3 m consistent with Fe Mg-phyllosilicates as this would be a necessary absorption for the identification for serpentine 4 4 RESULTS In total we processed and analyzed 10 624 CRISM images including all data products within the six target regions and 6 854 images outside of these regions between 70 N and 70 S latitude Table 4 1 Although this only represents 70% of all hyperspectral images available these remaining images still provide a global sampling of CRISM images across the planet 4 4 1 Target Transformation Fits The modeled target transformation results for the three spectral types of interest serpentine Mg-carbonate and talc saponite were visually inspected for goodness of it Typically this involved matching diagnostic and unique absorption features e g the 2 12 m absorption in serpentine Figure 1 as well as matching appropriate band shapes Band centers were also taken into consideration but with the awareness that if the fit was closely matched but not perfect the fit was likely to be a more accurate endmember than the tested spectrum indicating slightly different composition e g due to variations in cation content than the library test spectra This section shows typical target transformation fits for the three spectral types of interest and examples of an independent confirmation for each spectral type e g ratioed I F and banddepth parameters maps In general target transformation fits of modeled spectra in the Nili Fossae 114 region are stronger and cleaner than in most other regions To illustrate the variation in the quality of the results we have chosen representative spectra from both outside the Nili Fossae region Sections 4 4 1 1-4 4 1 3 and within the Nili Fossae region Section 4 4 1 4 Additionally two other regional and local settings show unique target transformation fits and inferred mineralogy: Leighton Crater within the Tyrhenna Terra S Isidis Region and Mawrth Vallis Remaining dataset Sections 4 4 1 5-4 4 1 6 those specific results are also reported in this section 4 4 1 1 Serpentine CRISM images with clear target transformation fits for serpentine always show welldefined absorptions at 2 12 m and well-defined asymmetric absorption at 2 32 m or in some cases just short of 2 32 m Figure 4 2 The best spectral match for serpentine in both ratioed I F spectra Ehlmann et al 2010 and via target transformation using independent eigenvectors is CRISM image FRT0000634B_07 in Claritas Rise Figure 4 2a In this case the target transformation fit matches both the shape and wavelength center of the 2 32 m absorption In some cases the modeled 2 32 m absorption is shifted short-ward Figure 4 2c this likely indicates a more realistic spectral endmember for those images relative to the target input spectrum provided As such this shift to slightly shorter wavelengths may indicate variable alteration to another Fe Mg-phyllosilicate mineral phase like talc or saponite 115 Figure 4 2 Three examples of excellent target transformation fits for serpentine Panels A-C show examples of CRISM images where serpentine has previously been identified Panel A Ehlmann et al 2010 where serpentine has been speculated Panel B Michalski and Niles 2010 and a new image outside of Nili Fossae with a clear fit for serpentine Panel C CRISM image FRT0000634B_07 shows the best spectral match for serpentine in both ratioed I F spectra Ehlmann et al 2010 and via target transformation using independent eigenvectors It was difficult to independently verify the presence of serpentine in CRISM images that show good target transformation fits for serpentine Except for surfaces identified in previous studies by Ehlmann et al 2009 2010 and Amador et al in revision Chapter 3 in Nili Fossae we were unable to independently identify the diagnostic 2 12 m serpentine feature using ratioed I F spectra in new flagged images However all images flagged showed clear surfaces with associated 2 3 m absorptions as mapped by the D2300 index Figure 4 2 This absorption is also necessary to uniquely identify serpentine Figure 4 1 This is further discussed in Section 4 5 1 116 4 4 1 2 Mg-Carbonate Target transformation fits for Mg-carbonate show two absorptions at 2 3 and 2 5 m Figure 3 Panel A Mg-carbonate e g magnesite can be distinguished from Ca Fe-carbonates e g calcite siderite using target transformation by the wavelength center and absorption shape Figure 4 1 Thomas and Bandfield 2014 Thomas and Bandfield in revision Clear fits to Mgcarbonate consistently show the correct band center and absorption shape in the target transformation modeled spectra e g Figure 4 3 Figure 4 3 Target transformation fit for Mg-carbonate in CRISM image HRL000095C7_07 in Chia Crater The presence of Mg-carbonate can be independently verified by viewing ratioed I F spectra and by displaying the BD2500 Mg-carbonate index map Mg-carbonate can typically be independently confirmed using ratioed I F spectra as in CRISM image HRL000095C7 which covers a portion of the southern rim of Chia Crater north of Juventea Chasma Valles Marineras Region Figure 4 3 This example shows a good fit for magnesite in its target transformation modeled fit and can be verified by the 2 5 m band-depth index map consistent with Mg-carbonates as well as by viewing the ratioed I F CRISM spectra from the image Figure 4 3b that also show the proper spectral shape and band centers for Mgcarbonate 117 4 4 1 3 Talc Saponite The third spectral phase we searched for in this study was talc saponite In the near-infrared wavelength region talc and saponite appear spectrally similar and can be difficult to disambiguate Figure 4 1 Both phases have narrow absorptions centered near 2 3 and 2 4 m with variable spectral contrast in the 2 4 m absorption Figure 4 1 There is often an additional weak absorption near 2 46 m present in laboratory spectra for talc but given the noise level within a typical CRISM image and other interfering factors this absorption is not expected to be identifiable in CRISM data The target transformation fits shown in Figure 4 4 are representative of the type of fits found for talc and saponite globally Fit spectra are typically quite noisy indicating the presence of these phases at low levels in the Figure 4 4 Target transformation fits for talc saponite spectral type Panels A and B show fits to talc and saponite respectively for one image in Her Desher Vallis Fit can be independently verified using ratioed I F spectra and D2300 colorized index map Panel C 118 data We found that with target transformation results alone it is difficult to determine whether the fits are more consistent with one phase over the other Despite this images flagged with positive fits always clearly show the necessary absorptions near 2 3 and 2 4 m compared to images that were not flagged Because of the spectral ambiguity between talc and saponite this spectral type was simply labeled as talc saponite CRISM image FRT00001756E_07 Figure 4 4 in Her Desher Vallis N Argyre Basin Region is an example of an image with good target transformation match for talc saponite The target transformation flag can be independently verified by both the D2300 band-depth index map as well as in the ratioed I F spectra Figure 4 4c that show two well-defined absorptions near 2 3 and 2 4 m This image has previously been reported as containing a phyllosilicate spectral signature attributed to saponite Buczkowski et al 2010 again giving confidence in this technique s ability to independently identify mineral phases of interest 4 4 1 4 Nili Fossae 76 695 E 22 018 N The Nili Fossae region has the highest concentration of images with strong target transformation modeled fits for serpentine and Mg-carbonate as well as five images that contain strong fits for a talc saponite spectral type Previously three images were known in Nili Fossae to show spectral evidence for serpentine Ehlmann et al 2009 2010 Amador et al in revision Chapter 3 With this study there are now a total of 16 images that show evidence for serpentine This region has been extensively studied and this study now provides additional and independent evidence for the presence of the spectral types of interest in the area CRISM image FRT000028BA_07 is one of two images in Nili Fossae where all three spectral types are found within a single CRISM scene These phases have previously been detected in this region using spectral ratios and band indices e g Ehlmann et al 2009 2010 Brown et al 2010 Viviano et 119 al 2013 Amador et al 2016 in revision Chapter 3 Here we show an independent means of identifying this mineralogical suite using factor analysis and target transformation Figure 4 5 Target transformation spectra fit the diagnostic 2 12 m absorption well follows the overall shape for the 2 3 m absorption as well as the position and shape of the broad 2 5 m absorption Figure 4 5a Figure 4 5 Representative target transformation fits for all spectral types in Nili Fossae from CRISM image FRT000028BA_07 Target transformation fits for serpentine exhibit diagnostic 2 12 m absorption and an additional minor absorption near 2 4 m similar to talc and saponite implying variable alteration of serpentine to a talc saponite phase 120 Notably the 2 32 m absorption is shifted slightly shorter than is typical of endmember serpentine measured in the lab and the modeled spectrum shows an additional minor absorption near 2 38 m where both talc and saponite have a minor absorption Figure 4 5a Figure 4 1 In this case the modeled target transformation spectrum is likely a more accurate spectral endmember than the test endmember shown The modeled target transformation fit for magnesite is clear both in band center and shape Lastly the target transformation fits for both talc and saponite show that there is clearly a spectral phase present with an absorption near 2 3 and 2 4 m but this test does not provide confidence in distinguishing between one over the other Figure 4 5 is representative of the types of positive fits for the spectral types of interest within Nili Fossae 4 4 1 5 Leighton Crater 57 752 E 3 08 N Target transformation fits for images in Leighton Crater a 60 km diameter impact crater on the southwestern flank of Syrtis Major were clear and matched well with a range of mineral phases including magnesite siderite serpentine talc saponite and montmorillonite Al-smectite Figure 4 6 Target transformation fits for CRISM image FRT0000A546_07 for example are most consistent with a Ca Fe-carbonate such as siderite Figure 4 6ab and fits for serpentine show an additional absorption near 2 4 m likely indicating that serpentine is found mixed with a talc saponite phase Figure 4 6c Target transformation fits for a talc saponite spectral type are most consistent with saponite in this image Figure 4 6de and target transformation results also point to an Al-phyllosilicate endmember most consistent with montmorillonite Figure 4 6f 121 Figure 4 6 CTX mosaic of Leighton Crater with outlines of all overlapping CRISM images Green stamps indicate images with fits for serpentine magenta stamp and magenta circles indicate images with fits for Mg-carbonate gray stamps indicate images with no fits for investigated phases Spectra come from CRISM image FRT0000A546_07 starred Fits are strong for all investigated phases and an Al-phyllosilicate phase consistent with montmorillonite 4 4 1 6 Mawrth Vallis 343 027 E 22 43 N Target transformation fits for CRISM images found in the Mawrth Vallis region similarly showed a range of interesting mineral phases Four images showed clear fits for serpentine in the region three of which are within the main Mawrth Vallis plateau where high concentrations of phyllosilicates have been identified previously e g Bishop et al 2008 Poulet et al 2014 As with previously discussed target transformation fits for serpentine those matched in Mawrth Vallis show the diagnostic 2 12 m absorption and an 2 30 m absorption shifted to slightly shorter wavelength centers compared to library endmember spectra for serpentine Figure 4 1 Figure 4 7a Mg-carbonates are detected in 12 CRISM images throughout the Mawrth Vallis region Figure 4 7b including a confirmation of Mg-carbonate previously reported in nearby McLaughlin Crater Michalski et al 2013 One CRISM image HRS0000307A_07 shows 122 evidence for talc and a poor target transformation fit for saponite Figure 4 7cd In this case the talc saponite spectral type is more consistent with a talc spectral endmember Target transformation modeled fits also showed abundant evidence for a Fe Mg-phyllosilicate phase consistent with nontronite Figure 4 7e as well as several fits consistent with an Al-phyllosilicate like montmorillonite Figure 4 7f Figure 4 7 Viking MDIM 2 1 mosaic of the Mawrth Vallis region with all overlapping CRISM images Small black squares indicate CRISM images with no fits for investigated phases Green stamps indicate images with fits for serpentine magenta stamps indicate fits for Mg-carbonate and blue stamp indicates fit for talc saponite Representative target transformation fits shown to the right Mg-carbonate and serpentine fits are clear talc saponite fits appear more consistent with talc Additionally target transformation techniques clearly identify a Fe Mg-phyllosilicate phase consistent with nontronite and an Al-phyllosilicate phase consistent with montmorillonite 4 4 2 Global Distributions Globally fifty-one CRISM images were identified with good fits to serpentine All the CRISM images flagged also contained Fe Mg-phyllosilicate-bearing surfaces as highlighted by 123 the D2300 index e g Figure 4 2 Additionally none of the CRISM images flagged occur in unlikely geologic settings where these general phases have not been previously identified Figure 4 8 Serpentine occurrences are distributed across the southern highlands and are concentrated in Nili Fossae Mawrth Vallis along the Thaumasia Highlands and south-west of Meridiani Planun In addition several occurrences are present around Hellas Basin and Tyrhenna Terra Figure 4 8 We consistently find serpentine where Ehlmann et al 2010 show confident detections and corroborate one out of their six probable detections from that study Figure 4 8 Similarly we also find serpentine in five of the seven locations that Viviano-Beck et al 2017 identified near Claritas Rise Valles Marineris and the Thaumasia Highlands Figure 4 8 CRISM images identified with good fits for serpentine often show additional mineralogical diversity nearly half of those images flagged also showed spectral evidence for Mg-carbonate or Ca Fe-carbonate phases Table 4 6 All images flagged except HRL00006C8A_07 located in the Thaumasia Highlands either have olivine-enriched surfaces within the image scene or have phyllosilicate-bearing surfaces with a ferrous component to its spectral signature e g McKeown et al 2009 as indicated by a steep positive slope between 1 0 and 1 8 m This ferrous component could be due to olivine or ferrous chlorites or ferrous micas McKeown et al 2009 The geologic context for these exposures are quite diverse and range from layered exposures in crater rims and valley walls to layers within knobby eroded terrain Table 4 6 124 125 Figure 4 8 Global distribution of target transformation fits for serpentine green squares Mgcarbonate magenta squares and talc saponite blue squares over MOLA shaded relief map Results from this study are shown with serpentine detections from previous studies Ehlmann et al 2010 and Viviano-Beck et al 2017 Regions of interest are marked with black boxes Region A: Claritas Rise Region B: Valles Marineris Region C: N Argyre Basin Region D: S Tyrhenna Terra S Isids Region E: Nili Fossae and Region F: Terra Sirenum Table 4 6 Description of Images with Serpentine Detections Region CRISM Image ID Associated Olivine Associated Secondary Minerals Talc Saponite Geologic Context N Argyre Basin FRT00001756E_07 Ferrous component N Argyre Basin HRL00009B61_07 Ferrous component - Claritas Rise FRT000040DB_07 Ferrous component Siderite Claritas Rise FRT0000634B_07 Illite Claritas Rise FRS00032AF6_01 - Knobby terrain Nili Fossae FRT000028BA_07 Ferrous component Ferrous component Yes Layered outcrop on walls of Her Desher Vallis Layered outcrop on wall of Her Desher Vallis Eroding mobilized layered from crater rim Knobby terrain Carbonate plains Nili Fossae FRT00003584_07 Yes Nili Fossae FRT00003FB9_07 Yes Nili Fossae FRT000064D9_07 Ferrous component Magnesite talc nontronite Magnesite nontronite Magnesite kaolinite Carbonate nontronite Nili Fossae FRT00007BC8_07 Yes Magnesite Carbonate plains Carbonate plains Nili Fossae trough floor near original proposed MSL proposed landing site ellipse Nili Fossae trough floor near original 126 Nili Fossae FRT000088D0_07 Yes - Nili Fossae FRT000095FE_07 Yes Nili Fossae FRT00009971_07 Yes Magnesite hydrated silica - Nili Fossae FRT0000A09C_07 Yes Nili Fossae Nili Fossae FRT0000AA03_07 FRT0000ABCB_07 Yes Yes Nili Fossae FRT0001B615_07 Ferrous component Nili Fossae Nili Fossae Nili Fossae Nili Fossae Terra Sirenum HRL000040FF_07 HRL000095A2_07 HRL00009ABE_07 HRL0000AB0A_07 FRT00008C90_07 Yes Yes Yes Yes Ferrous component Terra Sirenum Terra Sirenum FRT0000A106_07 Ferrous component Yes HRL00007C95_07 Magnesite talc Magnesite Magnesite kaolinite - Magnesite Kaolinite Nontronite Magnesite hydrated silica talc saponite Talc saponite - proposed MSL proposed landing site ellipse Eastern wall of Nili Fossae main trough Carbonate plains Western rim of main trough Carbonate plains Carbonate plains Layered outcrop Layered outcrop exposed on elevated terrain through Syrtis Major lava flow Carbonate plains Wall of main trough Layered outcrop Layered outcrop Knobby terrain between Ariadnes Colles Collis and K r n Valles Knobby terrain in Caralis Chaos Small-scale knobby plains with widespread phyllosilicate Small-scale knobby plains with widespread phyllosilicate Exposed layer Terra Sirenum HRL0000D002_07 Ferrous component Talc saponite Tyrhenna Terra S Isidis Tyrhenna Terra S Isidis Tyrhenna Terra S Isidis FRT00008144_07 Yes - FRT0000A33C_07 Yes - Exposed eroded layer from crater rim FRT0000A377_07 Yes Carbonate Erosional unit coming from ridges south of Isidis Basin 127 Tyrhenna Terra S Isidis Tyrhenna Terra S Isidis Tyrhenna Terra S Isidis Valles Marineris Remaining: Mawrth Vallis Remaining: Nilo-Syrtis FRT0000A546_07 Ferrous component HRS0000AA3A_07 Ferrous component HRL000067B5_07 ferrous component Siderite Central peak of crater near Oenotria Scopuli HRL000095C7_07 Ferrous component ferrous component Magnesite Floor of Chia Crater Nontronite kaolinite Layered exposures south of Mawrth Vallis Syrtis Major lava flow south-east of Antoniadi Crater Rim of Toro Crater on Syrtis Major FRT00003BFB_07 Siderite kaolinite Alphyllosilicate Magnesite FRT0000406B_07 Ferrous component - Remaining: Toro Crater FRT00009786_07 Ferrous component Remaining: SW Meridiani Planum Remaining: SW Meridiani Planum Remaining: West of Mare Serpentis Remaining: Mawrth Vallis FRT0000979C_07 Yes Magnesite hydrated silica talc saponite Magnesite FRT0000A063_07 Yes Magnesite FRT0000A22D_07 Ferrous component - FRT0000A425_07 Ferrous component Magnesite nontronite Alphyllosilicate FRT0000A8CE_07 Ferrous component Magnesite nontronite Alphyllosilicate Remaining: Rutherford Crater East of Mawrth Vallis Central peak of Leighton Crater Floor of Leighton Crater Continuous exposure at southern Meridiani Planum edge Exposures in elevated terrain near southern Meridiani Planum edge Crater rim Layered exposures within Mawrth Vallis MSL Mars2020 proposed landing ellipse Exposed terrain on outer rim of Rutherford Crater 128 Remaining: Mawrth Vallis HRL000043EC_07 Ferrous component Nontronite Alphyllosilicate Remaining: SW Meridiani Planum Remaining: Thaumasia Highlands Remaining: West of Hellas Basin Remaining: Mawrth Vallis HRL00005865_07 Yes Magnesite HRL00006C8A_07 No Siderite HRL0000814A_07 Yes HRL00009A5F_07 ferrous component Remaining: Nilo-Syrtis HRS00002FC5_07 Yes Remaining: Nilo-Syrtis HRS000030A2_07 Yes Remaining: Thaumasia Planum HRS0000A8D3_07 Ferrous component Layered exposures west of Mawrth Vallis MSL Mars2020 proposed landing ellipse Small-scale exposures around and near craters Heterogeneous terrain continuous exposures Crater floor discontinuous exposures Nontronite Layered exposures within Mawrth Vallis MSL Mars2020 proposed landing ellipse Magnesite Discontinuous nontronite Al- exposures mobilized phyllosilicate sediments east of Negril Crater Magnesite Discontinuous exposures mobilized sediments coming from elevated ridges south of Negril Crater AlHeterogeneous phyllosilicate exposed layer Of the images surveyed 143 showed good fits for Mg-carbonate 72 of which are located within the heavily CRISM targeted Nili Fossae region and have generally been reported by previous studies e g Ehlmann et al 2008 Ehlmann and Edwards 2015 Thomas and Bandfield 2014 Thomas and Bandfield in revision Amador et al in revision Chapter 3 Other Mg-carbonate detections are concentrated near and on the walls of Valles Marineris in the Mawrth Vallis region within Aram Chaos and in Tyrhenna Terra Figure 4 8 129 Lastly there are 38 images with good fits for talc saponite distributed across the southern highlands Figure 4 8 Of the regions of focus for this study Terra Sirenum has the largest fraction of images with excellent fits for talc saponite Table 4 7 Similarly the walls of Her Desher Valles and Nirgal Vallis north of Argyre Basin also show talc saponite spectral signatures Table 4 7 Detections for investigate spectral types Region Total Images Northern Claritas Nili Terra Tyrhenna Valles Remaining Argyre Rise Fossae Sirenum Terra S Marineris Global Isidis 463 122 229 558 1 306 1 092 6 854 Images with Serpentine Images with MgCarbonate Images with Talc Saponite 4 5 2 3 16 4 6 1 19 3 0 72 3 13 9 43 6 0 5 10 4 2 12 DISCUSSION 4 5 1 Usefulness of Factor Analysis and Target Transformation in Searching for phases Associated with Serpentinization The use of factor analysis and target transformation has been successful in globally mapping the CRISM images and locations with the highest probability of containing serpentine Mg-carbonate and talc saponite spectral phases This corroboration of previous detections using an alternative method provides additional confidence in the ability of target transformation to identify specific phases of interest Our positive fits for a talc saponite phase and Mg-carbonate phases were more easily confirmed independently using traditional I F spectral ratios and band-depth parameter maps In contrast in most cases it was not possible to independently identify serpentine-bearing surfaces in CRISM images even with clear target transformation fits to a serpentine library spectrum One of the values of the factor 130 analysis and target transformation method is that if the significant eigenvectors can be reconstructed to fit a test library spectrum then that endmember is a component of the system as a whole in this case the entire CRISM scene and that it is possible that this endmember exists in its pure form in the image Bandfield et al 2000 This method can also find components to the system even if the endmember only exists as a spectral mixture in the scene Bandfield et al 2000 Therefore even though for our application we were unsuccessful in finding specific CRISM pixels that contained enough serpentine to be detectable in their reflectance spectra it does not indicate that our technique was incorrect in predicting its presence Rather it likely indicates that serpentine exists at low enough concentrations across the entire CRISM scene to affect the independently varying eigenvectors of the scene The target transformation uses the statistical variation present within all the data used to calculate the eigenvectors If the phase of interest is present but variable at a low concentration within a CRISM image it may still be identified even though it may be undetectable in spectral ratios and index images Additionally the serpentine that is present is likely to be variably altered evidenced by the slight variation in the reconstructed modeled target transformation fits for serpentine compared to the laboratory endmember spectrum e g Figure 4 2bc Figure 4 5a In addition to corroborating previous detections of serpentine this study consistently predicts serpentine in regions where we would most expect it to occur from regional geologic context and past studies for example in the carbonate plains in Nili Fossae See Section 4 5 2 4 for more details In this sense this method has enabled the detection prediction of surfaces containing serpentine that would otherwise be missed using traditional CRISM data analysis techniques Given these confidence checks on our technique for the remainder of this study we will refer to CRISM images with clear target transformation fits for phases of interest as identifications or detections acknowledging that these are not direct detections and the discussed uncertainties of this method 131 4 5 2 Global Distributions Spatial Correlations between Phases and Regions of Interest In general occurrences of serpentine Mg-carbonate and a talc saponite spectral type are still quite rare across the planet Figure 4 8 New identifications of serpentine especially around Tyrhenna Terra Terra Sirenum and in Meridiani Planum show no spatial correlation with other phases of interest that would indicate a common geologic or geochemical process Similarly the serpentine detections do not appear to be directly associated with ultramafic exposures or regions other than in Nili Fossae although 9 of 35 CRISM images with serpentine detections outside of Nili Fossae show spectral evidence for olivine-enriched surfaces within the image scene The one spatial factor that all detections have in common is their association with relatively dustfree regions Figure 4 9 The global surface and atmospheric dust on Mars obscures much of the surface from these types of spectroscopic analyses resulting in an observational bias to the compositional interpretations that can be made from orbit The dusty regions often hinder our interpretation of the surface composition using orbital instrumentation However this is a commonality shared amongst most secondary alteration products observed to date e g Carter et al 2013 The lack of spatial correlation between spectral types of interest does provide value to our understanding of how these phases formed and under what conditions For example the talc saponite spectral type that was investigated because of its mineralogical and spectral context in Nili Fossae has been observed across the southern highlands Given that it is rarely found in association with serpentine and Mg-carbonate outside of Nili Fossae it is more likely that this spectral type is due to a saponite phase rather than a talc Saponite can readily form from the low-temperature alteration of basalt whereas on Earth talc is most commonly found in association low-grade metamorphosed ultramafic rocks Evans and Guggenheim 1988 Given that the martian crust is predominantly composed of basalt and most sites do not show elevated mafic compositions the more favorable alteration sequence results in the formation of saponite not talc 132 The global distribution of serpentine detections appears to fall into one of two categories Most detections are seemingly isolated occurrences found within crater walls knobby terrain or impact ejecta such as in Chia Crater though they tend to be distributed widely across the southern highlands The second category includes detections that appear to be part of a greater regional local context with respect to the geology such as in Claritas Rise and along the Thaumasia Highlands boundary or other phases identified within the image scene or nearby scenes such as Leighton Crater Mawrth Vallis and Nili Fossae These two categories and specific locales within them have different implications for local and regional habitability as well as implications for general global serpentinization processes throughout Mars history We will discuss the importance of the first category of detections for global-scale serpentinization on Mars and then focus on three local regions from the first group and discuss their implications for serpentinization induced habitable environments 133 Figure 4 9 Global distribution of target transformation fits for investigated spectral types over colorized OMEGA dust map As expected and consistent with other studies searching for secondary alteration minerals our detections are associated with relatively low dust covered areas This low dust coverage provides an orbital window to interpret the mineralogy of exposed surfaces 134 4 5 2 1 Globally Isolated Detections of Serpentine Most detections of serpentine occur in seemingly isolated occurrences across the southern highlands These detections are not often found with other investigated minerals and often do not relate to any general geologic or geochemical process that would have formed them We attribute these detections to low concentrations of serpentine that likely formed during past subsurface serpentinization at depth We can speculate that this may be evidence for variable olivine-compositions at depth across the martian subsurface or indicate variations in crustal heat flow and fluid circulation perhaps due to local magmatic processes or impact induced hydrothermal systems However most of these detections are in CRISM images that show exposures of reworked ancient terrains with little geologic context Regardless though the number of serpentine detections are still low compared to other hydrated minerals on Mars they are found across the southern highlands 4 5 2 2 Leighton Crater Michalski and Niles 2010 found spectral evidence in Leighton Crater for both carbonates likely a Ca or Fe-bearing carbonate such as siderite and phyllosilicate phases including a speculated spectral mixture of serpentine vermiculite saponite though without the necessary 2 12 m absorption for serpentine It was suggested that these exposures are evidence for a deep crustal reservoir of sedimentary carbonate that was subsequently altered by volcanic lava flows and ultimately exposed by the impact that formed Leighton Crater Michalski and Niles 2010 Detections from this study are consistent with the mineralogical interpretation put forth by Michalski and Niles 2010 We present strong evidence that a serpentine spectral component is present within Leighton Crater as well as saponite likely implying that these exposures have experienced subsurface serpentinization Figure 4 6 This study also corroborates Michalski and Niles 2010 interpretation of a Ca or Fe-bearing carbonate versus a Mg-carbonate Figure 4 6 and illustrates the 135 sensitivity of this method to varying cation content As hypothesized by Michalski and Niles 2010 given the serpentine s association with Al-bearing clays it is unlikely that the impact simply excavated evidence for serpentinization of an ultramafic protolith but instead has exposed a complicated series of alteration assemblages The exposures in Leighton Crater present clear mineralogical evidence for serpentinization a set of reactions that imply a habitable environment Additionally the range of carbonate chemistry and Fe Mg- and Al-phyllosilicate phases implies that exposed rocks in Leighton Crater have experience a range of aqueous alteration processes that likely promoted habitable environments However given that these reactions likely occurred in the subsurface and were later chemically altered and ultimately excavated by violent impact processes Michalski and Niles 2010 the astrobiological implications for these samples are less clear 4 5 2 3 Mawrth Vallis Mawrth Vallis has been studied extensively using both near-infrared e g Bishop et al 2008 Wray et al 2008 McKeown et al 2009 Loizeau et al 2015 and thermal-infrared spectral datasets Rogers and Bandfield 2009 Michalski et al 2013 The compositional stratigraphy found in Mawrth Vallis has been identified in several other martian locales including western Nili Fossae and consists of Fe Mg-phyllosilicates e g nontronite overlain by Al-phyllosilicates e g kaolinite montmorillonite This compositional stratigraphy is thought to be produced by extensive surface leaching and weathering of the upper unit e g Murchie et al 2009 Additionally the Mawrth Vallis region exposes some of the highest concentration of phyllosilicates on the planet Poulet et al 2014 Rogers and Bandfield 2009 From this study serpentine and Mg-carbonate appear to be common in the area with most detections concentrated on the main Mawrth Vallis plateau where the highest concentration of phyllosilicates has been observed by others e g Poulet et al 2014 This supports previous 136 identifications of serpentine around Mawrth Vallis Ehlmann et al 2010 and detections of Mgcarbonate in McLaughlin Crater Michalski et el 2013 with additional new detections Figure 4 7 We were unable to directly detect Mg-carbonate or serpentine-enriched surfaces using I F spectral ratios or using band-depth parameters maps in the images flagged using factor analysis and target transformation However as discussed in Section 4 5 1 this does not preclude the existence of these spectral phases as being components of the overall CRISM scene Given that this area has been highly weathered from the late-Noachian through the early-Hesperian Loizeau et al 2015 it may be possible that serpentinization was an active process in the past perhaps an early global process However the geologic context for these reactions in Mawrth Vallis is less clear and somewhat ambiguous compared to other martian regions There is not abundant evidence for olivine-rich basalts as in Nili Fossae nor is there any evidence for an initial source of heat such as a nearby volcanic source or an impact-induced hydrothermal system The target transformation results in Mawrth Vallis are consistent with the known high mineralogical diversity in the region Detections from target transformation fits for phases not specifically associated with serpentinization where clearly identified in this region Exceptional fits for a Fe Mg-phyllosilicate phase like nontronite and an Al-phyllosilicate phase like a montmorillonite kaolinite mixture are present Figure 4 7f These identifications are not new e g Bishop et al 2008 Wray et al 2008 McKeown et al 2009 Loizeau et al 2015 but are clearly observed and corroborated using this independent technique speaking to the quality and likely volume of phyllosilicate exposures in Mawrth Vallis From an astrobiological perspective Mawrth Vallis presents one water of the three water energy nutrients organics key ingredients for life The region shows clear evidence for sustained aqueous alteration for a long enough period to produce the globally recognized compositional stratigraphy of Fe Mg-phyllosilicates overlain by Al-phyllosilicates Our detections of serpentine implies 137 that evidence for past serpentinization exists within these exposures but the geologic context and timing for when the serpentinization reactions occurred and what subsequent geochemical processes have since occurred makes the astrobiological potential of this region less clear However the rich diversity of mineralogical products in this region implies an extremely interesting aqueous history that likely connects to a global process that led to the globally recognized compositional stratigraphy discussed such as in western Nili Fossae 4 5 2 4 Nili Fossae Nili Fossae is considered one of the most mineralogically diverse regions on Mars with a range of both primary and secondary alteration minerals Hoefen et al 2003 Hamilton and Christensen 2005 Poulet et al 2005 Bibring et al 2006 Mangold et al 2007 Mustard et al 2007 2009 Ehlmann et al 2008 2009 2010 Tornabene et al 2008 Brown et al 2010 Viviano et al 2013 Edwards and Ehlmann 2015 Previous studies using traditional I F spectral ratios and band-depth parameters maps showed evidence for three CRISM images in the region with serpentine-bearing surfaces Figure 4 10 Ehlmann et al 2009 2010 Amador et al in revision Chapter 3 The evidence for serpentine-bearing surfaces in Nili Fossae from these studies were limited and the diagnostic 2 12 m absorptions are often weak and less clear than other serpentine examples elsewhere such as in Claritas Rise Ehlmann et al 2010 The target transformation fits for serpentine presenting in this study show well defined 2 12 m absorptions e g Figure 4 5a that are often more clear than those retrieved from traditional I F spectral ratios Though the implications for serpentinization and habitability in Nili Fossae have been discussed by several other studies e g Ehlmann et al 2009 2010 Brown et al 2010 Viviano et al 2013 Amador et al in revision Chapter 3 this work presents several new components to the story that could only be gathered with the aid of factor analysis and target transformation Modeled target transformation 138 fits for serpentine are consistent with a variably altered spectral endmember Given that the 2 32 m absorption is shifted to slightly shorter wavelengths and the presence of a minor absorption near 2 4 m it is likely that serpentine exposures have been partially altered to a talc saponite phase The process of carbonation the alteration of serpentine Figure 4 10 Colorized MOLA over THEMIS Day-IR mosaic of Nili Fossae centered around 76 09 E 19 98 N White inset shows area described in Figure 4 11 Colored stamps and circles indicate CRISM images with target transformation fits for investigated spectral types Green indicates serpentine magenta indicates Mg-carbonate and blue indicates talc saponite The three starred CRISM images FRT0000ABCB_07 FRS0002AE17_01 and HRL0000B8C2_07 are where previous studies have detected serpentine previously 139 Figure 4 11 Colorized MOLA over THEMIS Day-IR mosaic Most serpentine detections are concentrated in this region east of the main Nili Fosse troughs Black insets indicate areas shown in detail in Figure 4 12 140 Figure 4 12 Colorized MOLA over THEMIS Day-IR mosaic Panel A shows proposed Mars2020 landing site Carbonate Plains Panel B shows proposed Mars2020 landing site NE Syrtis Both landing sites would put a rover near the spectral types of interest to form talc and magnesite has been proposed for this region by Viviano et al 2013 and our results corroborate this idea as the target transformation fits for serpentine consistently show this additional absorption at 2 4 m Furthermore given the mineralogical context in Nili Fossae specifically the observed 2 4 m absorption is likely to be due to talc and or talc saponite rather than saponite alone as this region with high abundances of ultramafics has undergone low-grade metamorphic processes e g Viviano et al 2013 Amador et al in revision Chapter 3 In this sense there is a clear geochemical means to produce talc in this region unlike other observations of a talc saponite spectral type such as in Her Desher Vallis See Section 4 4 1 3 These three phases serpentine Mg-carbonate and talc found in association with olivine-rich basalt point to low-temperature serpentinization processes 141 followed by carbonation in this region as discussed by other studies e g Viviano et al 2013 Amador et al in revision Chapter 3 Here we have also shown that serpentine is much more widespread across the Nili Fossae region than previously recognized and it is commonly found in association with Mg-carbonate Figure 4 10 Known serpentine occurrences have expanded from three isolated images found across the region Ehlmann et al 2009 2010 Amador et al in revision Chapter 3 to 16 images predominately clustered in the eastern carbonate plains Figure 4 10 inset Figure 4 11 Figure 4 12 This area also corresponds to the highest concentrations of olivine within the olivine-rich basalt stratigraphic unit in the region e g Ody et al 2013 Talc detections are also concentrated in the eastern portion of Nili Fossae though they are less common and geographically dispersed Figure 4 10 These results are consistent with the overall story that serpentinization and carbonation reactions were likely the cause of the mineral suite observed in the eastern portion of Nili Fossae e g Viviano et al 2013 and were more pervasive than previously thought There are other isolated exposures of olivine-enriched basalt across the Nili Fossae region but the mineral assemblage associated with serpentinization appears to be most common within the olivineenriched exposures in the east though there are some occurrences of serpentine carbonate and talc on the plateau west of the main Nili Fossae trough There are several unique geologic factors that could have promoted the serpentinization and subsequent carbonation of the subsurface in the eastern portion of Nili Fossae This is the area with the most expansive and highest concentration of olivine in the region e g Hamilton and Christensen 2005 Ody et al 2013 this would have provided the necessary protolith for the initiation and continuation of serpentinization Additionally the carbonate plains are found within a lower topographic elevation compared to much of the plateau around the Nili Fossae troughs as there is a south-east trending topographic gradient in the region towards the Isidis Basin to the east Figure 4 13 This may point to a path for fluid migration during the late-Noachian early-Hesperian 142 Eras when these processes were likely occurring e g Viviano et al 2013 Amador et al in revision Chapter 3 likely concentrated fluids towards the now exposed carbonate plains and making this location particularly susceptible to serpentinization and subsequent alteration to Mg-carbonate and talc Figure 4 13 Colorized MOLA topography over THEMIS Day-IR mosaic with 200 m contour lines Color stamps indicate CRISM image with target transformations fits for serpentine green Mgcarbonate magenta and talc saponite blue The highest concentration of the mineral suite of interest is found at lower elevations relative to Nili Fossae possibly along a hydrologic flow gradient from the higher Nili Fossae plateau towards Isidis Basin The Nili Fossae region particularly around and to the south of the carbonate plains provides abundant evidence for a once habitable environment The observed mineralogical suite indicates that low-temperature serpentinization was once an active process in the region and this study shows how 143 pervasive those reactions were Additionally the presence of this mineralogical suite associated with serpentinization found within an olivine-rich unit indicates that these reactions took place in-situ with minimal geochemical and tectonic reworking making the eastern portion of Nili Fossae a particularly compelling site to study with respect to past habitability 4 5 3 Implications for global serpentinization processes on Mars and searching for regions with the highest potential for containing once habitable environments This study had shown abundant spectral evidence for the presence of serpentine across the southern highlands of Mars For the most part serpentine occurrences are isolated and occur at low enough concentrations that its detection in the available CRISM data necessitates the use of factor analysis and target transformation Though these detections are somewhat ambiguous and their context can be difficult to place within a larger habitability framework their detection is very interesting Clearly large-scale regional serpentinization processes in the near-subsurface like in Nili Fossae were rare on Mars However the fact that these low-concentration occurrences are found distributed across the southern highlands implies a global process Given that the concentrations for these occurrences are so low and the serpentine is typically not found with other minerals that are usually associated with serpentinization they probably represent old and reworked material This may mean that serpentinization was a more common process very early on in Mars history when the planet was more geologically active Only several regions on the planet contain serpentine-bearing exposures at high enough concentrations that they are detectable directly from ratioed I F spectral data: Claritas Rise Ehlmann et al 2010 Viviano-Beck et al 2017 along the Thaumasia Highlands Viviano-Beck et al 2017 Chia Crater Ehlmann et al 2010 and in Nili Fossae Ehlmann et al 2009 2010 Amador et al in revision Chapter 3 The geologic context and the processes that led to the exposure of serpentine-bearing surfaces in Claritas Rise and in Nili Fossae appear to be most straightforward In Claritas Rise and along the edge of the Thaumasia Highlands the serpentine-bearing rocks have likely been excavated from 144 substantial depth uplifted and exposed at the modern-day surface e g Viviano-Beck et al 2017 This region has been tectonically modified due to its position to the southeast of the Tharsis region for much of the Noachian and Hesperian e g Carr and Head 2010 This region also shows spectral evidence for zeolites and chlorite Viviano-Beck et al 2017 further implying that this region has been exposed to secondary alteration processes that are not associated with serpentinization but controlled by the tectonics of the region inducing low-grade metamorphism The serpentine exposed in this region helps constrain the tectonic setting of the region as described by Viviano-Beck et al 2017 however the astrobiological and habitability implications are limited given how reworked these surfaces are The geologic setting of serpentine-exposures in Nili Fossae is also unique compared to others across the planet Serpentine-bearing surfaces are all found within an expansive olivine-rich basalt unit Hoefen et al 2003 Hamilton and Christensen 2005 Mustard et al 2007 Tornabene et al 2008 approximately 30 000 km2 in area This unit is the largest continuous exposures of olivine-rich bedrock on the planet Ody et al 2013 and contains between 20 and 30 wt% olivine ranging in composition from Fo68-75 Hamilton and Christensen 2005 Koeppen and Hamilton 2008 Edwards and Ehlmann 2015 implying a more Mg-rich composition along the olivine solid-solution series This olivine-rich unit may have formed contemporaneously as an Isidis-related impact melt Mustard et al 2009 or alternatively as post-Isidis impact event volcanic lava flows Hamilton and Christensen 2005 Tornabene et al 2008 It may be that this expansive olivine-rich unit makes Nili Fossae a unique setting for serpentinization on Mars The other large impact basins on Mars Argyre and Hellas Basins also have circumferential olivine-rich exposures e g Ody et al 2013 However we did not identify any serpentine-bearing surfaces near the olivine-rich exposures around Argyre Basin and only identified one location with serpentine regionally near an olivine-enriched exposure on the northern rim of Hellas Basin Figure 4 8 Additionally the olivine-rich surfaces near Nili Fossae have morphological and 145 compositional differences from those found around the other large impact basins The circumferential olivine associated with both Argyre and Hellas Basins are typically discontinuous and are found on the crests of knobs in hilly terrain e g Ody et al 2013 Additionally the concentration of olivine at Nili Fossae is higher than for the other two large-scale circumferential olivine exposures around Argyre and Hellas Basins and may also have a larger olivine grain sizes Ody et al 2013 It may be that the expansive and continuous exposures of relatively high olivine abundances in Nili Fossae e g Ody et al 2013 aided in the initiation and continuation of serpentinization in the region However the fact that unaltered olivine remains in the area and it is only variably altered to serpentine carbonate and talc saponite implies that the amount of serpentinization that occurred in the area was limited and the reactions did not go to completion perhaps due to limited water availability Amador et al in revision Chapter 3 The other geologically unique aspect to Nili Fossae relative to other sites with olivine-enriched bedrock is its proximity to the large Syrtis Major volcanic province Syrtis Major was active beginning in the early-Hesperian 3 7 Gya Hiesinger and Head 2004 this regional heat source in conjunction with the extensively fractured nature of the region e g Saper and Mustard 2013 and the olivineenriched protolith may have provided the necessary conditions for a well-established low-temperature serpentinizing system likely in the subsurface These reactions would have lasted long enough to variably alter the olivine-rich basalt to serpentine with subsequent alteration to both Mg-carbonate and talc e g Viviano et al 2013 Amador et al in revision Chapter 3 4 6 SUMMARY AND CONCLUSIONS Minerals associated with serpentinization reactions such as serpentine Mg-carbonate talc saponite have been identified across the southern highlands of Mars Though found widespread occurrences of these phases are still limited These detections are not typically spatially correlated with one another or with ultramafic exposures as initially predicted except for in Nili Fossae 146 Serpentine detections were typically only made possible using target transformation techniques of the available spectral data not using I F spectral ratios implying that serpentine concentrations are low albeit present when taking all the available spectral information from a given scene into account However their presence across the southern highlands is widespread implying global serpentinization processes likely occurring early in martian history as most exposures are reworked Noachian terrains Some exceptional regional to local settings were also highlighted using factor analysis and target transformation Leighton Crater and Mawrth Vallis though previously recognized as having highly altered phases at exceptionally high volumes in Mawrth Vallis now show additional evidence for more pervasive serpentinization and other phases such Ca- or Fe-carbonate and Al-phyllosilicates The serpentine detected in these two regions are low in concentration relative to the other phases identified in the region and similarly necessitated the use of target transformation and may be representative of the global low-concentration serpentine detected across the highlands Especially in the case of Mawrth Vallis the results of this study highlight the range and concentration of phyllosilicates present in the region Lastly Nili Fossae stands out as a unique locale with clear detections of serpentine Mgcarbonate and a talc saponite spectral phase likely to be more consistent with talc in this case all within a well-defined olivine-rich layer indicating a once in-situ low-temperature serpentinizing system in the region The astrobiological potential for Nili Fossae due to serpentinization has been discussed in detail in Amador et al in revision Chapter 3 This study shows that a minerals associated with serpentinization are more pervasive in Nili Fossae than previously thought and b that this region is unique across Mars where we have access to exposures of the martian surface from available remote sensing data In the search for once habitable environments on Mars Nili Fossae provides some of the most direct evidence for once having substantial aqueous activity under relatively low temperatures a 147 chemical means for metabolic energy in the form of H2 and the geochemical means for creating loworder organics that are common in serpentinizing systems like CH4 These reactions appear to have occurred in-situ particularly concentrated in the eastern portion of Nili Fossae around and to the south of the carbonate plains From an astrobiological standpoint this region stands out as a compelling site for detailed analyses by future landed missions 148 Chapter 5 CONCLUSIONS The search for habitable environments on Mars will continue over the next decades with several new rovers and landers slated for launch by NASA and the European Space Agency in addition to the inevitable human exploration of the martian surface that is to come To send these exploration missions to the most promising locales for the highest scientific return requires the detailed interrogation of available orbital datasets Given that many of NASA s scientific objectives rally behind the common goal of understanding the potential for habitable environments beyond modern Earth the future of Mars exploration will require the adjustment of goals currently driven by the search for hydrated and aqueous environments to the more refined search for environments that show compelling evidence for metabolic energy sources a means for acquiring organics and nutrients in addition to clement aqueous conditions Furthermore with the ever-increasing load of planetary mission data being returned to Earth from Mars new ways of analyzing spectral datasets will provide a more comprehensive understanding of the martian surface This dissertation advances our understanding of the past aqueous history and habitability potential of key locales on Mars by: 1 demonstrating that the Nili Fossae capping unit previously thought to be unaltered shows evidence for elevated concentrations of bulk-silica likely due to increased aqueous activity and adding to the known mineralogical diversity in the region 2 demonstrating that the spectral suite and therefore minerals observed within the olivine-rich basalt unit in Nili Fossae are similar to those from the Lost City Hydrothermal Field on Earth implying a once habitable low-temperature serpentinizing system in the regions past and 3 investigating the distributions of minerals associated with serpentinization across the martian surface from available orbital data concluding that regionalscale near-surface serpentinizing systems were rare on Mars with the exception of the Nili Fossae region Furthermore this dissertation advances our understanding of ways to best leverage and analyze spectral 149 wavelength regions and datasets by: 1 developing the Weighted Absorption Center Colorized Index maps with THEMIS multispectral data and showing that these indices can be correlated with nearinfrared CRISM spectral data 2 using thermal-infrared emissivity measurements in concert with nearinfrared reflectance measurements to fully describe the bulk composition and spectral characteristics of an Earth astrobiological and spectral analog site to Nili Fossae Mars and 3 applying factor analysis and target transformation methods to the CRISM dataset in a global and comprehensive manner to find locales containing minerals associated with serpentinization that would have otherwise been missed using traditional analysis techniques I include summaries of these findings below 5 1 SUMMARY OF WORK Chapter 2 The Nili Fossae region of Mars contains some of the most mineralogically diverse bedrock on the planet Previous studies have established three main stratigraphic units in the region: a phyllosilicate-bearing basement rock a variably altered olivine-rich basalt and a capping rock Chapter 2 presents evidence for the localized alteration of the northeast Nili Fossae capping unit previously considered to be unaltered Both near-infrared and thermal-infrared spectral datasets were analyzed including the application of a method for determining the relative abundance of bulk-silica SiO2 over surfaces using Thermal Emission Imaging System THEMIS images Elevated bulk-silica exposures are present on surfaces previously defined as unaltered capping rock Given the lack of spectral evidence for phyllosilicate hydrated silica or quartz phases coincident with the newly detected exposures - the elevated bulk-silica may have formed under a number of aqueous scenarios including as a product of the carbonation of the underlying olivine-rich basalt under moderate water:rock scenarios and temperatures Regardless of formation mechanism the detection of elevated bulk-silica exposures in the Nili Fossae capping unit extends the history of aqueous activity in the region to include all three of the main stratigraphic units 150 Chapter 3 Low-temperature serpentinization is a critical process with respect to Earth s habitability and the Solar System Exothermic serpentinization reactions often produce hydrogen as a direct byproduct and typically produce short-chained organic compounds indirectly Chapter 3 presents the spectral and mineralogical variability in rocks from the serpentine-driven Lost City Hydrothermal Field on Earth and the olivine-rich region of Nili Fossae Mars Near- and thermal-infrared spectral measurements were made from a suite of Lost City rocks at wavelengths like those for instruments collecting measurements of the martian surface Results from Lost City show a spectrally distinguishable suite of Mg-rich serpentine Ca-carbonates talc and amphibole minerals Aggregated detections of low-grade metamorphic minerals in rocks from Nili Fossae were mapped and yielded an additional serpentine exposure in the region previously undetected Direct comparison of the two spectral suites indicate similar mineralogy at both the Lost City Hydrothermal Field Earth and in the Noachian 4 to 3 7 Ga bedrock of Nili Fossae Mars Based on mapping of these spectral phases the implied mineralogical suite appears to be extensive across the region and implies that serpentinization was once an active process implying sustained liquid water an energy source and a means for prebiotic chemistry during a period when life was first emerging on Earth Although the mineralogical assemblages identified on Mars are unlikely to be directly analogous to rocks that underlie the Lost City Hydrothermal Field it is likely that similar geochemical processes and associated sources of biologically-accessible energy were once present in the subsurface making Nili Fossae a compelling candidate for a once-habitable environment on Mars Chapter 4 Chapter 4 aimed to understand the global distribution of minerals associated with serpentinization like those found in Nili Fossae and their relationship if any to other ultramafic regions on Mars This distribution would provide a better understanding of the regions on Mars that once had the highest potential for habitability To do this we performed a comprehensive analysis of the entire CRISM 151 spectral dataset Given the magnitude of images 13 000 and the subtle weak spectral features associated with serpentine we used factor analysis and target transformation methods to efficiently parse through the available CRISM data These methods not only allow for the timely analysis of thousands of images but provide a quantitative means to determine the significant spectral constituents of an image even if they are only contained as spectral mixtures These methods resulted in a global distribution map of CRISM images with a significant likelihood of containing the spectral types of interest The methods used were successful in corroborating previous detections of serpentine using traditional CRISM analysis techniques and found additional detections across the martian southern highlands Serpentine detections were not particularly associated with ultramafic regions or with other mineral phases investigated Mgcarbonate and talc saponite other than in Nili Fossae Most serpentine detections were found in isolated exposures associated with crater ejecta knobby terrain or as part of discontinuous layers in crater or valley walls Some serpentine detections were found within a more complicated geologic or mineralogical context such as in Claritas Rise in Mawrth Vallis and in Nili Fossae Overall the detection of serpentine from orbit were quite rare though detections were found dispersed across the southern Highlands Nili Fossae showed more pervasive and extensive detections of serpentine than previously thought particularly in the eastern portion of Nili Fossae where the highest concentration of olivine-rich basalts is located These findings imply that large regional-scale near surface serpentinizing systems were likely rare on Mars at least as observable today Low-concentration serpentine detections across the southern highlands do however point to a global serpentinization system likely early in Mars history when the planet was more geologically active Nili Fossae appears to be unique amongst other olivine-enriched regions potentially due to its proximity to the nearby Syrtis Major volcanic province Northeast Nili Fossae shows the strongest evidence for a sustained low-temperature serpentinizing system in its history and is a compelling site for further study with respect to astrobiology 152 5 2 FUTURE WORK The fourth chapter of this dissertation demonstrated the power of factor analysis and target transformation applied to specific scientific questions like the distribution of minerals associated with serpentinizing systems on Mars Similar global-scale questions remain elusive in Mars research and the ability to parse through thousands of images in an efficient and quantitative manner can provide substantial support to the types of interpretations made from the terabytes of available data One of these outstanding questions that could be supported using factor analysis and target transformation involves the nature of the martian atmosphere and the reconciliation of contradicting predications for atmospheric CO2 stored as carbonate in the surface and near-subsurface of Mars Orbital and ground based observations indicate episodes of sustained liquid water on the martian surface while both empirical observations and theoretical models indicate low atmospheric pressure for much of Mars history thereby precluding the stability of liquid water One important piece to this puzzle is understanding the occurrence of carbonates a potential sink for atmospheric CO2 in contact with liquid water Additionally recent literature provides highly varying constraints on the martian carbonate 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the Hellas and Isidis Impact Basins on Mars J Geophys Res 94 17 333 17 357 Williams K B Sonzogni Y Treiman A H 2014 Amphibole in the Tissant Martian Meteorite: Composition and Implication for Volatile Content of Parental Magma 45th Lunar and Planetary Science Conference Abs 1435 170 Wray J J Ehlmann B L Squyres S W Mustard J F Kirk R L 2008 Compositional stratigraphy of clay-bearing layered deposits at Mawrth Vallis Mars Geophysical Research Letters 35 L12202 Wray J J S T Hansen J Dufek G A Swayze S L Murchie F P Seelos J R Skok R P Irwin Iii and M S Ghiorso 2013 Prolonged magmatic activity on Mars inferred from the detection of felsic rocks Nature Geosci 6 12 1013-1017 doi: 10 1038 ngeo1994 Wray J J Murchie S L Bishop J L Ehlmann B L Milliken R E Wilhelm M B Seelos K D Chojnacki M 2016 Orbital evidence for more widespread carbonate-bearing rocks on Mars Journal of Geophysical Research: Planets 121 652-677 Doi:10 1002 2015JE004972 171 SUPPLEMENTARY MATERIAL Table 5 8 Initial THEMIS Day IR DCS 8-7-5 images visually inspected for compositional variability and Purple THEMIS Product ID I02244005 I36226026 I36638042 I18432016 I01283009 I02394009 I36251026 I36713013 I18607041 I01308005 I02444002 I36276032 I36775013 I18744008 I01308005 I02469002 I36301013 I36800017 I18919007 I01595009 I02494006 I36326013 I36875018 I19006009 I01645007 I02631005 I36351028 I36900022 I19031010 I01770008 I02706002 I36426026 I37062019 I19056011 I01982006 I02731002 I36538025 I37087020 I19081013 I01982006 I02781003 I36613020 I37112002 I19181014 I02007009 I03505002 I36688013 I37187009 I19206009 I02032005 I36925042 I37262020 I19543016 I03555002 I02057002 I37237015 I37287050 I19830005 I04491005 I02319008 I37499019 I37349016 I22251040 I02344005 I04741008 I37549006 I37374015 I26057010 I02519006 I05215009 I37786007 I37524007 I26606030 I02681006 I05490020 I38360010 I37811010 I26631016 I02756002 I05515022 I39296009 I37861031 I26831012 I03430002 I05827010 I39533002 I38173010 I27018033 I04566009 I07974020 I39608004 I38410010 I27093046 I05727011 I08798006 I43901003 I38460008 I33468008 I09609022 I10158009 I44263002 I38485006 I35240010 I10283010 I10258011 I44288005 I38622040 I11094006 I35602005 I10308046 I44413003 I38909007 I35727009 I11743007 I10470015 I44750003 I38934013 I35752006 I13278010 I10645014 I45087012 I39009007 I13303004 I35777009 I11668005 I45137009 I43876003 I13565008 I35802012 I11843005 I45499019 I13927007 I35864010 I12467007 I44001007 I45549047 I17908015 I35889015 I12492006 I44026005 I45811018 I18195011 I35914015 I12679004 I44238003 I45861011 I18457007 I35939015 I13253008 I44500002 I46173009 I18532009 I36014018 I13690011 I44600002 I46223006 I36039022 I18769007 I17072009 I44675009 I47484014 I19106013 I36064012 I17471015 I44725002 I47796006 I19755006 I36089015 I17783020 I44912007 I47896005 I27043033 I36114022 I17808018 I45012009 I48208013 I28216011 I36151021 I18095022 I45112007 I52029004 I28478006 I36176021 I18145014 I45374016 I52054004 I28528002 I36201025 I18220006 I45424044 I01570009 I35390009 I36376029 I18270012 I45686010 I01857006 I35677010 I36401029 I18295015 I45836007 I01932008 I35964015 I36488026 I18320008 I45886016 I02194005 I35989015 I36513026 I18357015 I45911007 172 I45936008 I46011010 I46298007 I46348016 I46373018 I46435017 I46872007 I47097024 I47646011 I47821006 I47871005 I51292006 I52491007 I52741007 I52853010 I52903017 I52978009 I53003013 I53153006 I53540006 173 Table 5 9 Down-selected high quality THEMIS images with Purple and Yellow Amber Units in regional proximity These THEMIS images were atmospherically correct and used for all further TIR analyses THEMIS Image ID I01308005 I01595009 I01982006 I02007009 I02319008 I02681006 I02731002 I03430002 I09609022 I18532009 I35390009 I36613020 I39296009 I39533002 I39608004 I44288005 I47484014 174 Table 5 10 THEMIS line and sample numbers used for spectra in Figure 2 6 THEMIS ID Spectral Type I36613020 I36613020 I36613020 I36613020 I36613020 Typical terrain Amber Yellow Purple Phyllosilicatebearing typical terrain Fuchsia Orange 161-216 I35390009 X-axis Pixel Numbers 41-44 106-107 141-148 123-131 52-58 Y-axis Pixel Numbers 413-416 523-526 838-848 516-525 409-415 Bands 1086-1113 3-9 3-9 3-9 3-9 3-9 3-9 175 Table 5 11 CRISM Multispectral Product images IDs listed below were visually inspected for 8 phase and or hydration index maps A qualitative and subjective characterization of yes or no was assigned to each index if high index values were or were not present in a structurally coherent formation CRISM Product OLINDEX BD1900 BD2100 SINDEX ID 0000366C_01 yes yes no no 000037E8_03 yes no no no 0000397F_05 yes yes no no 00004FD2_01 yes no no no 000052D4_01 yes no no no 000058B0_01 yes yes no no 00005AC1_01 000062D3_01 000070A8_05 00007526_07 00007C18_01 000080AF_03 0000902D_01 0000C752_01 000106BC_03 00012518_01 00013755_01 00014007_01 00015218_01 0001582D_05 0001969A_01 0001A9F9_01 0001ACED_01 00026F8F_01 Dusty or noisy image yes yes x yes yes yes yes yes yes no yes yes yes yes yes yes yes no no yes x yes yes no yes yes yes no yes yes no yes no yes yes no no no x no no no no no no no no no no no no no no no no no x no no no no no no no no no no no no no no no BD2210 BD2250 D2300 BD2500 no no no no no no no no no no no no yes no yes no no yes no no no no no no no no x no no no no no no no no no no no no no no no no no x no no no no no no no no no no no no no no no no yes x yes yes no yes yes yes no yes yes no yes no yes yes no no no x no no no no no no no no no no no no no no no 176 Table 5 12 CRISM Multispectral Image IDS used in Figure 2 7 Images were cropped between 19 0 and 25 0 N CRISM Product ID MSP0000B32F_01_IF214L_TRR3 MSP00002F1D_01_IF214L_TRR3 MSP00002F1D_03_IF214L_TRR3 MSP0000B5AC_01_IF214L_TRR3 MSP0000366C_01_IF214L_TRR3 MSP0000C752_01_IF214L_TRR3 MSP000036A9_03_IF214L_TRR3 MSP0000CD24_01_IF211L_TRR3 MSP000037E8_03_IF214L_TRR3 MSP0000CE39_01_IF211L_TRR3 MSP0000397F_05_IF214L_TRR3 MSP0001028C_05_IF214L_TRR3 MSP00003F2C_03_IF214L_TRR3 MSP000106BC_03_IF214L_TRR3 MSP00004FD1_07_IF214L_TRR3 MSP00010AB0_01_IF214L_TRR3 MSP00004FD2_01_IF214L_TRR3 MSP0001138D_01_IF214L_TRR3 MSP0000516B_01_IF214L_TRR3 MSP0001185D_01_IF214L_TRR3 MSP000052D4_01_IF214L_TRR3 MSP0001185D_03_IF214L_TRR3 MSP000056D8_01_IF214L_TRR3 MSP00012F58_01_IF214L_TRR3 MSP000058AF_07_IF214L_TRR3 MSP00013755_01_IF214L_TRR3 MSP000058B0_01_IF214L_TRR3 MSP0001396B_01_IF214L_TRR3 MSP00005AC1_01_IF214L_TRR3 MSP0001396C_01_IF214L_TRR3 MSP000062D3_01_IF214L_TRR3 MSP00014007_01_IF214L_TRR3 MSP000062D3_03_IF214L_TRR3 MSP0001423B_03_IF214L_TRR3 MSP00006DD9_07_IF214L_TRR3 MSP0001423B_05_IF214L_TRR3 MSP000070A8_05_IF214L_TRR3 MSP000148C2_01_IF214L_TRR3 MSP000070A8_07_IF214L_TRR3 MSP00014DA9_01_IF214L_TRR3 MSP00007526_07_IF214L_TRR3 MSP00015218_01_IF214L_TRR3 MSP00007A27_05_IF214L_TRR3 MSP0001582D_05_IF214L_TRR3 MSP00007A27_07_IF214L_TRR3 MSP0001BA1F_01_IF214L_TRR3 MSP00007C18_01_IF214L_TRR3 MSP0001C6C5_01_IF213L_TRR3 MSP000080AF_03_IF214L_TRR3 MSP0001C6C6_01_IF213L_TRR3 MSP00008DEE_01_IF214L_TRR3 MSP0001DE75_01_IF214L_TRR3 MSP00008E3E_01_IF214L_TRR3 MSP00026F8F_01_IF213L_TRR3 MSP0000902D_01_IF214L_TRR3 MSP000271E3_01_IF211L_TRR3 MSP0000941C_01_IF214L_TRR3 177 Table 5 13 CRISM MSP sample and line numbers for spectra used in Figure 2 9 Location Spectral CRISM ID Type Olivine-rich Basalt MSP0000366C_01 Phyllosilicatebearing Fuchsia Orange MSP0000366C_01 MSP000037E8_03 Numerator Target Pixels X: 58-61 Y:1023-1027 X: 53-55 Y:1068-1073 X: 25-37 Y: 1901- 1918 Denominator null known Pixels X: 58-61 Y: 988-992 X: 53-55 Y: 966-972 X:25-37 Y: 1754-1771 Bands 5: 5: 5: 178 Table 5 14 CRISM MSP sample and line numbers used for Yellow Amber Unit spectrum in Figure 2 9 CRISM ID Numerator Target Pixels MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 MSP0000366C_01 Bands X: 54-55 Y: 1032-1033 X: 54-55 Y: 1032-1033 X: 53-54 Y: 1034-1035 X: 55-57 Y: 1033-1036 X: 56-58 Y: 1035-1036 X: 55-56 Y: 1035-1037 Denominator null known Pixels X: 54-55 Y: 1012-1013 X: 54-55 Y: 197-978 X: 53-54 Y:1012-1013 X: 55-57 Y: 981-984 X: 56-58 Y: 973-975 X: 55-56 Y: 973-975 X: 34-35 Y: 1117-1118 X: 6-7 Y: 1114-1115 X: 34-35 Y: 1147-1148 X: 6-7 Y: 1142-1143 5: 5: 5: 5: 5: 5: 5: 5: 179 Table 5 15 Spectral end-member library used for thermal-infrared deconvolution modeling Unless otherwise noted spectra come from the ASU Spectral Library speclib asu edu Mineral Group Serpentine Phyllosilicate Feldspar Mineral Name Mineral ID Antigorite HS-8 4B Antigorite BUR-1690 Antigorite NMNH96917 Chrysotile JB-528 Lizardite ECL-SRP109 Lizardite NMNHR4687 b Chlorite WAR-1924 Illite Imt-1 Montmorillonite Swy-1 Nontronite Nau-1 Saponite Eb-1 Saponite MINUN-29 Talc BUR-4640C Andesine BUR-240 Albite WAR-0612 Labradorite WAR-4524 Perthite WAR-5802 Bytownite WAR-1384 Labradorite WAR-RGAND01 Labradorite BUR-3080A Anorthite WAR-5759 180 Mineral Group Mineral Name Mineral ID Oligoclase WAR-0234 Microcline BUR-3460 Anorthoclase WAR-0579 Orthoclase WAR-RGSAN01 Mg-Hornblende HS-315 4B Anthophyllite BUR-4760 Actinolite HS-116 4B Fe-Hornblende HS-326 4B Hornblende BUR-2660 Tremolite WAR-0979 Hornblende NMNH-R7208 Glaucophane WAR-0219 Calcite ML-C9 Aragonite C11 Dolomite C20 Magnesite C60 Siderite C62 Calcite C2 Dolomite C17 Pyroxene Spodumene HS-210 4B Pyroxenoid Wollastonite WAR-8884 Pyroxmangite WAR-6894 Bronzite BUR-1920 Amphibole Carbonate Orthopyroxene 181 Mineral Group Mineral Name Mineral ID Enstatite HS-9 4B Diopside HS-15 4B Augite HS-119 4B Augite BUR-620 Hedenbergite NMNH-R11524 Diopside BUR-1820 Apatite ML-P1 Meta-Variscite ML-P8 Pyromorphite ML-P6 Turquoise ML-P5 Pyromorphite ML-P3 Forsterite BUR-3720A Fayalite WAR-RGFAY01 Muscovite WAR-5474 Biotite BUR-840 Phlogopite HS-23 3B Epidote Epidote BUR-1940 Iron Oxide Hematite BUR-2600 Hematite GTSH4-300 Goethite GTS4 Magnetite WAR-0384 Ilmenite WAR-4119 Quartz BUR-4120 Clinopyroxene Phosphate Olivine Mica Quartz 182 Mineral Group Mineral Name Mineral ID Chert 56 Gypsum ML-S5 Barite ML-S1 Selenite ML-S8 Almandine BUR-120A Pyrope WAR-5850 Malachite C13 Azurite C14 Kyanite WAR-4482 Andalusite WAR-0482 Sillimanite WAR-7362 Opal Opal-CT 02-031 Hydroxide Brucite RAN-45 Sulfate Garnet Hydrous Carbonate Al-Silicate Clark et al 2007 CRISM Library CHRYSOTILE W15 FROM D DYAR COLLECTION SEEO_HANLEY & DYAR 1998 ASBESTOS FIBERS Bishop et al 2002B 183 Table 5 16 CRISM images taken after 2011 these images were not looked at by previous studies and were searched for this study FRS00031442_01_IF168L_TRR3 HRS00024571_07_IF175L_TRR3 FRS00031260_01_IF168L_TRR3 HRS0001EC8F_07_IF174L_TRR3 FRS00031204_01_IF168L_TRR3 HRS0001EBA1_07_IF174L_TRR3 FRS00030232_01_IF168L_TRR3 HRS0001E23E_07_IF175L_TRR3 FRS000301CF_01_IF168L_TRR3 HRL0002422E_07_IF182L_TRR3 FRS0002FE75_01_IF168L_TRR3 HRL00024023_07_IF183L_TRR3 FRS0002FE20_01_IF168L_TRR3 HRL00020BA3_07_IF183L_TRR3 FRS0002F056_01_IF168L_TRR3 HRL0001FC92_07_IF182L_TRR3 FRS0002EE3C_01_IF168L_TRR3 HRL0001E20D_07_IF183L_TRR3 FRS0002EC89_01_IF168L_TRR3 HRL0001D976_07_IF183L_TRR3 FRS0002DE3A_01_IF168L_TRR3 HRL0001D93D_07_IF182L_TRR3 FRS0002DC3A_01_IF168L_TRR3 FRT000251C0_07_IF165L_TRR3 FRS0002DA94_01_IF168L_TRR3 FRT00024C1A_07_IF165L_TRR3 FRS0002DA46_01_IF168L_TRR3 FRT00024A87_07_IF165L_TRR3 FRS0002CABF_01_IF168L_TRR3 FRT000246CF_07_IF166L_TRR3 FRS0002C92B_01_IF168L_TRR3 FRT00023728_07_IF166L_TRR3 FRS0002C8E9_01_IF168L_TRR3 FRT00023565_07_IF166L_TRR3 FRS0002BB98_01_IF168L_TRR3 FRT00021F08_07_IF165L_TRR3 FRS0002BA97_01_IF168L_TRR3 FRT00021DA6_07_IF166L_TRR3 FRS0002B58A_01_IF168L_TRR3 FRT00021C5A_07_IF166L_TRR3 FRS0002B44A_01_IF168L_TRR3 FRT00020C77_07_IF166L_TRR3 FRS0002B2F2_01_IF168L_TRR3 FRT000203DE_07_IF165L_TRR3 FRS0002AF61_01_IF168L_TRR3 FRT0001FD76_07_IF166L_TRR3 FRS0002AE17_01_IF168L_TRR3 FRT0001FB74_07_IF166L_TRR3 FRS0002ADC4_01_IF168L_TRR3 FRT0001ECBA_07_IF166L_TRR3 FRS0002AC52_01_IF168L_TRR3 FRS00039936_01_IF168L_TRR3 FRS0002A9B2_01_IF168L_TRR3 FRS00038CD4_01_IF168L_TRR3 FRS00029FDB_01_IF168L_TRR3 FRS00038C02_01_IF168L_TRR3 FRS00029EEC_01_IF168L_TRR3 FRS00038BC9_01_IF168L_TRR3 FRS00029EA8_01_IF168L_TRR3 FRS00037F03_01_IF168L_TRR3 FRS00029DA6_01_IF168L_TRR3 FRS00037D63_01_IF168L_TRR3 FRS00028DFB_01_IF168L_TRR3 FRS00036666_01_IF168L_TRR3 FRS0002842A_01_IF168L_TRR3 FRS00036634_01_IF169L_TRR3 FRS00028280_01_IF168L_TRR3 FRS000364CA_01_IF168L_TRR3 FRS000281D1_01_IF168L_TRR3 FRS000355D1_01_IF168L_TRR3 FRS0002762C_01_IF168L_TRR3 FRS000328A0_01_IF168L_TRR3 FRS0002753B_01_IF168L_TRR3 FRS00032837_01_IF166L_TRR3 FRS00027508_01_IF169L_TRR3 FRS0003166F_01_IF168L_TRR3 FRS000273E6_01_IF168L_TRR3 FRS0003161E_01_IF168L_TRR3 FRS000272AC_01_IF168L_TRR3 FRS0003161D_01_IF169L_TRR3 184 Table 5 17 Thermal-infrared deconvolution model results for the non-carbonate rocks used for this study Rows highlighted in green indicate abundances well within the detection limits for this study Rows highlighted in red fall within known limits of the technique and can be noted but should not be used quantitatively 185 186 187 Serpentinite Spectral Type E Endmember Lizardite Serp BUR Antigorite Synthetic-packed Goethite Ilmenite Hematite Anorthite Forsterite Chrysotile Apatite Meta-variscite Quartz Calcite Opal-CT Goethite-derived Hematite Chert Turquoise Group Serpentine Serpentine Iron Oxide Iron Oxide Iron Oxide Feldspar Olivine Serpentine Phosphate Phosphate Quartz Carbonate Opal Iron Oxide Quartz Phosphate Normalized Abundance % 40 48 14 98 10 72 7 94 5 84 3 36 2 93 2 74 2 42 2 04 1 84 1 46 1 19 0 97 0 77 0 33 188 Table 5 18 New CRISM detections of Mg-carbonate Talc and or saponite and serpentine in Nili Fossae from this study Images correspond to stamps mapped in Figure 3 8 New Mg- New New Serpentine Carbonate Talc Saponite Detections Detections Detections FRT00003F75_07 FRT00023728_07 FRS0002AE17_01 FRT0000527D_07 FRS0002AE17_01 FRT00005A3E_07 FRS00027639_01 FRT000067E1_07 FRS0003161D_01 FRT000069CA_07 FRS00036666_01 FRT0000722C_07 FRT00007D61_07 FRT00008530_07 FRT00009971_07 FRT0000B1B5_07 FRT0000BEEB_07 FRT0000C62B_07 FRT0000C968_07 FRT000107A7_07 FRT0001182A_07 FRT00012149_07 FRT000161EF_07 FRT000165F7_07 FRT00016A73_07 FRT00017103_07 FRT000174F4_07 FRT0001821C_07 FRT00018524_07 189 New Mg- New New Serpentine Carbonate Talc Saponite Detections Detections Detections FRT000186FA_07 FRT00021F08_07 FRT00023565_07 FRT00023728_07 FRS00029EEC_01 FRS0002AE17_01 FRS0002B2F2_01 FRS0002BA97_01 FRS0002FE75_01 FRS00031260_01 FRS00031442_01 FRS00036666_01 FRS00037F03_01 HRL00006408_07 HRL000086CA_07 HRL0000A8EC_07 HRL0000AB0A_07 HRL0000CC16_07 190 Table 5 19 CRISM sample and line numbers for spectra shown in Figure 3 9 and Figure 3 10 FIGURE CRISM Image ID Label Number 3 9 FRT00003E12_07 Olivine-rich Numerator Denominator column row column row 133-137 274- 133-137 258-262 278 Mg-carbonate- 136-140 bearing 107 FRT0000ABCB_07 Mg-serpentine- 103- 136-140 211-215 253-257 60-62 253-257 17 bearing FRT0000A053_07 Talc saponitebearing 3 10 FRS0002AE17_01 CRISM Talc 104-108 409- 104-108 416-421 413 151-156 175- 151-156 155-147 181 CRISM 79-82 129-131 79-82 142-143 Serpentine CRISM 489-497 Carbonate 126 120- 489-497 107-113 191 Table 5 20 Reference Spectra for Library Spectrum for Figure 4 1 Endmember Reference Sample ID Serpentine Bishop et al 1995 LACR01 Talc JPL ASTER Spectral PS-14A Library Saponite Bishop et al 1995 LASA51 Mg-Carbonate Mustard and Pieters CACB06 1989 Ca-Carbonate Mustard and Pieters E95-15A 1989 Fe-Carbonate Mustard and Pieters CBCC07 1989 192 VITA Elena Sophia Amador Esamador at uw edu 831 295-1117 Education Ph D in Earth and Space Sciences and Astrobiology University of Washington UW 2017 Dissertation: Characterizing Habitable Environments on Mars using Infrared Spectroscopy From Orbit B S in Earth and planetary sciences concentration in planetary sciences minor in astrophysics University of California Santa Cruz 2010 Grants 2016-2020 2014-2015 2013 NASA Planetary Science and Technology Through Analog Research Co-I Field Exploration and Life Detection Sampling for Planetary and Astrobiology Research FELDSPAR current NASA Mars Data Analysis Program Student Co-I Integrated Analyses of Martian Surface Compositions Using Near-Infrared through Thermal-Infrared Spectroscopic Data past American Philosophical Society Lewis and Clark Fund for Research PI 5 K Towards Revealing the Habitability Productivity and Microbial Diversity of Icelandic Lava Fields: An Interdisciplinary Approach Manuscripts in Preparation Amador E S Bandfield J L and N H Thomas A search for minerals associated with serpentinization across Mars using CRISM spectral data Icarus Salvatore M R Goudge T A Bramble M S Edwards C S Bandfield J L Amador E S Ehlmann B L Mustard J F and P R Christensen Bulk mineralogy of the NE Syrtis and Jezero crater regions of Mars derived through thermal-infrared spectral analyses Icarus Manuscripts in Review Revision Amador E S Bandfield J L Brazelton W J and D S Kelley The Lost City Hydrothermal Field as a spectroscopic and astrobiological Analog for Nili Fossae Mars Astrobiology in revision Gentry D M Amador E S Cable M L Chaudry N Cullen T Jacobsen M B Murukesan G Schwieterman E W Stevens A H Stockton A Tan G Yin C Cullen D C Geppert W Correlations between life-detection techniques and implications for sampling site selection in planetary analogue mission Astrobiology in revision Cloutis E A Jonatanson V Bandfield J L Amador E S Rivera-Hern ndez F Mann P and S A Mertzman Hydrothermally-altered dacite terrains in the Methana peninsula Greece: Relevance to Mars Planetary and Space Sciences in revision Published Manuscripts Amador E S and J L Bandfield Elevated bulk-silica exposures and evidence for multiple aqueous alteration episodes in Nili Fossae Mars Icarus doi:10 1016 j icarus 2016 04 015 2016 Bandfield J L and E S Amador Extensive aqueous deposits at the base of the dichotomy boundary in Nilosyrtis Mensae Mars Icarus doi: 10 1016 j icarus 2016 04 002 2016 Amador E S et al Synchronous in-field application of life detection techniques in planetary analog 193 missions Planetary and Space Science http: dx doi org 10 1016 j pss 2014 11 006 2014 Bandfield J L Amador E S and N Thomas Extensive Hydrated Silica Materials in western Hellas Basin Mars Icarus 10 1016 j icarus 2013 08 005 2013 McKeown N Bishop J Cuadros J Hillier S Amador E S Makarewicz H Parente M and E Silver Interpretation of Reflectance Spectra of Clay Minerals- Silica Mixtures: Implications for Martian Clay mineralogy at Mawrth Vallis Clay and Clay Minerals 2011 Oral Presentations Invited 2017 2016 2015 2014 Searching for habitable environments on Mars: Using Serpentinization as a Tracer Western Washington University Department of Geology Colloquium Jan 10 2017 Spectral Evidence for Serpentinization on Mars: Implications for Habitability Centro de Astrobiologia Madrid Spain Sept 23 2016 What can the surface of Mars tells us about ancient habitability University of Washington NASA Space Grant Research Seminar May 1 2015 Water and Weathering Profiles on Mars: Implications for Ancient Habitability University of Washington Department of Forestry Water Soils and Watersheds Seminar Jan 10 2014 Conferences 2016 2016 2014 2013 2012 The Lost City Hydrothermal Field: A Spectroscopic and Astrobiological Analog for Nili Fossae Mars 4th International Serpentine Days Conference Sete France Spectral Characteristics of Dark Slope Streaks on Mars: A Global Survey with CRISM Lunar and Planetary Science Conference XLVII 2696 Alteration of Olivine-rich Basalts on Mars: A THEMIS CRISM Joint Investigation Lunar and Planetary Science Conference XLV 1521 The Lost City Hydrothermal Field: A Spectroscopic and Astrobiological Analog for Nili Fossae Mars Lunar and Planetary Science Conference XLIV 2742 Elevated Bulk Silica Deposits in Nili Fossae Mars: Implications for Habitability Astrobiology Science Conference Atlanta Georgia Conference Poster Presentations 2015 2012 2011 2010 2009 Localized Alteration of the Capping Unit in Nili Fossae Mars: Evidence for Multiple Episodes of Aqueous Alteration Lunar and Planetary Science Conference XLVI 1189 Elevated Bulk Silica Compositions Associated with Olivine-rich Basalts in Nili Fossae Mars Lunar and Planetary Science Conference XLIII 2508 Mars Aqueous Mineralogy: A Comparison of Thermal Infrared and Visible Near-Infrared Spectral Data European Space Agencies: Exploring Mars Habitability Lison Portugal Regional Mapping and Spectral Analysis of Mounds in Acidalia Planitia Mars Lunar and Planetary Science Conference XLI 1037 Detection of Kaolinite at Mawrth Vallis Mars: Analysis of Laboratory Mixtures and Development of Remote Sensing Parameters Lunar and Planetary Science Conference XXXX 2188 Honors and Awards 2016 2016 David A Johnston Award for Research Excellence presented by the Dept of Earth and Space Sciences University of Washington 5 000 SETI Institute and NASA Astrobiology Institute Travel Award 600 194 2016 2015 2014 2014 2013 2013 2013 2012 2012 2012 2011 2011 2010 Best Overall Planetary or Space Science Presentation at the ESS Dept Gala 250 Distinguished Graduate Student Research Fellowship presented by the UW Earth and Space Science Department 1 quarter RA Distinguished Graduate Student Research Fellowship presented by the UW Earth and Space Science Department 1 quarter RA Lunar and Planetary Institute s Career Development Award 1 000 Stephen E Dwornik Award for Best Graduate Oral Presentation presented by the Planetary Geology Division of the Geological Society of America at LPSC XLIV 500 Geochemical Society Student Travel Grant to 2013 Goldschmidt Conference Florence Italy 1 400 Best Overall Oral Presentation presented by the UW Earth and Space Sciences Dept Research Gala 200 Coombs Fellowship presented by UW Earth and Space Sciences Department 1 quarter RA Chevron Graduate Field Support Award NSF Graduate Research Fellowship Honorable Mention NSF Graduate Research Fellowship Honorable Mention Best Research Poster in Climate Planets and Space presented by the UW Earth and Space Sciences Department 100 NSF IGERT Astrobiology Research Fellow 1 year RA Teaching and Professional Experience 2016 2016 2015 2012 2009 2008-2010 Teaching Assistant ASTROBIO 115 Introduction to Astrobiology UW Teaching Assistant ESS 421 Introduction to Remote Sensing UW Field Instructor Nordic-NASA Astrobiology Summer School Iceland Teaching Assistant ESS 421 Introduction to Remote Sensing UW Lunar and Planetary Institute Intern NASA Johnson Space Center under Dr Carl Allen and Dr Dorothy Oehler Undergraduate Research Assistant SETI Institute under Dr Janice Bishop Workshops Attended 2014 2012 2011 Jet Propulsion Laboratory s Planetary Science Summer School Nordic-NASA Summer School Water Ice and the Origin of Life in the Universe NAI and Centro de Astrobiologia Madrid Spain Astrobiology Summer School Mars Exploration: Unveiling a Habitable Planet Academic Service and Leadership 2016 2015 2014 2014 2013 14 2011- Workshop Organizer for UW Astrobiology Workshop to Mt Rainier Life Detection Techniques in Analog Field Environments September 2016 Executive Secretary NASA Solar System Workings Panel Executive Secretary NASA PDART Panel Executive Secretary NASA PSTAR Panel Graduate Student Representative to the Faculty UW Earth and Space Sciences Department Science Communications Fellow Pacific Science Center Seattle WA
  • 2016
    • A. Truitt, Chad - M.S. Research Paper
      Planetary Penetrators for Sample Return Missions 2016, A. Truitt,Chad,Chad A. Truitt Planetary Penetrators for Sample Return Missions Chad A Truitt A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science University of Washington 2016 Committee: Robert M Winglee Michael McCarthy Erika Harnett Program Authorized to Offer Degree: Earth and Space Sciences Copyright 2016 Chad A Truitt University of Washington Abstract Planetary Penetrators for Sample Return Missions Chad A Truitt Chair of the Supervisory Committee: Professor Robert M Winglee Earth and Space Sciences Sample return missions offer a greater science yield when compared to missions that only employ in situ experiments or remote sensing observations since they allow the application of more complicated technological and analytical methodologies in controlled terrestrial laboratories that are both repeatable and can be independently verified The successful return of extraterrestrial materials over the last four decades has contributed to our understanding of the solar system but retrieval techniques have largely depended on the use of either soft-landing or touch-and-go procedures that result in high V requirements and return yields typically limited to a few grams of surface materials that have experienced varying degrees of alteration from space weathering Hard-landing methods using planetary penetrators offer an alternative for sample return that significantly reduce a mission s V increase sample yields and allow for the collection of subsurface materials and lessons can be drawn from previous sample return missions The following details progress in the design development and testing of penetrator sampler technology capable of surviving subsonic and low supersonic impact velocities 98 I89H: QR 0 2333 F8:8 G 7898: 9
    • Allstadt, Kate - Ph.D. Dissertation
      Surficial Seismology: Landslides, Glaciers, and Volcanoes in the Pacific Northwest through a Seismic Lens 2016, Allstadt,Kate,Kate Allstadt Surficial Seismology: Landslides Glaciers and Volcanoes in the Pacific Northwest through a Seismic Lens Kate Allstadt A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2013 Reading Committee: John Vidale Chair Juliet Crider Stephen Malone Ken Creager Program Authorized to Offer Degree: Earth and Space Sciences Copyright 2013 Kate Allstadt University of Washington Abstract Surficial Seismology: Landslides Glaciers and Volcanoes in the Pacific Northwest through a Seismic Lens Kate Allstadt Chair of the Supervisory Committee: Professor John Vidale Department of Earth and Space Sciences The following work is focused on the use of both traditional and novel seismological tools combined with concepts from other disciplines to investigate shallow seismic sources and hazards The study area is the dynamic landscape of the Pacific Northwest and its wide-ranging earthquake landslide glacier and volcano-related hazards The first chapter focuses on landsliding triggered by earthquakes with a shallow crustal earthquake in Seattle as a case study The study demonstrates that utilizing broadband synthetic seismograms and rigorously incorporating 3D basin amplification 1D site effects and fault directivity allows for a more complete assessment of regional seismically induced landslide hazard The study shows that the hazard is severe for Seattle and provides a framework for future probabilistic maps and near real-time hazard assessment The second chapter focuses on landslides that generate seismic waves and how these signals can be harnessed to better understand landslide dynamics This is demonstrated using two contrasting Pacific Northwest landslides The 2010 Mount Meager BC landslide generated strong long period waves New full waveform inversion methods reveal the time history of forces the landslide exerted on the earth that is used to quantify event dynamics Despite having a similar volume 107 m3 The 2009 Nile Valley WA landslide did not generate observable long period motions because of its smaller accelerations but pulses of higher frequency waves were valuable in piecing together the complex sequence of events The final chapter details the difficulties of monitoring glacier-clad volcanoes The focus is on small repeating low-frequency earthquakes at Mount Rainier that resemble volcanic earthquakes However based on this investigation they are actually glacial in origin: most likely stick-slip sliding of glaciers triggered by snow loading Identification of the source offers a view of basal glacier processes discriminates against alarming volcanic noises and has implications for repeating earthquakes in tectonic environments This body of work demonstrates that by combining methods and concepts from seismology and other disciplines in new ways we can obtain a better understanding and a fresh perspective of the physics behind the shallow seismic sources and hazards that threaten the Pacific Northwest Table of Contents Chapter 1: Landslides triggered by earthquakes: A scenario study of seismically induced landsliding in Seattle using broadband synthetic seismograms Chapter 2: Seismogenic landslides a new way to study landslide dynamics: Part a: Extracting source characteristics and dynamics of the August 2010 Mount Meager landslide from broadband seismograms Part b: The seismic story of the Nile Valley landslide Chapter 3: Glacier-quakes mimicking volcanic earthquakes: Swarms of repeating stick-slip glacial earthquakes triggered by snow loading at Mount Rainier Appendices Appendix 1 Representative Shear Wave Velocity Surficial Profiles for Seattle and Map of Units Chapter 1 Appendix 2 High resolution maps 2 of relative seismically induced landslide hazard for a Mw 7 0 Seattle fault earthquake for dry and saturated soil conditions Chapter 1 Appendix 3 Details of Inversion Methods Chapter 2a Chapter 1 - Landslides triggered by earthquakes: A Scenario Study of Seismically Induced Landsliding in Seattle using Broadband Synthetic Seismograms The content of this chapter was published in: Allstadt K Vidale J E and Frankel A D 2013 A Scenario Study of Seismically Induced Landsliding in Seattle Using Broadband Synthetic Seismograms Bull Seism Soc Am 103 No 6 doi: 10 1785 0120130051 with some added details from: Allstadt K and Vidale J E 2012 Seismically Induced Landsliding in Seattle: A Magnitude 7 Seattle Fault Earthquake Scenario USGS NEHRP Final Tech Report Grant : G11AP20012 39p 1-1 Table of Contents Summary 1-3 1 Introduction 1-4 2 Background 1-8 3 Methods 1-12 4 Synthetic Seismogram Generation 1-14 5 Incorporating Site Amplification 1-19 6 Model Outputs 1-23 7 Validation of Ground Motions 1-25 8 Validation of Landslide Simulation 1-29 9 Results of Landslide Simulation for Mw 7 0 Seattle Fault Earthquake 1-31 10 Infrastructure Impacts 1-36 11 Discussion 1-38 12 Conclusions 1-44 13 Data and Resources 1-46 14 Acknowledgements 1-47 15 References 1-48 1-2 Summary We demonstrate the value of utilizing broadband synthetic seismograms to assess regional seismically induced landslide hazard Focusing on a case study of an Mw 7 0 Seattle fault earthquake in Seattle WA we computed broadband synthetic seismograms that account for rupture directivity and 3D basin amplification We then adjusted the computed motions on a fine grid for 1D amplifications based on the site response of typical geologic profiles in Seattle and used these time series ground motions to trigger shallow landsliding using the Newmark method The inclusion of these effects was critical in determining the extent of landsliding triggered We found that for inertially triggered slope failures modeled by the Newmark method the ground motions used to simulate landsliding must have broadband frequency content in order to capture the full slope displacement We applied commonly used simpler methods based on ground motion prediction equations for the same scenario and found that they predicted far fewer landslides if only the mean values were used but far more at the maximum range of the uncertainties highlighting the danger of using just the mean values for such methods Our results indicate that landsliding triggered by a large Seattle fault earthquake will be extensive and potentially devastating causing direct losses and impeding recovery The high impact of landsliding predicted by this simulation shows that this secondary effect of earthquakes should be studied with as much vigor as other earthquake effects 1-3 1 Introduction Landslides triggered by earthquakes have caused significant damage and casualties worldwide For example seismically triggered landslides were responsible for more than half of the damage caused by the 1964 Good Friday Earthquake in Alaska Keefer 1984 and the 2008 Wenchuan earthquake in China triggered about 60 000 landslides that destroyed entire towns and caused tens of thousands of deaths about a third of the total Yin et al 2009 Huang and Fan 2013 Other recent examples include the 1999 Chi-chi earthquake Hung 2000 and the 1994 Northridge earthquake Harp and Jibson 1996 Despite these examples and calls for more focused attention to this secondary earthquake hazard e g Huang and Fan 2000 Wasowski et al 2000 seismically induced landslide hazard has not been quantitatively investigated or fully incorporated into seismic hazard assessments for many areas that are particularly at risk This is not for a lack of methods Researchers have been developing and implementing methods to assess seismically induced landslide hazard for years Some of these methods use soil and slope characteristics of landslides triggered by past earthquakes either qualitatively e g Stewart 2005 Keefer 1984 or through logistic regressions and neural network analysis e g Lee and Evangelista 2006 Keefer 2000 A limitation is that complete post-earthquake landslide distributions needed for many of these methods are rare Keefer 2002 and the applicability of these methods from one area to a different setting that does not have a similar dataset is an issue More sophisticated methods of estimating coseismic landslide triggering have also been developed such as those using dynamic finite-element modeling to simulate the permanent slope deformations induced by the input ground motion throughout the potential failure mass e g Seed et al 1973 Lee 1974 Prevost 1981 However these types of methods are both computationally intensive and require dense high-quality site-specific soil data in order 1-4 for the modeling efforts to be worthwhile Jibson 2011 Kramer 1996 As a result they are not feasible in most cases and certainly not for regional hazard mapping studies As a compromise between the empirical statistical approaches and detailed numerical models of slope performance the Newmark method Newmark 1965 has emerged as a dominant approach to seismically induced landslide hazard mapping and analysis e g Wilson and Keefer 1983 Jibson et al 2000 Miles and Ho 1999 Ambraseys and Menu 1988 Jibson and Michael 2009 Saygili and Rathje 2009 Variations abound but the core of the method is that slope displacements accumulate each time the ground acceleration exceeds a critical threshold value This threshold value depends on the slope geometry material properties and groundwater conditions The Newmark method is simple enough that it is well suited to regional seismically induced hazard mapping studies Jibson et al 2000 A major limitation to all of these methods of assessing seismically induced landsliding hazard is that they require ground motion information for future earthquakes Previous studies have gotten around this by using recordings of past earthquakes if they exist e g Peng et al 2009 Jibson et al 1998 or by using ground motion prediction equations to obtain a simplified ground motion parameter for a specific scenario earthquake such as peak ground acceleration PGA e g Ambraseys and Menu 1988 Lee and Evangelista 2006 or Arias intensity e g Jibson et al 1998 This is then coupled with regression equations to estimate the performance of slopes with various characteristics e g Jibson 2007 Rathje and Saygili 2009 Others take the peak ground acceleration for a specified return period straight from probabilistic seismic hazard maps e g Jibson and Michael 2009 Blake et al 2002 Saygili and Rathje 2009 More rigorous solutions include rescaling recordings of earthquakes in other locations or in the case of Miles and Ho 1999 producing simple stochastic synthetic seismograms for a specific event 1-5 Though some of these methods have ways of approximating site amplifications they are often generalized based on recordings of earthquakes all over the world in different settings not tailored to the peculiarities of a particular location This means variability and thus uncertainty is high and they are missing the characteristics in the time series such as coherent pulses from the finite fault rupture or increased duration due to basin amplification which can be important to landslide triggering Furthermore for studies that use a single ground motion parameter like PGA instead of a time series recording one more step of approximation with its own uncertainties is required to tie PGA to the slope displacement Fortunately seismological methods and computing power have advanced to the point where it is possible to generate realistic broadband synthetic seismograms for scenario earthquakes These methods are capable of accounting for finite fault rupture basin amplification coherent pulses and directivity effects specific to a particular event and locale that are poorly approximated by other methods In this study we used such methods to generate broadband synthetic seismograms on a fine grid 210-meter for a scenario earthquake striking the city of Seattle and rigorously adjusted these ground motions for site amplification due to soil layering on an even finer grid 5-meter using methods from geotechnical earthquake engineering and engineering geology Then we used these ground motions and pre-existing static slope stability data throughout the city to simulate seismically induced landsliding based on the Newmark method We show that using the full time-series recordings that account for the details of ground motion variability such as rupture directivity basin amplification and site response makes a substantial difference in determining the extent of landsliding triggered relative to simpler methods 1-6 We focus our efforts on simulating shallow landsliding triggered by a large crustal earthquake within the city limits of Seattle Washington in order to develop and test the methodology The reason we focus on Seattle is that it is a prime example of a city at risk of seismically induced landsliding that has not been thoroughly investigated The city is highly susceptible to landsliding in general Harp et al 2006 and is also located in an area of elevated seismic hazard that has been well quantified Frankel et al 2007 We simulate a magnitude 7 0 event on the Seattle fault a crustal reverse fault that lies directly below the city Blakely et al 2002 We focus on this fault because it is a primary contributor to the seismic hazard Around 900 A D an earthquake on this fault sent entire forested hillsides sliding into Lake Washington Jacoby et al 1992 and triggered lake-wide turbidity currents Karlin and Abella 1992 Karlin et al 2004 indicating that landsliding was widespread from both this most recent Seattle fault earthquake and previous earthquakes If such landsliding were to occur today the consequences could be dire: the steep hillsides along Lake Washington and Puget Sound are now densely populated In order to be prepared and to build a more resilient city such hazards must be quantified We use the methods described above and detailed in the methods section to demonstrate how they can be used to quantify the hazard posed by landsliding triggered by a scenario shallow crustal earthquake close to the city We map relative hazard but also take the scenario approach further and assign actual slope failures estimate areas in potential runout zones and look at potential intersections with infrastructure We address the critical questions of where landslides are most likely to occur how many might be triggered what effect soil saturation levels will have on the number of landslides triggered and how many buildings and critical infrastructure are at risk This scenario approach yields a tangible picture of the extent of landsliding and the 1-7 areas and infrastructure that could be at risk but represents just one of the countless scenarios that are possible However now that the framework is established for this scenario-based approach it can be used to run a suite of likely scenarios that could even eventually be compiled to develop a probabilistic seismically induced landslide hazard map similarly to how urban probabilistic seismic hazard maps are generated e g Frankel et al 2007 In the following sections we discuss the background of seismically induced landsliding in Seattle then present and validate the methods we used to simulate shallow landsliding triggered by a Seattle fault earthquake for the city of Seattle This is followed by the results of our seismically induced landslide simulation a discussion of the patterns and extent of landsliding triggered potential impacts on infrastructure the importance and sensitivity of various components of our methodology and a comparison to simpler methods Finally we conclude and discuss how broadband synthetic seismograms and these scenario-based methods could be refined for application to more scenarios to improve awareness of and preparedness for seismically induced landsliding in Seattle and other cities 2 Background Seattle s location near the convergence of the Juan de Fuca and North American plate Figure 1-1 inset leaves the city and surrounding region prone to three major earthquake sources: deep earthquakes within the subducted Juan de Fuca plate offshore megathrust earthquakes on the Cascadia subduction zone and shallow crustal earthquakes within the North American Plate Frankel et al 2007 Locally the latter type could be the most disastrous of the three if a large shallow crustal earthquake occurred close to the city The closest crustal fault that threatens Seattle is the Seattle fault which has not had a large earthquake since western settlement The zone of south-dipping reverse faults extends east-west across the Puget Lowland 1-8 just south of downtown Seattle Figure 1-1 forming the southern boundary of the Seattle basin Blakely et al 2002 Paleoseismic studies have revealed that the last major earthquake on this fault was around 900 A D Bucknam et al 1992 with an estimated magnitude of 7 5 ten Brink et al 2006 This event triggered some of the landslides preserved in Lake Washington and rock avalanches in the Olympic Mountains Jacoby et al 1992 Karlin and Abella 1992 Karlin et al 2004 Schuster et al 1992 If the 900 A D event is characteristic the next event could be thousands of years away Johnson et al 1999 Pratt et al 1997 but trenching of a backthrust of the Seattle Fault shows earthquake recurrence intervals in the fault zone range from 200 to 12 000 years Nelson et al 2003 and glacial loading and unloading could have disturbed the cycle Thorson 1996 Seattle itself is particularly prone to strong shaking because it was built directly over the Seattle Basin - a deep sedimentary basin that amplifies ground motion generates strong basin surface waves and tends to increase the duration of shaking Frankel et al 2002 On top of this deeper structure is a veneer of unconsolidated soils: layers of clay sands and till primarily deposited by retreating ice sheets at the end of the Pleistocene Troost et al 2005 These deposits compose steep slopes of unconsolidated material found throughout the city that have been further destabilized by human activity stream erosion and wave erosion along coastal bluffs Tubbs 1974 This steep unconsolidated surficial geology coupled with a wet climate make landsliding a frequent issue in Seattle most commonly triggered by some combination of human activity and heavy precipitation Landslides triggered by water have been the topic of many investigations specific to Seattle e g Tubbs 1974 Harp et al 2006 Baum et al 2005 Montgomery et al 2001 Coe et al 2004 Laprade et al 2000 Salciarini et al 2008 1-9 Figure 1-1 Map of Seattle showing location of Seattle Fault Zone dotted line frontal fault location used for rupture model for landslide simulation line of triangles and potential landsliding areas designated by the City of Seattle Neighborhoods and landmarks mentioned in the text are labeled Inset map shows regional tectonic setting and volcanoes triangles Earthquake-triggered landslides on the other hand occur only episodically and receive far less attention because of the long intervals between significant earthquakes in western Washington At least 15 earthquakes have triggered landsliding in the region since the mid1800 s Chleborad and Schuster 1998 Noson et al 1988 Keefer 1983 Hopper 1981 but nearly all of the historical examples were moderate earthquakes and the historical record is short in this part of the country All three major historical Puget Sound earthquakes Mw 7 1 in 1949 1-10 Mw 6 5 in 1965 and Mw 6 8 in 2001 caused ground failures throughout Western Washington and Northern Oregon Chleborad and Schuster 1998 Highland 2003 but not extensively because all three were deep Benioff zone earthquakes with relatively moderate ground motions and lower than normal or average antecedent rainfall Stewart 2005 Since its founding the city has yet to experience its most dangerous earthquakes: large crustal earthquakes on nearby faults and subduction megathrust earthquakes It is only when we look further back that we find that seismically induced landsliding has shown the potential to cause as much or more damage than other earthquake effects Oral traditions of the native Salish tribes report specific locations where earthquake-triggered landsliding or other earthquake effects occurred Ludwin et al 2005 Furthermore as mentioned earlier there is significant geologic evidence of seismically triggered landslides including sunken forests on giant block landslides submarine landslides and lake-wide turbidite layers preserved in Lake Washington Jacoby et al 1992 Karlin and Abella 1992 Karlin et al 2004 These deposits have been tied to landsliding triggered by as many as seven earthquakes in the last 3 500 years Karlin et al 2004 Despite this there are few rigorous studies of seismically induced landsliding in Seattle Of those that exist most characterize past seismically induced ground failures triggered by historical earthquakes in the area and identify the types of soils that failed e g Chleborad and Schuster 1998 Noson et al 1988 Keefer 1983 Hopper 1981 Stewart 2005 Highland 2003 McCalpin 1997 took a more quantitative approach and used ground motion prediction equations to calculate slope stability for some probabilistic and scenario earthquakes but did not include the level of detail that we have found to be necessary to accurately assess seismically induced landslide hazard in Seattle 1-11 3 Methods In this study we focus on shallow disrupted landslides which are generally the most abundant types of landslides triggered by earthquakes Keefer 1984 and are also the most common type of landslide in Seattle Baum et al 2005 The failure surface of this type of slide is within a few meters of the ground surface Deep-seated landsliding and liquefaction-related ground failure are also significant hazards that need to be addressed but are beyond the scope of this study We model co-seismic landslide movement using Newmark s method Newmark 1965 which approximates a slope as a rigid block sliding against friction down an inclined plane that is subjected to ground motion the block accumulates downslope displacement each time a threshold acceleration is exceeded The final displacement is termed the Newmark displacement Though the model is simplistic with some modifications it is currently the most widely used tool for looking at regional susceptibility of natural slopes to landsliding triggered by earthquakes e g Miles and Ho 1999 Ambraseys and Menu 1988 Jibson et al 1998 Peng et al 2009 Jibson and Michael 2009 For natural slopes the Newmark displacement is not the actual displacement that will occur but is instead considered an index for the likelihood of slope failure Jibson et al 2000 We take a similar approach Some have improved on the Newmark method to make it more realistic by allowing internal deformation within the failure mass e g Makdisi and Seed 1978 Bray and Rathje 1998 Rathje and Bray 2000 However we did not use these modifications because they are too computationally intensive to be applied on a citywide scale We discretized the city limits of Seattle into 5-meter cells To apply the Newmark method each cell was approximated as a rigid block sitting on a ramp with an incline equal to 1-12 the average slope within that cell The block is initially stable and has a threshold ground acceleration in the downslope direction above which the block starts to slide down the ramp This value is known as the critical acceleration ac sometimes referred to as the yield acceleration and is dependent on the slope the soil properties and the saturated thickness of the failure mass As the shaking progresses whenever the critical acceleration is exceeded the block accumulates displacement down the ramp The final Newmark displacement is calculated by integrating time intervals of the seismogram that exceed the threshold acceleration to determine the velocity time-history of the block when mobilized and then by integrating this result to determine the displacement history In this study after integrating once to velocity we assumed a symmetrical pulse shape in order to bring the velocity back to zero after each exceedance as in Goodman and Seed 1966 and then integrated once more to obtain displacement In order to speed up calculations we only calculated Newmark displacement for slopes equal to or greater than 15 the minimum slope for which shallow disrupted landslides typically occur Keefer 1984 We did not calculate Newmark displacement for slopes greater than 64 because only manmade structures are that steep at the resolution of our slope map 5m The factor of safety FS and slope angle of each cell was used to calculate the critical acceleration ac which is the acceleration in the downslope direction required to reduce the factor of safety to 1 This can be calculated by the relation ac FS-1 gsin where g is the acceleration due to gravity Newmark 1965 High-resolution 1 8 m slope information was available from the Puget Sound LIDAR Consortium The factor of safety is the ratio of resisting forces to driving forces thus a factor of safety of less than 1 means a slope is unstable Fortunately Harp et al 2006 conducted a detailed study of slope stability under static conditions in Seattle and calculated the factor of safety for dry and completely saturated soil 1-13 conditions on a 2-m grid for the entire city using typical engineering properties for each geologic unit They assumed a uniform failure thickness of 2 4 m to simulate shallow landslides of the same type we are investigating in this project so we were able to use their results The factor of safety reported by Harp et al 2006 was less than 1 for some cells because it was calculated on a large scale using a simple model For this study we assumed that all slopes were at least marginally stable prior to the simulated earthquake and raised all cells with a factor of safety below 1 to 1 01 4 Synthetic Seismogram Generation To accurately assess landslide hazard in Seattle it is necessary to use synthetic seismograms that account for rupture directivity and the effects of the Seattle basin The final input required for the simulation is a set of broadband synthetic seismograms generated on a fine grid throughout the city We chose to simulate an Mw 7 0 earthquake as a compromise between the estimated maximum magnitude the fault is capable of generating Mw 7 6 to 7 7 Pratt et al 1997 and the size of the earthquake that could be generated by the estimated slip accumulated since the last earthquake on the main fault 75-120 cm Johnson et al 1999 which would produce an Mw 6 6 to 6 7 earthquake if completely released Wells and Coppersmith 1994 We used the surface projection of the frontal fault Figure 1-2A from Blakely et al 2002 as the rupture plane We ruptured a 45-km segment from the middle of the fault from 315 km depth We assumed a rupture dip of 45 resulting in a rupture width of about 17 km The rupture plane was divided into 3 150 subevents that were spaced 500 m apart and had a mean Mw of 4 6 Figure 1-2b We used methods developed by Frankel et al 2007 to model the slip distribution and the moment distribution among the subevents as a spatial random field with a correlation length for asperities that corresponds to the magnitude of the earthquake Mai and 1-14 Beroza 2002 To simulate a finite fault rupture the point source subevents were set to break first at the lower eastern edge of the fault Then the rupture propagated updip and westward at rupture velocity that was set to 70% of the shear wave velocity so that it slows as the rupture approaches the surface The rupture velocity is randomized by 25% and constrained to never exceed the shear wave velocity in order to avoid unrealistically large directivity pulses Figure 12c In addition the rake of each subevent was varied randomly by 20 We deviate from the methods of Frankel et al 2007 slightly in the calculation of the rise time TD by making it dependent on the shear wave velocity at the point of rupture by TD 16Lf0 5 7 1 5 Stein and Wysession 2003 in which L is the length of the fault is the shear wave velocity and f is the ratio of width to length By doing so the source-time function at shallower depths was slightly longer than at greater depths which caused shallower subevents to radiate lower frequency energy than deeper ones This step helped maintain realistic ground acceleration levels We then used this fault rupture model to generate broadband seismograms by calculating long-period motion 1 Hz stochastically on a 210-meter grid throughout the city and combined them using methods developed by Frankel 2009 To compute the deterministic low-frequency ground motions we used the fault rupture model as input to a finite-difference code developed by Liu and Archuleta 2002 that propagates seismic waves through a 3D velocity model of the Seattle basin developed by Delorey and Vidale 2011 This simulates amplification and surface wave generation in the Seattle basin To isolate the influence of the Seattle basin on ground motions and consequently on the extent of landsliding triggered we also generated synthetic seismograms for a 1D velocity model 1-15 formulated from the out-of-basin velocities in Delorey and Vidale s 2011 3D model Both velocity models had a shear-wave velocity of 600 m s at the surface Figure 1-2 a The surface projection of fault rupture used to generate synthetic seismograms triangles corresponds to the frontal fault of the Seattle Fault Zone as defined by Blakely et al 2002 This is just one of the set of faults that make up the entire Seattle Fault Zone gray dotted lines b Contoured moment distribution of subevents on the fault rupture plane 0 km is westernmost end of ruptured segment c Rupture time in seconds from the start of the earthquake Higher frequency portions of the seismogram were computed stochastically using the constant stress-drop model proposed by Frankel 2009 derived from Boore 1983 1996 Subevents were assigned stress drops using a fractal distribution with a root-mean-square value of 10 MPa The assigned stress drops were used to calculate a theoretical spectrum for each subevent which was then multiplied by Gaussian white noise in the frequency domain so that 1-16 each subevent had a realistic seismogram when transformed into the time domain and tapered These subevent waveforms were then adjusted for attenuation geometrical spreading and travel times between each source and each station and summed up at each station The high- and lowfrequency components of the synthetics were combined with a crossover at 1 Hz using a matched filter to form broadband seismograms Figure 1-3 Examples of a North b East and c vertical component synthetic accelerograms starting from south of the surface trace of the fault at bottom moving northward toward the top of the plot Distance to the closest point on the frontal fault trace is shown to the left of each seismogram Locations of each synthetic seismometer used are shown as black dots on Figure 4 1-17 Figure 1-4 Maximum horizontal peak ground accelerations on a 210-m grid of broadband synthetic seismograms of the simulated Mw 7 0 Seattle fault earthquake generated using a a 1D velocity model of the Puget Lowland outside the Seattle basin compared with b a 3D velocity model Delorey and Vidale 2011 that simulates 3D basin amplification Triangles delineate the rupture used to generate seismograms dotted lines show the Seattle fault zone Sample synthetic seismograms are shown in Figure 1-3 These seismograms contain important features that would not be represented using ground-motion values from average ground-motion prediction equations For stations within about 5 km of the fault trace there is a forward rupture directivity pulse that greatly increases the peak acceleration The synthetics for stations in the Seattle basin also exhibit substantial basin surface waves generated at the edges of the Seattle basin These basin surface waves increase the amplitude and duration of long-period shaking The peak horizontal ground accelerations for this earthquake for the 3D velocity model and the 1D velocity model are shown in Figure 1-4 This is a randomized iteration of a possible 1-18 Seattle Fault earthquake and represents just one possible scenario As expected the synthetics generated using the 3D velocity model that accounted for amplification within the Seattle basin resulted in higher peak ground accelerations and more spatial variability within the basin north of the Seattle fault than the 1D velocity model particularly along the northern edge of the basin 5 Incorporating Site Amplification The broadband seismograms we generated by the methods described above represent shaking at the surface with a base shear wave velocity of 600 m s but most of the city is underlain by shallow layers of soil with much lower shear wave velocities that can amplify ground motion Pratt and Brocher 2006 Frankel et al 2002 Pratt et al 2003 Snelson et al 2007 Hartzell et al 2000 In order to simulate realistic ground motions we needed to account for site amplification relative to the 600 m s base layer No effective simple methods yet exist for adjusting a full seismogram in the time domain for site effects on a regional scale Most methods depend on the average shear wave velocity in the top 30 meters Vs30 which some argue is a poor predictor of site amplification e g Castellaro et al 2008 They are also developed to adjust response spectra Choi and Stewart 2005 Borcherdt 1994 and are thus not appropriate for adjusting Fourier spectra which is required to adjust time series seismograms As an intermediate approach we developed 67 representative shear wave velocity Vs profiles that represent the range of typical surficial geologic profiles in Seattle The complete profiles are reported in Appendix 1 We then used ProShake a software package that uses equivalent linear methods to approximate soil non-linearities to develop 1D site amplification transfer functions for each Vs profile using the base synthetic seismograms as the input ground motion level This method does not correctly handle the surface waves or P-waves in the waveforms but at the 1-19 frequencies being amplified and for horizontal components S-waves are dominant so it should be a good approximation We built the representative Vs profiles based on the geologic map of Seattle crosssections and typical thicknesses for each unit Troost et al 2005 and typical engineering properties shear wave velocity ranges and measured shear wave profiles for these units Savage et al 2000 Williams et al 1999 Wong et al 2010 Palmer et al 2004 The geologic units and the range of engineering properties we used to construct these representative profiles are shown in Table 1-1 For simplicity all unconsolidated deposits older than the last glaciation the Vashon stade of Fraser glaciation were lumped together as Qpf These units are nearly all classified as very dense and hard because they have been overconsolidated by one or more glaciations so we considered them to be equivalent to the base layer of 600 m s We assumed linear behavior of these units because soils of this site class NEHRP class C do not generally show much non-linear behavior Choi and Stewart 2005 The few soft rock sites all located in the southern part of the city were treated similarly We concentrated our efforts in the development of these representative shear wave profiles on areas that could generate landslides Consequently profiles for flat-lying areas such as the Duwamish valley Harbor Island and Interbay are highly oversimplified and should be improved if used for any other purpose Figure 1-5 shows the average shear wave velocity in the top 30 meters Vs30 calculated from these representative profiles 1-20 Table 1-1 Description of geologic units used in the development of the representative Vs profiles and the range of thicknesses and engineering properties they were assigned Wet density range Typical Thickness range m Vs range m s Qvt 8 400-600 2160-2400 Vashon Till Qva 10-50 300-600 1920-2160 Advance Outwash Deposits Description Age kg m3 Fraser Glaciation Vashon Stade pleistocene Unit 5 250-350 1680-1800 Recessional Outwash Deposits 5 250-350 1560-1800 Recessional Lacustrine Deposits Qvlc 15-30 200-500 1560-1920 Lawton Clay Qpf NA 450-600 2160-2400 Pre-fraser Deposits pleistocene Tertiary Tb NA 350-600 2300-2400 Blakely Formation weakly lithified sandstone soil 1 100 1440 Soil Qp 10 60 1260 Peat Qal 6-30 120-180 1440-1620 Alluvium Qt 6 120-130 1440 Terrace deposits Qls 3-10 120-140 1440-1500 Landslide deposits Fill 2-10 120-140 1440-1500 Artificial Fill Qb 8 120-140 1440-1500 Beach Ql 3 130-150 1560-1680 Lake Deposits postglacial holocene Qvr Qvrl Once we applied the corresponding transfer functions that we developed to each 5-meter grid cell the spatial variability of the ground motions increased significantly Figure 1-6 The ground motions in some of the low-lying areas with low shear wave velocities were deamplified due to soil non-linearity particularly areas of fill and alluvium where liquefaction is more likely than landsliding Areas that were significantly amplified relative to the base seismograms include 1 old landslide deposits along many of the steep coastal bluffs that overlie higher velocity undisturbed deposits 2 areas where thin lower velocity deposits such as recessional outwash or soil overlie pre-Vashon deposits and 3 soft rock sites that behave linearly The soft rock sites have a higher Vs30 than much of the city yet they also have some of the highest amplifications because they behave linearly and high impedance contrasts between the rock and overlying shallow soil and weathered layers can cause amplification at higher frequencies where 1-21 there is more seismic energy Accelerations reach 2g in a few of these localized areas on the hanging wall of the fault Figure 1-5 Average shear-wave velocity down to 30 m Vs30 computed from the representative Vs profiles compiled for this study 1-22 Figure 1-6 Maximum horizontal peak ground acceleration for a the base synthetic seismograms generated using the 3D basin velocity model with a surface layer velocity of 600 m s and b the same seismograms adjusted for 1D site amplification due to the shallow surficial soil layers at right Seattle fault zone is indicated by dotted lines 6 Model Outputs Next the critical acceleration for both dry and saturated soil conditions and ground motions for the scenario earthquake assigned to each cell were used to calculate the Newmark displacement for each cell using the methods described above We used the final Newmark displacement as an index for the relative likelihood of landsliding as in Jibson and Michael 2009 We designated seismically induced landslide hazard zones based on an empirical relation between Newmark displacement and probability of failure developed by Jibson et al 2000 This relation was derived from the landsliding catalog from the Northridge earthquake While the 1-23 soils and rocks that failed in the 1994 Northridge earthquake are different than the soils of Seattle using the probability curve developed for Northridge is currently the best option available due to the dearth of complete post-earthquake landslide surveys This is something that needs to be improved upon in future work We divided hazard into four zones: Low Moderate High and Very High Cells with more than 0 cm of displacement up to 3 5 cm of displacement corresponding to a less than 10% chance of failure were designated as Low seismically induced hazard The Moderate seismically induced landslide hazard zone corresponds to areas with Newmark displacements between 3 5 and 7 cm or 10-20% probability of failure High corresponds to 7 to 12 cm or 20-30% probability of failure and Very High corresponds to anything with more than 12 cm of displacement or a probability of failure above 30% The reason the highest landslide hazard zone cutoff is at a mere 30% probability of failure is because Jibson et al 2000 found that the probability of failure levels off at 34% beyond about 18 cm of displacement due to natural variability We generated relative seismically induced landslide hazard maps using these designated landslide hazard zones but also went one step further towards the scenario approach and designated predicted slope failures to assess the extent of landsliding one might expect To do this a random number generator chose a number between 0 and 1 for each cell If the chosen number was lower than the probability of failure assigned to that cell the slope represented by that cell fails Failure is defined as a detachment of the slope The failure of each cell is independent of all the others Once the distribution of failed cells throughout the city was determined adjacent failed cells were clustered together into landslide source areas Each cluster of adjacent failed cells was counted as one source Landslide damage can occur both in the source area and in downslope cells Deterministic models of runout are not practical on the scale required for this study and 1-24 empirical runout estimation methods that currently exist often based on the travel distance angle e g Hunter and Fell 2003 are derived from datasets of landslides primarily triggered by water not ground motion and are not appropriate for this scenario study where the water content of failed materials could be significantly lower Therefore we were not able to estimate runout from each failed cell in the scenario However Harp et al 2006 recommended a runout buffer zone of 60 meters below steep slopes based on the mean runout length of a set of landslides in Seattle We used this runout distance of 60 meters or until the slope reached 2 whichever came first to quantify the extent of infrastructure and buildings that are potentially at risk 7 Validation of Ground Motions In order to validate the methods we used to generate synthetic seismograms we calculated spectral accelerations for 5% critical damping of the synthetic seismograms and compared them to the spectral accelerations predicted for an Mw 7 0 thrust fault earthquake on the Seattle Fault by three of the Next Generation Attenuation NGA relations that account for basin depth: Campbell and Borzognia 2008 Chiou and Youngs 2008 and Abrahamson and Silva 2008 There is a directivity pulse in the broadband synthetics because of the updip rupture that appears primarily on the fault-normal North component so we also included a modification to the NGA relations developed by Shahi and Baker 2011 that accounts for a directivity pulse We calculated response spectra for the base synthetic seismogram NEHRP Class C site condition corresponding to each grid point on the 210-m grid and binned them in 2km wide bins based on the closest distance to the fault The mean spectral accelerations 1 standard deviation of the synthetics at a range of horizontal distances to the fault are shown in Figure 1-7 Spectral accelerations are shown for synthetics computed using both the 1D and 3D velocity models left and right respectively These are compared with the spectra for three NGA 1-25 Figure 1-7 Response spectra 5% critical damping of the broadband synthetics generated with the a 1D basin velocity model and the b 3D basin model compared with the mean values for three Next Generation Attenuation relations that are modified to include a directivity pulse using methods developed by Shahi and Baker 2011 Black is the mean of the synthetics at the distance bin noted 1km with one standard deviation indicated by the error bars The thick gray line is the mean of the three attenuation relations CB08 dash-dot is the response spectra for Campbell and Borzorgnia 2008 CY08 dotted is Chiou and Youngs 2008 and AS dashed is Abrahamson and Silva 2008 The bump at about T 3 seconds is due to the directivity pulse 1-26 relations and the mean of all three combined assuming the same distance for all types of distances to the fault required for each equation The fit is quite good particularly taking into account the large variability between the NGA attenuation relations themselves and their respective uncertainties the spatial variability within the synthetics as shown by the error bars and the fact that the y-axis is linear rather than logarithmic The synthetics made using the 3D model show much higher spectral accelerations at long periods because of basin amplification particularly around 17 km from the fault where there is strong amplification at the northwestern edge of the Seattle basin The directivity pulse at a period of 3 seconds in the synthetic seismograms matches the period predicted by Shahi and Baker 2011 for this event Their predicted pulse also matches the amplitude quite well for the 1D model but is exceeded by the 3D synthetics suggesting that amplification within the 3D structure also occurs at these frequencies To validate the transfer functions that we computed for representative Vs profiles throughout Seattle using ProShake we generated transfer functions for them using recordings of the 2001 Nisqually earthquake as the input ground motions We then compared the resulting transfer functions to the spectral ratios of the recorded Nisqually ground motions at several accelerometers located throughout the city using a soft rock site in Seward Park SEW as the reference site Comparisons between our modeled transfer functions for representative profiles and the spectral ratios of the real data are shown in Figure 1-8 We did not expect to fit the exact peaks and troughs of amplification shown in the spectral ratios because representative profiles cannot replicate site-specific peculiarities Instead we aimed to roughly match the frequencies and amplitudes of amplification for most sites The transfer functions match well for many stations e g WEK THO BRI MAR SEU particularly at less than 10 Hz but they diverge at 1-27 higher frequencies where shallow layers dominate the site response e g TKCO ALO BHD CRO HOLY Amplifications on this fine scale are beyond our ability to reproduce using representative profiles but most of the energy in the seismograms is below 10 Hz so this is not detrimental A few transfer functions do not match the spectral ratios as well e g NOWS QAW SEA These differences could be due to finer scale geological variability than is reflected in the geologic map of Seattle or issues with station or site response They illustrate the limitations of simplifying shear wave profiles into representative units for such a large region but the differences are not severe and only occur at a fraction of the sites Figure 1-8 The spectral ratio of the recorded ground motions of the Nisqually earthquake at 24 accelerometers using the soft-rock reference station SEW shown on the station map at right thin lines North is dashed East is solid compared to the transfer functions computed in ProShake for the corresponding representative Vs profiles computed using the Nisqually earthquake ground motions as the input ground motions thick black line 1-28 8 Validation of Landslide Simulation The 2001 Mw 6 8 Nisqually earthquake located at 52 km depth with a hypocenter 57 km SSW of Seattle location from the Pacific Northwest Seismic Network is the only one of the three large historic Puget Sound earthquakes for which dense ground acceleration records exist The earthquake triggered about 100 landslides throughout Puget Sound Stewart 2005 fewer than expected since the earthquake occurred during a rare winter dry period Highland 2003 Only landslides that caused damage and losses were included in a post-quake report on landsliding by Highland 2003 Most of these occurred closer to the epicenter south of Seattle Only two of the reported landslides in this report were within city limits: landsliding in one location of West Seattle damaged some houses and lateral spreading caused some damage to a viaduct downtown No comprehensive landslide survey was done due to the scarcity of significant landsliding within city limits As the best validation available we ran the Nisqually ground motions through the seismically induced landslide simulation model using the factor of safety map for dry conditions to see if it reproduced the observed scarcity of landsliding To do this we used 33 strong ground motion records the locations of these stations are shown on the map in Figure 1-8 In order to infer ground motion throughout the city from this sparse and irregular sampling we removed site amplification using spectral ratios relative to a reference site on a soft rock site in Seward Park SEW Then each 210-m grid point was assigned the closest actual recording with the recording station s site effects removed and corrected for geometrical spreading We then readjusted the ground motions for site effects using transfer functions developed in ProShake using actual recordings of the Nisqually earthquake as the ground motion input and the representative Vs profiles we developed Ground motions during the Nisqually earthquake were much lower than those for the Seattle fault simulation so 1-29 the site amplifications in the simulation for most representative profiles are actually higher for the Nisqually earthquake than for the Seattle fault event because they are not moderated as much by non-linear effects The landslide simulation for dry conditions - representative of the conditions during the Nisqually earthquake - predicted 26 landslide sources with a total area of about 1 000 m2 Tables 1-2 and 1-3 They are located in ten localities Figure 1-9 almost exclusively on extremely steep median slope of 40 undeveloped coastal bluffs and ravines - nearly half in city parks The simulation predicted that only 0 001% of the land area of Seattle had high landsliding potential nmdisp 7cm 20% probability of failure We consider this dearth of predicted landsliding and their locations in extremely steep undeveloped areas where they would be unlikely to affect structures or infrastructure or even be noticed to be a validation that our earthquake-induced landslide simulation generates realistic results We also ran the same landslide simulation of the Nisqually earthquake but for saturated soil conditions instead to see what might have happened if the earthquake had occurred after an extended period of heavy rainfall The results are drastically different: nearly 7 500 landslide sources were triggered 9 of those greater than 500 m2 in area These sources cover 0 3 km2 of the city and 0 4% of the land area of the city had high potential for landsliding nmdisp 7cm Tables 1-2 and 1-3 1-30 Figure 1-9 Percentage of cells in each area where failures were triggered as defined in the text for the a dry and b saturated soil conditions using ground motions from the 2001 Mw6 8 Nisqually earthquake For visibility individual failures are indicated for dry soil simulation because there were so few landslides triggered In reality so few shallow disturbed landslides were triggered by this quake that no post-quake landslide survey was done the location of just one damaging landsliding was documented by Highland 2003 which is indicated by an asterisk at left For the saturated soil simulation the shading corresponds to the percentage of 5-meter cells in each area that failed in the simulation smoothed with a 20x20 cell Gaussian kernel 9 Results of Landslide Simulation for Mw 7 0 Seattle Fault Earthquake The results of our seismically induced landslide simulation of the scenario Mw 7 0 Seattle fault earthquake for the best- and worst-case scenarios dry and saturated soil conditions respectively are summarized on Tables 1-2 and 1-3 Individual failures of 5-meter cells are too small to see on a citywide map so Figure 1-10 instead shows the percentage of cells that failed 1-31 in each area of the city smoothed with a 20x20 cell kernel 100 m x 100 m In addition high resolution maps of relative seismically induced landslide hazard for a Mw 7 0 Seattle fault earthquake are provided in Appendix 2 Figures A1 and A2 Zoom-ins on a few areas of interest of this map are shown in Figure 1-11 Hazard zone levels are based on Newmark displacement and the corresponding probability of failure as described above Table 1-2 Summary of landslide sources triggered by seismically induced landslide simulations Mw 6 8 Nisqually Earthquake Simulation Mw 7 0 Seattle Fault Earthquake Simulation Dry Conditions Saturated Conditions Dry Conditions Saturated Conditions Number of failed 5x5m cells 40 13 720 9 698 77 765 Number of sources 26 7494 4 977 30 699 Median slope of source cells degrees 40 35 29 26 Results using nearest original ground motion recording of the 2001 Nisqually earthquake for each cell with site effects removed and then adjusted for site amplification using the corresponding transfer functions developed for this study Results using broadband synthetic seismograms generated using a 3D velocity model and including site amplification Sources are clustered - adjacent failed cells are counted together as one source Table 1-3 Total land area potentially affected by seismically induced landsliding Mw 6 8 Nisqually Earthquake Simulation Dry Conditions Sources Saturated Conditions Mw 7 0 Seattle Fault Earthquake Simulation Dry Conditions Saturated Conditions Area km2 % Land area Area km2 % Land area Area km2 % Land area Area km2 % Land area 0 001 0 0004% 0 3 0 1% 0 2 0 1% 1 9 0 8% nmdisp 0cm 0 025 0 01% 3 2 1 4% 2 6 1 2% 10 1 4 4% nmdisp 3 5cm 0 006 0 001% 1 2 0 5% 0 9 0 4% 6 5 2 8% nmdisp 7cm 0 003 0 001% 0 9 0 4% 0 6 0 2% 5 6 2 4% nmdisp 12cm 0 002 0 001% 0 8 0 3% 0 4 0 2% 4 7 2 1% Results using nearest original ground motion recording of the 2001 Nisqually earthquake for each cell with site effects removed and then adjusted for site amplification using the corresponding transfer functions developed for this study Results using broadband synthetic seismograms generated using a 3D velocity model and including site amplification Percent of total land area of Seattle Seattle has a land area of 229 km2 nmdisp Newmark Displacement In our simulation for dry soil conditions 4 977 landslide sources are triggered by the earthquake covering 0 2 km2 - 0 1% of the total land area of the city In addition 0 2% of the city is in a high landslide hazard zone for this event nmdisp 7 cm probability of failure 20% 1-32 Landsliding is concentrated in the southern half of the city along the coastal bluffs of West Seattle the western side of Beacon Hill and scattered throughout Delridge The coastal bluffs of Magnolia and Queen Anne show some less concentrated landsliding and North Seattle escapes relatively unharmed with the exception of localized landsliding along coastal bluffs in North Ballard near Carkeek Park and in Lake City Figure 1-10 left locations of places mentioned are shown on Figure 1-1 Figure 1-10 Percentage of cells in each area where failures were triggered as defined in the text for the a dry and b saturated soil conditions for the Mw 7 0 Seattle Fault earthquake simulation For the same exact scenario but using the factor of safety map for saturated soil conditions instead the results are more drastic More than 30 000 landslide sources are triggered covering 1 9 km2 equal to 0 8% of the land area of the city In this case 2 4% of the city is in a 1-33 high landslide hazard zone nmdisp 7 cm Fortunately this simulation represents an unlikely scenario where the water table is effectively at the surface everywhere due to higher than normal seasonal rainfall followed by an intense precipitation event followed in turn by a lowprobability earthquake The distribution of landslide sources for saturated conditions contrasts with the dry scenario Figure 1-10 place names on Figure 1-1 In this simulation the southern half of Seattle experiences dense landsliding concentrated not only on the coastal bluffs and the slopes bordering the Duwamish river valley but also scattered inland throughout West Seattle Delridge Beacon Hill Seward Park and Rainier Valley Landsliding rims both Magnolia and Queen Anne hills and extends north all the way to Portage bay along Interstate-5 I-5 The northern half of Seattle though less hard-hit than the rest of the city is more severely affected in this case than in the dry scenario The coastal bluffs along Puget Sound experience dense landsliding in incised valleys up to 1 km from the coast particularly in the northwest corner of the city because of the strong amplification of low frequencies at the edge of the basin In both cases areas of steep topography on the hanging wall of the Seattle fault are most severely affected by seismically induced landsliding consistent with observations of landsliding triggered by other earthquakes worldwide e g Tang et al 2011 Overall patterns of predicted landsliding correspond to areas that are generally known to be landslide prone In fact 66% of known historical landslides in Seattle from the City of Seattle dataset lie within landslide hazard zones predicted by the Seattle fault earthquake simulation for dry conditions 80% for the saturated soil conditions However if we look at existing landslide hazard maps for static no ground shaking conditions a significant percentage of the landslides predicted by the simulation are in areas of low and medium relative hazard 1-34 Figure 1-11 Zoom-ins of the relative seismically induced landslide hazard map for a dry and b saturated soil conditions superimposed on infrastructure and building outlines Full high resolution versions are included in the electronic supplement Figures S1 and S2 Locations of each zoom-in are shown on the map of Seattle at right A Coastal bluffs in the northern part of Seattle are most affected when soils are saturated Many single family homes are located within landslide hazard zones as well as downslope from potential source areas where they could be 1-35 affected by runout B There are several areas along the I-5 corridor that are highly susceptible to landsliding for all soil saturation levels such as the area shown here near the access point to the West Seattle bridge C The hillsides in West Seattle along the Duwamish valley are at risk of seismically induced landsliding such as the area shown here There are industrial as well as residential buildings that could be affected by runout from landsliding in these areas D The coastal bluffs along Puget Sound in West Seattle on the hanging wall of the fault such as the area shown here are the most highly susceptible areas to landsliding in the city numerous residential structures are at risk from both potential landslide source areas and runout North is up on all maps based on static slope stability as delineated by Harp et al 2006 : 28% of the total landslides triggered by our dry soil conditions simulation occur in medium and low static landslide hazard areas for dry conditions and 40% for the saturated soil simulation Similarly a comparison between the cells that failed in the seismically induced landslide simulation and areas designated as potential sliding areas in the City of Seattle corporate GIS database also shows that a significant percentage of the predicted landsides lie outside the designated areas: for dry conditions 36% of failed cells are outside potential sliding areas 38% for saturated conditions The City of Seattle potential sliding areas were designated based on the contact between a permeable and an impermeable geologic unit Esperance sand and Lawton clay respectively where seepage occurs and many historical landslides have been triggered by water Clearly these maps are not adequate to delineate areas likely to produce landslides during earthquakes We cannot assume that seismically induced landslides will only be triggered in areas already designated as hazardous by studies focusing on static slope stability highlighting the importance of studies dedicated to seismically induced landslide hazard such as this one 10 Infrastructure Impacts Our results show that it is not only the relatively undeveloped coastal bluffs that are hit but landsliding also affects inland slopes that could threaten key transit routes and buildings 1-36 particularly in the saturated soil scenario To further investigate the infrastructure and buildings that may be at risk from seismically induced landsliding in such a scenario we calculated the number of buildings and total length of linear infrastructure such as roads and water lines that fall within the four different seismically induced landslide hazard zones as well as within a 60meter buffer or until the slope reaches 2 downslope from these hazard zones to determine susceptibility to potential runout from the triggered landslides as well Note that the numbers presented here do not mean that every single building and piece of infrastructure within these zones will be negatively affected when a Seattle fault earthquake eventually occurs The highest probability of failure for any hazard zone is 34% and most are much lower and the runout buffer zone is probably overestimated in most cases The numbers are simply a measure of the extent of infrastructure and buildings that are potentially at risk There are a significant number of buildings that are located directly within the seismically induced landslide hazard zones Figure 1-12 For dry soil conditions there are over 1 000 buildings that are within all hazard zones 400 of those in the two highest hazard designation zones 20% probability of failure Twice as many buildings are in the potential runout zones from these landslides For saturated soil conditions it is nearly an order of magnitude worse with 8 000 buildings within all hazard zones 5 000 of those within the two highest hazard zones 8 500 more buildings are within the potential runout from all hazard zones Additionally hundreds of total kilometers of linear infrastructure roads rail electric water and sewer lines also sit within these hazard zones The total length in kilometers of each type of infrastructure that is located within the two highest hazard zones 20% probability of failure and within the potential runout zone from these hazard zones is shown in Figure 1-13 We found that the majority of the length of linear infrastructure that is at risk is within the potential runout 1-37 areas rather than within the potential source areas For dry soil conditions with the exception of railroad tracks on the order of 1 km of each type is at risk from landslide sources while on the order of 10 km of each are in potential runout areas For saturated soil conditions the numbers are bumped up by an order of magnitude on the order of 10 km of each are within potential source areas and 100 km are within potential runout areas In any case the impacts to infrastructure from landsliding will be extensive when a large Seattle fault earthquake occurs for any soil saturation level and this could significantly slow down recovery Figure 1-12 The total number of buildings in each landslide hazard zone and also within a 60-meter runout buffer downslope from each hazard zone for both dry and saturated conditions Each building can only be designated in one hazard zone or potential runout zone so totals are mutually exclusive 11 Discussion The ground motions we developed include a much higher level of detail than is typically used to model seismically induced landsliding To determine which efforts and effects are most important and which could potentially be neglected without significantly altering the results we compared the total citywide Newmark displacement for various levels of ground motion complexity for dry conditions Summary on Figure 1-14 1-38 Figure 1-13 Total length of critical linear infrastructure that is located within the high or extremely high landslide zones and within the potential runout areas from these zones for saturated top and dry bottom soil conditions We first ran the simulation with and without site and basin amplification and found that both need to be rigorously accounted for in simulations like this Ignoring them could result in an under-prediction of seismically induced landsliding hazard For example the inclusion of 1D site amplification site effects quadruples the number of failed cells for dry soil conditions On top of that the inclusion of basin amplification using a 3D velocity model instead of 1D velocity model bumps up the number of slope failures by about 35% because the basin amplification is so strong in Seattle For an area that does not sit on a significant sedimentary basin the 1D velocity model may be sufficient but for Seattle using a 3D basin model to account for basin amplification is critical 1-39 Figure 1-14 Results of seismically induced landslide simulation for dry soil conditions for various levels of complexity Gray bars indicate the total number of failed cells as defined in text from the landslide simulation using both broadband seismograms and just the high frequency portion of the synthetic seismograms 1Hz using the 1D dark gray and 3D light gray velocity models for simulations that include and exclude 1D site amplification These results are compared with simpler methods black where ground motion prediction equations GMPE s are used to estimate ground motion parameters for a Mw 7 0 Seattle fault earthquake instead of synthetic seismograms and the Newmark displacement is calculated using a regression equation developed by Jibson 2007 Four Next Generation Attenuation relations were used to estimate PGA and Travasarou et al 2003 was used to estimate Arias Intensity Error bars indicate one standard deviation accumulated from both the GMPE s and the regression equations Next we compared the results of this study with what would be predicted by simpler methods Most previous regional assessments of seismically induced landsliding used empirical regression equations that estimate Newmark displacement as a function of simplified ground motion parameters that are obtained using ground motion prediction equations GMPE s We estimated landsliding for our scenario using these methods in order to compare the result with our more detailed simulation To do this we used four Next Generation Attenuation NGA relations Boore and Atkinson 2008 Abrahamson and Silva 2008 Chiou and Youngs 2008 Campbell and 1-40 Borzognia 2008 to estimate peak ground acceleration for each cell throughout the city for the same scenario earthquake All the NGA relations account for site effects by NEHRP site class that is based on the Vs30 of each site which we take from the Vs30 of the representative shear wave profile assigned to each cell The latter three NGA relations also require the depth to a defined shear wave velocity contour to account for basin depth We extracted those values from Delorey and Vidale s 2011 3D velocity model for each cell Once we obtained PGA we used the regression equation developed by Jibson 2007 that relates earthquake magnitude and PGA to Newmark displacement The mean number of failures triggered by each of the four NGA equations used is shown on Figure 1-14 along with error bars that span plus or minus one standard deviation for both the NGA predicted PGA values and the Newmark displacement predicted from it combined The four relations predict a similar number of ground failures between them but Boore and Atkinson 2008 predict the lowest values possibly because their methods do not account for basin amplification at all Arias intensity which depends on both shaking intensity and duration is considered a superior ground motion parameter for predicting landslide triggering Miles and Keefer 2000 Jibson 2007 so we computed it for each cell using the attenuation relationship developed by Travasarou et al 2003 and then used the regression equation developed by Jibson 2007 that relates Arias intensity to Newmark displacement The downside to this approach is that the uncertainties are much higher for Arias intensity than for PGA which explains why the positive error bar is literally off the charts The most obvious conclusion from Figure 1-14 is that the methods based on simplified ground motion parameters that are commonly used for seismically induced landslide hazard analyses predict far fewer failed cells than the full time series approach used in this study if just the mean values are used One possible explanation is that the ground motion prediction 1-41 equations are not able to account for 1D site amplification basin amplification and directivity as completely as we can with our synthetic seismograms that are specifically tailored to the city of Seattle But the error bars compounded from uncertainties in the attenuation relations used to predict the ground motion parameters and in the regression equations used to predict Newmark displacement exceed the number of failures calculated for the final results of our most detailed seismically induced landslide simulation This shows that approximating landsliding hazard using ground motion prediction equations and regression equations can be useful and is certainly simpler and less time consuming but the uncertainties are huge and must be taken into account Using just the mean values can severely underestimate the extent of landsliding Finally to test whether the most time consuming part of generating the synthetic seismograms - the long period deterministic portion of the synthetic seismograms - was important or could be neglected we ran the landslide simulation using only the stochastic portion of the synthetic seismograms 1 Hz This removes any directivity pulses basin surface waves and other coherent long period pulses For the synthetics calculated using the 3D velocity model removing the long periods cut the number of failed cells nearly in half For the 1D velocity model that does not account for basin amplification it cut the number of failed cells by about a quarter While theoretically the Newmark method depends on the absolute slope-parallel acceleration irrespective of the frequency of ground motion this finding illustrates that it does have some inherent frequency dependence Though the long period energy is too low in amplitude to cause much Newmark displacement on its own when combined with higher frequency energy final Newmark displacements are significantly increased because the long period motion boosts the higher frequency motion higher above the critical acceleration 1-42 This finding raises questions about the frequency dependence of seismically induced landslide triggering because if shallow landslide triggering is not sensitive to longer period ground motion then this simulation could be significantly overpredicting the seismically induced landslide hazard For example Jibson et al 2004 suggested that landslides triggered by earthquakes might be most sensitive to frequencies between 1 and 10 Hz based on field observations On the other hand laboratory studies have shown that the Newmark sliding block approximation is most valid when the resonant frequency of the landslide is much higher than the ground motion Wartman et al 2003 which would be the case in this study because these landslides are only a few meters thick and would have resonant frequencies between 20 Hz and 60 Hz much higher than most of the energy in the seismograms Clearly this is a topic that demands more research If shallow seismically induced landslides are solely triggered by inertial forces as modeled by the Newmark method then this study demonstrates that the ground motions used to simulate landsliding must have broadband frequency content in order to capture the full displacement particularly in areas with potentially strong long-period ground motion like the sedimentary basin underlying Seattle However if shallow landslide triggering is dependent on the frequency content of the ground motion whether due to site-specific amplifications in pre-weakened slopes e g Allstadt 2009 Moore et al 2011 or another mechanism such as the wavelength and coherence of ground motion then seismically induced landslide studies should only use band-limited ground motions This could simplify the calculation of synthetic seismograms significantly but introduces the issue of what frequency cutoff to use and whether the frequency cutoff varies depending on the size or shear wave profile of the potential failure mass This is not an insignificant decision In this study for example: if we highpass filter the seismograms at 1 Hz the total citywide Newmark 1-43 displacement is decreased by 50% However if we increase the frequency cutoff to just 2 Hz it is instead decreased by 80% hence the selection of a frequency cutoff cannot be chosen arbitrarily because it controls the results At this point in time the research on the matter is too feeble to justify using a band-limited version of the synthetic seismograms for this study so our final results are those generated using the full broadband synthetic seismograms 12 Conclusions This study shows that seismically induced landsliding will significantly impact Seattle s residents and its infrastructure when the next large earthquake occurs on the Seattle Fault The southern half of the city which is on the hanging wall of the fault will be particularly hard hit while North Seattle is less exposed with the exception of localized areas primarily along coastal bluffs Several hundred to thousands of buildings could be affected citywide many kilometers of roads could be obstructed including some key transit routes such as Interstate-5 and access roads to West Seattle If the groundwater table is low and shallow soils dry when the earthquake hits as simulated by the dry scenario the total area of landslide sources will be about an order of magnitude smaller than if soils are completely saturated We found that the geology of Seattle particularly on the hanging wall of the fault and over the Seattle basin as well as site amplification in the shallow unconsolidated subsurface played a dominant role in determining the final pattern of landsliding predicted The high impact of landsliding predicted by this simulation for a Seattle Fault earthquake shows that this secondary effect of earthquakes can be a significant contributor to overall earthquake hazard and should be studied on an equal level to other earthquake effects in landslide-prone areas In this paper we present the results of just one scenario event for Seattle to develop and demonstrate the methodology but now that the methods are compiled it would be 1-44 relatively easy to develop a library of plausible earthquake scenarios and the predicted extent of landsliding triggered by each to better quantify the seismically induced landslide hazard in the Seattle area and to assist emergency managers An ultimate goal could be to run hundreds of possible scenarios on various faults and for a range of ground saturation levels and use them to develop a probabilistic seismically induced landslide hazard map Another potential application is to set up the landslide triggering simulation to run automatically after an earthquake occurs to obtain a rapid estimate of affected areas similar to what was done in Godt et al 2008 using real ground motions from our ever-densifying urban strong ground motion networks such as the dense NetQuakes network recently installed in Seattle There are other cities nationwide and worldwide threatened by seismically induced landsliding that could also benefit from such an approach However in order to make such results more accurate and refined we have identified some areas that require further research First in order to better quantify uncertainties we need to develop a more robust relation between Newmark displacement and the probability that the slope will fail and the extent of that failure e g cracking vs complete detachment The relation we use in this study Jibson et al 2000 the only of its kind thus far is based on just one seismically induced landslide inventory However more complete post-earthquake landslide inventories are now available from more recent earthquakes and this relation should be improved for wider application Second there are currently no scientifically justifiable methods to estimate runout from seismically induced landslides Existing empirical runout estimation methods are based on datasets from water-induced landsliding whereas landslides triggered by earthquakes can be significantly drier and thus may have shorter runout lengths Since runout is often what causes the most damage because it covers more area and can reach less steep areas downslope 1-45 that are more likely to be developed we need to develop methods to estimate runout and its uncertainties for seismically induced landslides beyond the simple potential runout buffer-zone approach we used in this study Finally we found that the combination of high- and lowfrequency ground motions together results in much higher Newmark displacements and thus more slope failures than using the higher frequency ground motions alone However there has been little research on the frequency dependence of shallow seismically triggered landslides and it is not well understood Some suggest that these shallow landslides are not sensitive to longerperiod motions which would have important implications in the accuracy of assessing seismically induced landslide hazard in areas like Seattle where high long-period ground motions are expected The frequency dependence of seismically induced landslide triggering requires further investigation In conclusion in-depth scenario studies using broadband synthetic seismograms such as this one are becoming more practical with ever faster computing power the increasing availability of detailed geologic and geotechnical GIS databases evolving understanding of earthquake and landslide hazard and improving methods This type of study that integrates methods and data across disciplines to obtain a tangible final result serves as a good complement to the more thorough but less intuitive probabilistic hazard maps and can help us more effectively prepare for future earthquakes 13 Data and Resources Ed Harp and John Michael of the U S Geological Survey provided GIS files for the factor of safety maps developed for the Harp et al 2006 study that we used Andy Delorey provided us with the 3D velocity model of Seattle from Delorey and Vidale 2011 Ground motion recordings from the 2001 Nisqually earthquake were provided by the Pacific Northwest 1-46 Seismic Network and the USGS Seattle urban seismic array Strong motion records from PNSN stations are available via the Nisqually Earthquake Information Clearinghouse at http: www ce washington edu nisqually seis observations html last accessed May 2013 and data from the USGS array are available from ftp: ftpext usgs gov pub cr co golden hazards Carver Seattle last accessed May 2013 The City of Seattle GIS files used to calculate intersections between landslides and infrastructure were accessed from the Washington State Geospatial Data Archive available through the University of Washington library and from the publicly available Data Seattle Gov website last accessed October 2012 Public domain LIDAR GIS files were obtained through the Puget Sound LIDAR consortium Software packages used for this study include MATLAB from MathWorks ProShake from EduPro Civil Systems Inc ArcGIS from ESRI We also used MATLAB codes developed by the Baker Research Group at Stanford to compute the ground motions required using Next Generation Attenuation NGA relations these codes were accessed at http: www stanford edu bakerjw attenuation html in July 2012 14 Acknowledgements Research supported by the U S Geological 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Active Regions Eng Geol 58 v-vi Wells D L and Coppersmith K J 1994 New Empirical Relationships among Magnitude Rupture Length Rupture Width Rupture Area and Surface displacement Bull Seis Soc Am 84 974 1002 Williams R A W J Stephenson A D Frankel and J K Odum 1999 Surface Seismic Measurements of Near-Surface P- and S-wave Seismic Velocities at Earthquake Recording Stations Seattle Washington Earthquake Spectra 15 565-584 Wilson R C and D K Keefer 1983 Dynamic analysis of a slope failure from the 6 August 1979 Coyote Lake California earthquake Bull Seism Soc Am 73 863-877 Wong I K H Stokoe II B R Cox Y-C Lin and F-Y Menq 2010 Geotechnical Characterization and Evaluation of Site Amplification at Selected PNSN Strong Motion Sites Seattle Washington Final Technical Report submitted to USGS under the National Earthquake Hazards Reduction Program 38p 1-54 Yin Y F Wang and P Sun 2009 Landslide hazards triggered by the 2008 Wenchuan earthquake Sichuan China Landslides 6 139-151 1-55 Chapter 2 Seismogenic landslides a new way to study landslide dynamics: Part a: Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms Part b: The Seismic Story of the Nile Valley Landslide 2a- 1 Chapter 2a: Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms The content of this chapter was published in: Allstadt K 2013 Extracting Source Characteristics and Dynamics of the August 2010 Mount Meager Landslide from Broadband Seismograms J Geophys Res 118 p 1-19 doi: 10 1002 jgrf 20110 2a- 2 Table of Contents Summary 2a-4 1 Introduction 2a-5 2 Data 2a-10 2 1 Seismic data 2a-12 3 Methods 2a-17 3 1 Validation 2a-21 4 Results 2a-23 4 1 Rockslide initiation 2a-26 4 2 Debris flow 2a-30 4 3 Aftershock 2a-35 5 Discussion 2a-38 5 1 Improvements to landslide characterization 2a-38 5 2 Limitations 2a-44 6 Conclusions 2a-45 7 Acknowledgements 2a-47 8 References 2a-48 2a- 3 Summary Seismic methods can substantially improve the characterization of the dynamics of large and rapid landslides Such landslides often generate strong long period seismic waves due to the large-scale acceleration of the entire landslide mass which according to theory can be approximated as a single-force mechanism at long wavelengths I apply this theory and invert the long period seismic waves generated by the 48 5 Mm3 August 2010 Mount Meager rockslidedebris flow in British Columbia Using data from five broadband seismic stations 70 to 276 km from the source I obtain a time-series of forces the landslide exerted on the earth with peak forces of 1 0 x 1011 N The direction and amplitude of the forces can be used to determine the timing and occurrence of events and subevents Using this result in combination with other field and geospatial evidence I calculate an average horizontal acceleration of the rockslide of 0 39 m s2 and an average apparent coefficient of basal friction of 0 38 0 02 which suggests elevated basal fluid pressures The direction and timing of the strongest forces are consistent with the centripetal acceleration of the debris flow around corners in its path I use this correlation to estimate speeds which peak at 92 m s This study demonstrates that the time-series recording of forces exerted by a large and rapid landslide derived remotely from seismic records can be used to tie post-slide evidence to what actually occurred during the event and can serve to validate numerical models and theoretical methods 2a- 4 1 Introduction Direct time-dependent observations of natural landslides are critical to improving our understanding of landslide dynamics and hazard However such observations can be hard to come by due to the destructive nature of landsliding events uncertainty about when and where they will occur and their sometimes-remote locations Seismology is a potential tool to span this observational gap Assuming the landslide under investigation radiates enough seismic energy to be recorded at existing seismic stations and the seismograms can be correctly interpreted seismic data can provide a time series recording of landsliding events that can be used to extract information about landslide dynamics and source characteristics This approach is comparable to how seismologists have been using seismograms to study earthquakes for over a century - but landslide seismology has the added benefits of being able to access the source area and of knowing the driving stress gravity When combined with field investigation theoretical methods and numerical landslide modeling a much clearer interpretation of the event being investigated can emerge e g Favreau et al 2010 Moretti et al 2012 Guthrie et al 2012 In order to correctly interpret seismic signals of landslides one must first understand how landslides radiate seismic energy Energy is radiated on two scales: coherent long-period waves at periods of tens to hundreds of seconds generated by the acceleration and deceleration of the failure mass as a whole Kanamori and Given 1982 Eissler and Kanamori 1987 and a more stochastic higher frequency signal at periods from a few seconds to frequencies of tens of Hz generated by momentum exchanges on smaller scales such as flow over smaller scale topographic features frictional processes e g Schneider et al 2010 and impacts of individual blocks e g Huang et al 2007 2a- 5 Large and rapid landslides in particular are effective at generating strong long period seismic waves particularly surface waves which attenuate slowly and can be detected at seismic stations for hundreds to thousands of kilometers These long period seismic waves are not sensitive to heterogeneities in the crust on much shorter scales than their wavelengths so they can be studied using simplified earth velocity models and are thus easier to work with than higher frequency seismic energy The long period seismograms generated by such large landslides are often recorded at great distances and have been used for decades to study landslides Some authors have directly interpreted the timing of pulses and variations in amplitude in long-period landslide seismograms to determine the occurrence duration speed and timing of events Berrocal et al 1978 Weichert et al 1994 McSaveney and Downes 2002 Guthrie et al 2012 Others have taken analysis further and used the long period seismic waves to study the source process directly In contrast to the double-couple mechanism of earthquakes the equivalent force mechanism of a landslide is a single force applied to the surface of the earth proportional to the acceleration and mass of the moving material This is what generates the long period seismic waves Kanamori and Given 1982 Eissler and Kanamori 1987 Hasegawa and Kanamori 1987 Kawakatsu 1989 Fukao 1995 Julian et al 1998 Many authors have used forward modeling to determine the amplitude and duration of the forces exerted on the earth that could generate the observed seismic waves and used the result to estimate the mass or the acceleration of the landslide and to interpret the sequence of events e g Kanamori and Given 1982 LaRocca et al 2004 These methods have even been used to argue that what was thought to be an earthquake was actually a landslide e g Eissler and Kanamori 1987 Hasegawa and 2a- 6 Kanamori 1987 Others have used this approach to constrain rheological characteristics For example Brodsky et al 2003 estimated the coefficient of friction beneath three large volcanic landslides based on the forces they exerted on the earth Favreau et al 2010 used long period seismic observations of the 2004 Thurweiser landslide in Italy to determine the rheological parameters to use in a numerical landslide model Moretti et al 2012 used the long period seismic signals generated by the 2005 Mount Steller landslide in Alaska to invert for the forces it exerted on the earth and used both to constrain details about the flow dynamics in a numerical model Most recently Ekstr m and Stark 2013 inverted seismic waves generated by 29 large and rapid landslides recorded by the Global Seismographic Network They used their catalog of landslide force inversions combined with field data to build empirical relations between maximum forces and mass momentum potential energy loss and surface wave magnitude These relations allow for rapid order of magnitude estimates of landslide size without having to wait for other evidence However the long period seismic signals generated by the acceleration of the landslide as a whole that can be approximated as a single-force mechanism are not always observed If the mass is too small and or the average acceleration of the landslide too slow the forces the landslide exerts on the earth will be smaller Kanamori and Given 1982 and less likely to generate a long period signal above the noise level on nearby seismometers Furthermore the period of the waves generated depends on the duration of the forcing Kanamori and Given 1982 so a slow landslide with an extended duration may not emit waves at seismic frequencies The higher frequency signal generated by smaller scale processes on the other hand has been often observed for a wide range of landslide sizes and many authors have used this type of signal to study landslides as well Often referred to as emergent cigar-shaped or spindle-shaped the 2a- 7 higher frequency seismic energy typically builds up gradually emerging from the noise without a clear onset or obvious phase arrivals and then tapers back into the noise afterwards e g Norris 1994 Dammeier et al 2011 Deparis et al 2008 La Rocca et al 2004 Schneider et al 2010 Suri ach et al 2005 Such signals are useful for determining the occurrence duration and timing of landslides e g Norris 1994 Helmstetter and Garambois 2010 It is more challenging to use these signals to obtain quantitative landslide characteristics such as failure volume fall height or runout distance because only a small percentage of the energy is transmitted seismically for all landslides Berrocal et al 1978 Deparis et al 2008 Hibert et al 2011 and higher frequency waves attenuate rapidly and are much more affected by smaller scale heterogeneities in the crust Despite this several authors have been successful in estimating landslide characteristics such as volume and runout length within an order of magnitude or better particularly in the presence of dense nearby seismic networks Norris 1994 Deparis et al 2008 Hibert et al 2011 Helmstetter and Garambois 2010 Dammeier et al 2011 Schneider et al 2010 investigated the physical basis for variations in amplitude in the higher frequency seismic signal and found that increases in the relative amplitude could be attributed to increases in the loss of power due to frictional processes the frictional work rate The frictional work rate can be elevated for example after a sudden increase in speed after passing a step in the path or when the sliding material hits a flatter area at high speeds and begins to decelerate as frictional resistance increases Schneider et al 2010 Thus the relative amplitude of the high frequency seismic signature can be used to tie the timing of the seismic signal to the passage of material over particular sections of the sliding path 2a- 8 In this study I inverted the long period seismic signals generated by the August 2010 Mount Meager rockslide and debris flow in British Columbia to solve for the source process that generated them - the forces the landslide exerted on the earth over time I built on the initial characterization of the landslide by Guthrie et al 2012 and show that the characterization of the dynamics and source process of the landslide can be substantially improved by these methods The time-series recording of forces exerted on the earth during the landslide can be used to significantly reduce the level of interpretation required to tie post-slide observations to what actually happened during the event Though this study is based on the same seismic records Guthrie et al 2012 used as part of their characterization they used just the raw seismograms of this event to qualitatively interpret the timing of events from peaks in amplitude of the signal By inverting the seismic signals I take a much more direct and quantitative approach to obtain information about the source process by determining what forces actually generated the observed seismic waves at the source location This is comparable to the inversion of seismic signals generated by earthquakes to obtain information about the source history of an earthquake Just as this type of analysis has advanced our understanding of earthquake physics such an analysis of the seismic signals generated by landslides can contribute to a greater understanding of the landslide physics In the following sections I first detail the known characteristics of the Mount Meager landslide and the seismic data available Then I describe the inversion methods used test these methods with synthetic data and invert the long period T 30 to 150 s seismic signals to determine the forces exerted on the earth by the landslide with time I compare this result to the envelope of the higher frequency portion of the signal and piece together the sequence and timing of events I also calculate the speed of the landslide with higher certainty than was 2a- 9 possible using just the raw seismic data This provides a validation for other less-direct landslide speed estimation methods I use this result to discern the direction of failure of subevents extract the coefficient of dynamic friction during the rockslide and observe changes in the behavior of the debris flow over time - characteristics that are otherwise difficult to determine in the absence of seismic analysis This case study illustrates the benefits of including a seismic source analysis in landslide investigations and its potential to improve numerical models an option that is becoming more readily available as seismic networks become denser and high quality digital data more accessible 2 Data On 6 August 2010 at about 10:27 UTC 3:27 a m local time the secondary peak gendarme and southern flank of Mount Meager part of the Mount Meager Volcanic Complex in British Columbia collapsed in a massive rockslide that quickly mobilized into a debris flow Guthrie et al 2012 A rockslide is a failure of bedrock where sliding occurs dominantly on a single failure surface Cruden and Varnes 1996 while a debris flow is a poorly sorted internally disrupted and saturated flowing mass controlled by both solid and fluid forces Iverson et al 1997 According to the interpretation of the event by Guthrie et al 2012 once the rockslide converted to a debris flow it traveled down Capricorn Creek valley turning two corners sloshing up the sides of the valley and plowing down swathes of trees When it reached the end of the 7 8 km long valley the debris flow burst out into the adjacent Meager Creek valley and ran 270 vertical meters up the opposing valley wall It then split and flowed up and downstream 3 7 and 4 9 km respectively where it finally stopped leaving vast fields of deposits and temporarily blocking the Lilloet River and its tributary Meager Creek This sequence of events is illustrated on Figure 2a-1 Field evidence showed that some deposition began almost 2a- 10 immediately below the initiation zone though most material was deposited after the convergence with Meager Creek Very little material was entrained along the path though later activity incised into the primary deposits Guthrie et al 2012 Figure 2a-1 Overview of the sliding path overlain on a post-landslide satellite image with approximate boundaries outlined Refer to inset map on Figure 2a-3 for regional location of Mount Meager The source material was an estimated 48 5 million cubic meters of highly fractured and hydrothermally altered rhyodacite breccias tuffs and flows with a porphrytic dacite plug in the steeper areas Guthrie et al 2012 Additionally the source mass was highly saturated evidenced by the rapid mobilization of the rockslide to a debris flow requiring the availability of a lot of water as well as surface seepage and large springs observed along the failure surface Guthrie et al 2012 Assuming a density range of 2000-2500 kg m3 representative of typical values for these types of rocks the total mass was 1 0-1 2 x 1011 kg 2a- 11 2 1 Seismic data This highly energetic event generated strong seismic signals that were visible above the noise level at over 25 three-component broadband seismometers throughout Canada Washington State and Alaska A record section of the seismograms of this event recorded across British Columbia and Washington State by the Canadian National Seismograph Network CNSN and the Pacific Northwest Seismic Network PNSN Figure 2a-2 shows that the entire seismic signal lasted about 5 minutes before fading into the noise The onset of the seismic signal is dominated by long period pulses which are then overtaken by a more chaotic short-period signal The two distinct frequency bands corresponding to the two types of signals radiated by landslides described earlier are apparent in the spectrum of the signal and their distinct characters are made more apparent by high- and low-pass filtering the same signal around 0 2 Hz Figure 2a-3 Note that it is impossible to pick out the P and S wave arrivals separately because the amplitudes of the body waves in the higher frequency signal are below the noise at the start of the event Figure 2a-3b 2a- 12 Figure 2a-2 Record section of vertical component broadband velocity seismograms generated by the Mount Meager rockslide and debris flow Seismograms are corrected for station response and are all plotted on the same vertical scale which is shown under the inset map The inset map shows station locations relative to Mount Meager ring-shaped symbols indicate stations used in the inversion of long period seismograms The consistency in the signal between distant stations Figure 2a-2 demonstrates that both the low and high frequency portions of the signal largely reflect source effects and not path effects or site effects at individual stations However one interesting difference is that the amplitudes of the higher frequency ground motion are significantly stronger at station LLLB than station SHB though it is only 3 km further from the source area This could be due to lower attenuation rates east of the source area site amplification at the location of LLLB or both Another contributing factor could be that the landslide moved towards station LLLB and away from SHB This change in location would affect the amplitudes of the shorter period waves more 2a- 13 than the longer periods because anelastic attenuation is strongly frequency dependent Therefore the movement of the source 10% closer to LLLB could result in a noticeable reduction in the attenuation of higher frequency waves over the course of the event Suri ach et al 2005 observed a similar effect for smaller landslides In this study landslide speeds are almost two orders of magnitude slower than the seismic wave velocities so this is probably not true directivity as observed during earthquakes which is related to the Doppler effect Douglas et al 1988 Figure 2a-3 The vertical component velocity seismogram recorded at WSLR a lowpass filtered below 0 2 Hz to isolate the long period pulses that start first at point 1 and b highpass filtered above 0 2 Hz to isolate the shorter period signal that emerges from the noise about 20 seconds later at point 2 c The two distinct frequency bands are apparent as two separate broad peaks on the velocity spectrum of the entire signal By point 3 the long period signal shifts to shorter periods By point 4 the seismic signal is largely over but does not fade completely back into the noise until point 5 nearly 5 minutes after the start of the signal 2a- 14 From the seismic data available I selected those that had the best signal quality in the frequency band of interest by visual inspection Five of the seismic stations had significantly better signal quality than the rest Rather than using more data with questionable signal quality I used just the data from these five stations because test inversions detailed in section 3 showed that high quality seismic signals from just a few seismic stations should be more than sufficient to recover the force-time function The seismic stations used for the inversion are shown in relation to the location of the landslide on the map on Figure 2a-2 and are detailed on Table 2a-1 At least one component of each station had a signal to noise ratio SNR above 8 in the frequency band used in the inversion T 30-150s The highest SNR was 57 The noise characteristics of each component of each station used are displayed on Table 2a-1 Table 2a-1 Broadband seismic stations used in the inversion WSLR LLLB SHB PASS MRBL Latitude 50 1265 50 6090 49 5930 48 9983 48 5183 Longitude -122 9212 -121 8815 -123 8805 -122 0852 -121 4845 Distance km 70 115 118 208 276 Source to station azimuth clockwise from N 142 90 192 150 149 I prepared the seismic data by deconvolving the instrument response integrating the seismograms from ground velocity to ground displacement and rotating the horizontal components to the radial and transverse direction for each station The radial component refers to motion directly towards or away from the source and transverse is perpendicular to radial I then bandpass filtered the data between periods of 30 and 150 seconds using a second order minimum-phase causal Butterworth bandpass filter Using shorter period waves in the inversion would require a detailed velocity model of the region because shorter period seismic waves are more sensitive to smaller scale heterogeneities and topography Periods longer than 2a- 15 150 seconds couldn t be used because such long periods are beyond the fall-off in the response curves of all of the seismic stations and including them amplified the noise at these longer periods and overwhelmed the signal The data were weighted for the inversion by the inverse of the root mean squared rms value of the noise before the signal at the periods used These weights are reported on Table 2a-2 Table 2a-2 Noise characteristics and solution misfit at each station station name WSLR LLLB SHB PASS MRBL Component Signal to noise ratio amplitude % noise weight 1 rms noise x 100 rms noise nm rms misfit solution nm Z 23 2% 2 5 40 124 R 4 11% 0 2 530 1002 T 4 9% 0 3 316 434 Z 8 4% 2 0 51 131 R 7 5% 1 2 86 168 T 57 2% 4 7 21 66 Z 8 8% 0 6 157 170 R 8 18% 0 4 282 657 T 3 12% 0 5 206 416 Z 31 6% 1 1 89 105 R 4 10% 0 9 110 266 T 7 16% 0 4 239 232 Z 23 3% 3 2 32 88 R 8 26% 0 5 220 306 T 7 7% 1 1 93 191 Z R T refers to vertical radial and transverse components respectively 2a- 16 3 Methods For a landslide simplified as a block of constant mass m sliding down a slope the magnitude of the slope parallel force F comes from the driving force of gravity opposed by the frictional force Ff : F mg sin - Ff 1 where g is the magnitude of the acceleration due to gravity is the slope angle and bold font indicates a vector quantity The magnitude of the frictional force on the block is equal to: Ff Fn 2 where is the apparent dynamic coefficient of friction which accounts for both friction and the basal pore fluid pressures and Fn is the magnitude of the normal force The sum of forces in the direction perpendicular to the slope is zero because the landslide does not accelerate into or out of the slope so the magnitude of the normal force is equal to: Fn mg cos 3 This also means that the magnitude of the net force Fnet is equal to the magnitude of the slope parallel force F and equation 1 can be rewritten as: Fnet mg sin cos 4 If the frictional force and gravitational driving force are unbalanced as they are in the case of a mobilizing landslide the block will begin to accelerate According to Newton s second law the net force acting on an object is equal to its mass times its acceleration a so equation 4 becomes: Fnet ma mg sin cos 5 According to Newton s third law the forces of two bodies on each other are equal and opposite Therefore at the long wavelength limit as the sliding block feels a force due to its gravitational 2a- 17 acceleration the earth feels an equal point force Fe in the opposite direction Fe is a 3component vector that can be written more explicitly as a time dependent phenomenon: Fe t ma t 6 where bolding indicates a vector This is the equivalent force system that is responsible for generating the observed long period energy generated by large rapid landslides Kanamori and Given 1982 Eissler and Kanamori 1987 Hasegawa and Kanamori 1987 Kawakatsu 1989 Fukao 1995 Julian et al 1998 Fe t is comparable to the source-time function of an earthquake so I refer to it as the force-time function in this study Friction and slope angle control the acceleration of the sliding mass equation 5 which in turn determines the forces exerted on the earth equation 6 Equation 6 dictates that the force felt by the earth will be in the opposite direction to the landslide acceleration So as the source mass accelerates downslope the earth feels a single force applied in the upslope direction Then as the mass decelerates accelerates upslope the earth feels a single force in the same direction as the sliding mass i e downslope When the landslide banks a curve the acceleration is towards the center of the curve centripetal acceleration and thus the equivalent force points away from the center of the curve Julian et al 1998 also describes the torque due to lateral displacement of the landslide mass as a potential source of seismic radiation However Brodsky et al 2003 did not find it to be a significant contributor of seismic waves in their analysis of similarly large and rapid landslides For this study the inclusion of torque as a seismic source was not required to fit the data and was not incorporated into the analysis In this study I inverted the seismic data to determine Fe t Once obtained the force-time function can be used with equations 5 and 6 combined with the field evidence imagery and geospatial calculations compiled by Guthrie et al 2012 to extract information about the source 2a- 18 characteristics and dynamics of the landslide However there are a few caveats to using equations 5 and 6 directly for interpretation: the rigid block model of a landslide is of course a simplification of reality and these equations do not account for all spatio-temporal dependencies First the area of application of the force will migrate with the landslide mass and will change in total area over time In spite of this the landslide can still be treated as a stationary single force point source for long period and thus long wavelength seismic waves even though in this case the sliding mass moved more than 12 km This is because the shift in arrival times between waves generated at the start and the end of the sliding path would be less than 2 seconds at all stations for the slowest waves in the frequency band used: Rayleigh waves of a 30 second period Two seconds is a negligible fraction of the wavelength The difference in arrival times would be even smaller for the faster longer period waves Secondly the mass may vary with time Mass may be added due to erosion and entrainment and removed due to deposition Significant changes in mass over time are important for inferring acceleration from force equation 6 and must be taken into account in the interpretation Further the failure mass spreads out in space and becomes internally disturbed and agitated when it transforms from a rockslide to a debris flow To be a pure single force the dislocation of the sliding mass needs to be spatially uniform otherwise higher order force components can contribute seismic radiation Fukao 1995 The complexities of debris flow motion and its elongation over its sliding path can hinder the straightforward interpretation of the force-time function This is particularly true in the case of Mount Meager where there are several sharp bends in the sliding path and segments of the debris flow may be accelerating in different directions simultaneously resulting in opposing forces 2a- 19 In order to invert the seismograms to obtain Fe t I first set up the forward problem relating how the source process translates to the observed seismograms The seismogram recorded at each station after the station response has been removed represents the effects of the source itself as well as its path through the earth To a good approximation at long periods the earth is a linear system that can be characterized by the seismogram that would be recorded at the seismometer location from an impulse force applied at the source location The set of impulse responses between each source and station pair are known as the Green s functions and they account for all types of seismic waves as well as attenuation along the wave path The seismograms for a realistic source can then be obtained by convolving the Green s functions with a source-time function that describes the evolution of the source process over time e g Stein and Wysession 2003 In the case of a landslide this is the force-time function Fe t Green s functions can be calculated if the velocity structure of the material the seismic waves are passing through is known The periods used in this study T 30 150 s have wavelengths on the order of hundreds of kilometers and a low sensitivity to smaller scale heterogeneities in the regional velocity structure or topography For this reason a generalized earth model was sufficient to use in the calculation of the Green s functions In this study I used the 1D ak135Q earth velocity and anelastic attenuation model Kennett et al 1995 I calculated the Green s functions between each station and the landslide location using the wavenumber integration method Bouchon 1981 as implemented in Computer Programs in Seismology CPS Hermann 2002 Only the source to station distance and the velocity and anelastic attenuation model were required for this step of the calculation The radiation patterns of the seismic waves were accounted for in the inversion equations based on the source to station azimuth as explained in the Appendix The source to station distance did not change over time in 2a- 20 the inversion because the location of the single force applied to the earth by the landslide is assumed to be a stationary point source for reasons explained earlier in this section Once the forward problem was set up I inverted for the force-time function using damped least squares e g Aster et al 2005 Complete details of the inversion process are located in the Appendix 3 1 Validation To validate the robustness of this inversion method I first tested it with synthetic data to see if it was capable of recovering an input force-time function and to test the noise tolerance I started by using the forward model equation A1 to generate three-component synthetic seismograms for an arbitrary force-time function I then progressively increased the noise in the synthetic seismograms by adding Gaussian noise with a standard deviation equal to a percentage of the maximum absolute peak of the noise-free synthetic data Figure 2a-4 I then used these data to invert for the force-time function using the process described in the Appendix to see how well it returned the original signal after the addition of noise The results of this inversion for a range of noise levels first using a single three-component station WSLR and then three threecomponent stations WSLR LLLB SHB are shown on Figure 2a-5 and 2a-6 respectively The success of the inversion in retrieving the input test signal confirms that a force-time function very close to the original can be retrieved using data from just a few high quality threecomponent stations if the noise levels are low and random Even with just one three-component station and a significant amount of noise this inversion method recovered a force-time function close to the actual input model The ability of the inversion to recover the signal starts to break down when noise levels reach 30 - 40% but the noise levels for the real seismic signals of the landslide in the time immediately before the earthquake were mostly below 10% Table 2a-2 2a- 21 Figure 2a-4 The vertical component of one station WSLR of the synthetic seismograms generated for an arbitrary force-time function with 0 to 40% Gaussian noise added to illustrate the range in signal quality used in the test inversions Figure 2a-5 The three-component force-time function recovered by the test inversion of synthetic seismograms for a single three-component station WSLR with 0 to 40% noise added The original force-time function that was used to generate the synthetic seismograms bottom line is shown for comparison All force-time functions are scaled identically The relative root mean squared errors in arbitrary units between the force-time functions obtained by the inversions and the original are indicated at the right of each signal 2a- 22 Figure 2a-6 Same as Figure 2a-5 but for the inversion of synthetic data for three threecomponent seismic stations WSLR LLLB SHB with varying amounts of noise added to the signal 4 Results Using the methods described above and in the Appendix I inverted the seismic data to solve for the force-time function of the Mount Meager landslide The result is shown in Figure 2a-7 A-C This is compared to the raw seismogram from the closest station Figure 2a-7D and the azimuth of the force vector at each point in time Figure 2a-7E To quantify the fit of the resulting forcetime function I generated synthetic seismograms from the inversion solution by plugging the force-time function back into the forward model The synthetic seismograms fit the real data remarkably well Figure 2a-8 with a variance reduction of 80% The model can even closely reproduce data that was not used in the inversion EDB bottom of Figure 2a-8 The worst misfits were for the stations and components that had strong long period noise in the signal so it was encouraging that the solution did not fit that noise when it was present before and after the landslide signal The root mean squared rms errors between the original and synthetic 2a- 23 seismograms are comparable to the rms of the noise prior to the signal Table 2a-2 though the rms errors are nearly all higher than the rms of the noise This is because the forward model is approximate I am fitting 15 channels of noisy data simultaneously and the noise may not be entirely random as it was in the test inversions Figure 2a-7 A-C The three-component force time function for both the broadband five-station inversion and the solely long period inversion The vertical force is positive up and the zero of the time scale corresponds to the start of the landslide D the vertical component of the original unfiltered broadband seismic signal at the closest station WSLR and the envelope of the energy above 0 2 Hz in the signal shifted to line up in time with the force-time function Intervals 1-5 correspond with events described in text Points a-e indicate the peak in the force-time function within each interval that was used to tie the arrival of the center of mass of the landslide with arrival at points of peak forcing along the path The location and horizontal direction of the force at each of these points is plotted on Figure 2a-10 E The azimuth of the force vector over time 2a- 24 Figure 2a-8 Comparison of observed displacement seismograms dashed line with the synthetic seismograms generated by the force-time function obtained in the broadband inversion T 30150 s when plugged back into the forward model solid line The number in the right corner of each box indicates the relative weighting of the original data used in the inversion Data from EDB shaded 270 km from the source is shown to demonstrate how well the model reproduces data from a station not used to develop the model Vertical units are centimeters The force-time function of the Mount Meager landslide starts at 10:26:55 UTC has a duration of about 215 seconds and peak force amplitudes on the order of 1011 N This is of the same order of magnitude as the forces generated by the similarly sized Mount Steller landslide Moretti et al 2012 but one to two orders of magnitude smaller than some much larger landslides in other volcanic areas Kanamori and Given 1982 Brodsky et al 2003 and four orders of magnitude smaller than some huge submarine landslides Hasegawa and Kanamori 2a- 25 1987 Eissler and Kanamori 1987 This is to be expected because force scales linearly with mass equation 6 The forces are primarily horizontal consistent with the findings of other studies of landslide single-forces e g Kanamori and Given 1982 Brodsky et al 2003 The amplitudes of the vertical forces are much lower and more prone to noise in the solution In particular the dip in the amplitudes prior to the start of the landslide an artifact that only occurs on the vertical component suggests the overall amplitudes may be reduced by an unknown amount As a result I focused on the horizontal components in the quantitative interpretation requiring absolute amplitudes I use the vertical component of force only for the relative direction up or down of the horizontal forces and timing of events along the path With knowledge about the sliding path the timing and changes in direction of the force vector can be attributed to events along the path The initiating rockslide is well approximated as a sliding block allowing us to make first order calculations about landslide dynamics using equations 5 and 6 directly The subsequent debris flow is not well approximated by a sliding block but we can also make some inferences about the debris flow behavior and estimates speeds based on the timing of changes in direction of the forces relative to the debris flow path Numerical landslide modeling might be necessary to fully interpret the features of the force-time function but that is beyond the scope of this study 4 1 Rockslide initiation The Mount Meager rockslide failed toward the south and according to theory the direction of the initiating single force should be in the opposite direction: northward and upslope That is in fact what occurs first in the force-time function but instead of one wide pulse there are two pulses superimposed on each other with about 20 seconds between their peaks Interval 1 2a- 26 Figure 2a-7 The acceleration direction of the first pulse had an azimuth of 191 3 followed by another pulse of failure in a more southwesterly direction 217 3 The errors in azimuth are estimated as the standard deviation of the slope angle in interval 1 on Figure 2a-7E This sequence suggests a progressive mobilization of the flank of the mountain Based on the shape of the source volume Figures 2a-1 the landslide may have started with the release of material lower down on the flank of the slope toward the south generating the first pulse As this started to mobilize it may have destabilized the material above the bulk of which is to the northeast of the lower flank and may have failed in a more southwesterly direction as the azimuth of the second pulse suggests This two-part failure is consistent with the report of two loud cracks heard at the start of the landslide by campers nearby Guthrie et al 2012 Though this indicates the flank mobilized in two pulses they occur close enough in time to act as one bulk movement in the generation of the longest period seismic waves which are not sensitive to shorter-timescale subevents This is apparent in the force-time function obtained by inverting only the longer period waves T 75-150 s Figure 2a-7 A-C In this result the overall mobilization of the rockslide now appears as a longer period single pulse with an overall acceleration towards 213 5 Figure 2a-7 After these initiating pulses at t 40 seconds the force vector starts to point downwards and towards the south possibly due to the rockslide starting to decelerate but this is interrupted by a sharp upward and then downward force suggesting a rapid vertical collapse and impact start of interval 2 Figure 2a-7 This could signify the collapse of part of the secondary peak gendarme of Mount Meager or other steep material from the headwall that was left unsupported as the flank below mobilized It is probably not the entire secondary peak however because its total volume was estimated as 8 to 10 Mm3 N Roberts pers comm 2013 which would 2a- 27 generate a vertical force of about 2 x 1011 N if it collapsed vertically using equation 6 and assuming a density of 2300 kg m3 much higher than that observed The vertical force observed has an amplitude of 4-6 x 1010 N depending on what point is taken as its starting point so it s volume would be more on the order of 1 Mm3 if the collapse was nearly vertical According to Varnes 1978 classification the sliding surface of a rockslide is along one or a few shear surfaces within a narrow zone and though the source material is disintegrating it is moving en masse and is not yet elongated in space and flowing This type of behavior can be approximated as a sliding block which allows for a few simple calculations First equation 6 can be used to determine the acceleration of the block and determine the trajectory of the mobilizing flank as a whole assuming the mass is relatively constant Using the longer-period version of the force-time function T 75-150 s to represent the whole-scale mobilization of the rockslide I calculated the horizontal acceleration of the mass at each second in time Unfortunately it is not possible to calculate the acceleration of the subevents separately because their respective masses are unknown I integrated the acceleration twice to obtain the displacement of the center of mass of the landslide at each moment in time and fit the displacement curve with the equation of motion: d t do vot 0 5at2 to obtain a best estimate of the average horizontal acceleration of the rockslide a where d t is the horizontal displacement with time t The initial horizontal displacement do and initial velocity vo were set to zero The best fit was an average horizontal acceleration of 0 39 m s2 Figure 2a-9 The median slope angle of the source area from the postslide digital elevation model 15 m resolution resolved in the azimuth of slope failure 231 5 was 23 1 so the vertical acceleration corresponding to the horizontal acceleration calculated above should have been 0 17 m s2 and the total slope-parallel acceleration 0 43 m s2 By this 2a- 28 calculation the rockslide as a whole mobilized slowly taking 36 seconds to accelerate to a speed of 15 m s traveling about 250 meters horizontally and dropping about 110 meters in that time Figure 2a-9 The horizontal trajectory of the rockslide calculated from the long period T 75150 s force-time function assuming a mass of 48 5 million m3 The solid line shows a quadratic fit to the trajectory to the form of the equation of motion relating displacement acceleration and time The best fitting average acceleration was 0 39 m s2 Using a rigid sliding block approach it is also possible to estimate the areally averaged apparent dynamic friction at the base of the rockslide given the angle of the sliding plane Using a rearrangement of equation 5 sin a g cos 1 7 yields a best estimate of the apparent friction coefficient of 0 38 0 02 assuming a slopeparallel acceleration of 0 43 m s2 and a slope angle of 23 1 The apparent friction coefficient accounts for the effects of both friction and basal fluid pressure and this value suggests high basal fluid pressures To quantify this the apparent coefficient of friction can be related to the true coefficient of friction that would be felt in the absence of pore fluids by: n n P 8 2a- 29 where P is the mean basal pore pressure and n is the mean normal stress at the base of the sliding mass When rearranged equation 8 relates the difference between the apparent and true coefficient of friction to the ratio of basal pore pressure over basal normal stress: P n 9 While we don t know what the actual dynamic coefficient of friction in the absence of basal fluids was for the rocks composing Mount Meager we know from lab experiments that is nearly always greater than 0 6 for dry rocks of a wide variety of lithologies Byerlee 1978 so equation 9 indicates that basal fluid pressures were at least 22% of the basal normal stress during the rockslide for 0 38 This is corroborated by the large springs and surface seepages found throughout the source area after the landslide Guthrie et al 2012 suggesting that groundwater was instrumental in triggering this slide and its rapid mobilization to a debris flow The value obtained here is within the bounds on the coefficients of friction of 0 2 to 0 6 that Brodsky et al 2003 found for three large landslides also in volcanic environments but significantly higher than the value used by Guthrie et al 2012 to numerically model this part of the event 0 06 The reason for this discrepancy is addressed in the discussion section 4 2 Debris flow After the initiating pulses two longer period horizontal oscillations dominate the forcetime function Figure 2a-7 A-C intervals 2 and 3 Based on the direction of these vectors Figure 2a-7E they are most likely the manifestation of centripetal accelerations of the debris flow material turning the two major corners in its sliding path Unfortunately it is not possible to take the same approach as above and use equation 6 to estimate the trajectory of the debris flow directly because a debris flow is poorly approximated as a sliding block The flow becomes 2a- 30 elongated in space which could result in differing flow directions amongst segments of the failure volume and the material is flowing and agitated and can have complicated flow patterns Iverson et al 1997 Zanuttigh and Lamberti 2007 However under the assumption that the timing of peaks in the force-time function correspond to the times when the center of mass reached points of maximum forcing the timing of peaks can be tied to points along the sliding path to estimate the debris flow speeds I defined the starting point as the center of mass of the landslide calculated from the depleted thickness map from Guthrie et al 2012 marked with an x on Figure 2a-7 and placed the location of the first peak point a 75 meters downslope from there corresponding with the distance traveled by the rockslide by the time it reached its peak at t 21 s Figure 2a-9 For intervals 2 and 3 on Figure 2a-7 I assumed that the peak in the force-time function corresponded to the time that the center of mass of the debris flow passed the portion of the path with the highest curvature i e highest centripetal acceleration To find these points quantitatively I fit a polynomial to the horizontal sliding path that was delineated by Guthrie et al 2012 and calculated the curvature of this polynomial analytically I then placed the peak force vectors for each curve at these peak points of curvature Figure 2a-10 points b and c If the assumption that the peak force corresponds to the center of mass arriving at the location of peak forcing is valid the direction of the acceleration should point towards the center of a circle tangent to the point of maximum curvature To test this I placed circles with radii equal to the radius of curvature tangent to the point of maximum curvature and the peak acceleration vectors do point to within a few degrees of the center of these circles as expected for a centripetal acceleration Figure 2a-10 2a- 31 Figure 2a-10 Outline of sliding path with the azimuth of the major peaks in the force-time function from Figure 2a-8 placed at locations of maximum forcing black arrows The acceleration is in the opposite direction gray arrows The path trace dashed line is from Guthrie et al 2012 except from segment d to e which was estimated from satellite imagery The x marks the approximate location of the start of the center of mass Peaks in the force-time function correspond to the arrival of the center of mass of the landslide at the designated locations and were used to estimate the average speed of the landslide between these intervals as summarized on Table 2a-3 and labeled along the path The next interval interval 4 is characterized by an eastward and upward force that I interpreted as the debris flow decelerating rapidly upon reaching the confluence with Meager creek and running into the opposing valley wall point d At this point the debris flow split and flowed both up and downstream and also left significant deposits at the confluence of the two valleys This complicated the interpretation of the force-time function in interval 5 because there were opposing accelerations and a significant decrease in moving mass However the distinct pulse of force toward the northwest point e is consistent with another centripetal acceleration of some of the debris as it sloshed up the side of a steep hill before making its final turn to the 2a- 32 northern depositional area point e Figure 2a-7 and 2a-10 I placed the location of this peak force vector at the estimated point of maximum curvature of this turn and used it to estimate the speed for this last segment To conservatively account for uncertainties in the determination of distances between points I assumed a possible distance interval range of 400 meters I assumed a timing error range of 2 seconds The location assigned to each major peak labeled on Figure 2a-7 is shown on Figure 2a-10 The direction of the force vector at each of these peak times is also plotted along with the corresponding acceleration vector pointing in the opposite direction I estimated the errors in the azimuth of the peak force as the standard deviation of the angle within the interval containing the peak force Figure 2a-7E All error ranges are within a few degrees except for point d probably due to the opposing flow directions of the material at this confluence Table 2a-3 Table 2a-3 Distances and speeds between points along path and corresponding azimuth of the force at each point Point Distance from previous point m Time from previous point s Average speed best estimate m s Possible range m s Azimuth of Force 75 21 2 4 3- 4 33 5 b 1850 400 48 2 39 32- 45 205 5 c 3360 400 44 2 76 64- 90 7 4 d 2400 400 26 2 92 71- 117 114 29 e 700 350 52 2 13 6- 22 290 3 Refer to Figure 2a-7 for the timing and Figure 2a-10 for the location of points a-e a The average speed of the center of mass of the landslide between each of these points calculated by simply dividing the distance over the time is reported on Table 2a-3 and plotted as the solid black line on Figure 2a-11 By this analysis the average speed from the starting point to the first curve was 39 m s increasing to 76 m s going into the second curve and to 92 m s as the 2a- 33 debris flow traversed the third segment and burst into the adjacent valley After reaching the opposing valley wall at point d the average speed decreased significantly and the portion of debris that continued downstream slowed to an estimated 13 m s before turning the final curve to main depositional area Figure 2a-11 The average speed of the center of mass along path distance from this study black dots with error bars The average speed estimates are plotted halfway between the distance markers defining each interval The solid line shows a linear interpolation to these points shading shows the error range The zero point corresponds to the location of the center of mass of the source area and the average speed estimates were plotted halfway between the distance markers used This result is compared to speed estimates by the three methods used by Guthrie et al 2012 Schneider et al 2010 showed that the relative amplitude of the envelope of the high frequency seismic signal correlates well with the total frictional work rate Frictional forces will be higher than the gravitational forces when the landslide reaches a slope shallower than the arc tangent of the coefficient of friction Schneider et al 2010 For the apparent coefficient of friction determined in this study 0 38 that angle would be 21 The slope of the sliding path is consistently less than 21 just past the toe of the source area so there should have been an increase in the amplitude of the higher frequency signal almost immediately after the rockslide 2a- 34 left the source area This is in fact what occurred: the envelope of the higher frequency 0 2 Hz energy started to build up about 20 seconds after the start of the landslide Figure 2a-7D As the mass started to disintegrate flow and reach high speeds the random kinetic energy should have increased as well This in turn should have increased the frictional resistance due to higher shearing rates and thus higher seismic amplitudes This is observed: the envelope of the higher frequency energy rose and reached a plateau after turning the first curve in the path interval 2-3 This is the part of the sliding path where the debris flow reached high speeds 76 m s over a relatively straight interval and random kinetic energy should have been high After passing the second curve point c Figure 2a-7 the amplitude of the envelope reached an even higher plateau this is where the estimated speeds reached their highest point but were followed by a rapid deceleration as the debris hit the wall was deflected and slowed down as it spread over the depositional area This section interval 4 has the highest amplitudes of high frequency shaking most likely due to high frictional resistance forces as the mass rapidly decelerated 4 3 Aftershock About 2 minutes after the end of the main landslide event there was an aftershock a smaller landslide that occurred after the main event This landslide also generated a long period seismic pulse I inverted the long period seismograms of this event to obtain its force-time function Figure 2a-12 I had to use shorter period seismic waves T 20 50 seconds in the inversion to capture this smaller event The shortest period waves used are too short to be accurately represented by the Green s functions so this is a more approximate inversion than the main event I also only used the closest three stations in the inversion because their mean signal to noise ratio SNR was 4 while the two more distant stations had a mean SNR of 2 with the lowest component having an SNR less than 1 The force-time function for this event indicates a 2a- 35 primarily vertical collapse towards the south-southeast probably off the now over-steepened headscarp The collapse quickly took on a more horizontal trajectory in the southeast direction The absence of a strong subsequent downward force suggests that there was no impulsive vertical impact so the material may have disintegrated along the slope as it fell The force of the vertical collapse is an order of magnitude smaller than the main event peaking around 6 x 109 N The second vertical pulse occurring about 30 seconds after the first could have been a second collapse or could be forces generated along the sliding path of the first collapse Since there is no way of estimating the volume of this secondary landslide from satellite data because it occurred just minutes after the main event I used the result of this inversion to estimate the volume solely from the seismic data To do this I assumed the same frictional value found for the main event 0 38 and took the arc tangent of the vertical over the horizontal forces at the peak of the vertical collapse to estimate a slope of 72 This results in an acceleration of 8 2 m s2 by equation 7 Since the magnitude of the forces at this point was 5 8 x 109 N using equation 6 this yielded an estimated mass of 7 x 108 kg or a volume of 0 3 million m3 assuming a density of 2300 kg m3 This volume of material is two orders of magnitude smaller than the main event yet the forces are only one order of magnitude smaller probably because accelerations were higher due to the near-vertical failure direction 2a- 36 Figure 2a-12 a A second smaller landslide an aftershock occurred a few minutes after the end of the main landslide as shown in the seismic data b-d Three components of force of the aftershock obtained by inverting seismic data at periods of 20 to 50 seconds from the three closest three-component stations WSLR LLLB SHB The time scale is consistent between all four plots 2a- 37 5 Discussion 5 1 Improvements to landslide characterization The time series recording of the forces exerted by the landslide allowed for significant improvements in the characterization of the dynamics of this event particularly when combined with the extensive field evidence and geospatial data compiled by Guthrie et al 2012 In particular the availability of the force-time function reduces the qualitative interpretation typically required to tie post-slide evidence to what happened during the event It also eliminates guesswork required to interpret the source of pulses in the raw seismograms directly by using the seismograms to find what the source was quantitatively As mentioned the force-time function showed that the rockslide initiation occurred in two pulses which I interpreted as a progressive failure of the flank of the mountain These events were followed soon after by a nearly vertical collapse that was smaller in volume This sequence of events is in contrast with the interpretation of Guthrie et al 2012 They proposed that the near-vertical collapse of the steep gendarme occurred first and its impact onto the shallower slopes below caused the flank to mobilize due to undrained loading and rapidly turn into a debris flow This is a reasonable interpretation from the evidence that was available at the time but with the additional information provided by the force-time function it is clear that the failure of the flank of the mountain started first and was likely the cause of the vertical collapse - though the collapse of this material onto the already-mobilizing flank still could have been responsible for its rapid disintegration and mobilization to a debris flow This is a reasonable argument given that the higher frequency portion of the signal attributable mainly to the debris flow rises quickly after the vertical collapse 2a- 38 The results of this study also improve on the interpretation of Ekstr m and Stark 2013 who included the 2010 Mount Meager landslide in their inversion of long period seismograms from 29 catastrophic landslides worldwide recorded on the Global Seismographic Network Though they do not include the entire force-time function in their results they reported peak forces of 1 48 x 1011 N for this event comparable but higher than the peak magnitude of the force found in this study of 1 0 x 1011 N However the start time they reported for the start of the event was two minutes later than the start time found in this study and reported by Guthrie et al 2012 Their start time corresponds instead to the time of the peak at point d Figure 2a-7 and 2a-10 This suggests they interpreted what this study found to be a centripetal acceleration of the debris flow around the second curve in the path as the initiation of the rockslide This discrepancy may explain why their estimated runout of 4 6 km was much shorter than the actual runout 12 km and highlights the care that must be taken when interpreting the force-time functions of landsliding events Though the methods used to estimate the speed of the landslide from the force-time function in this study still required some interpretation they are the closest to a direct measurement of the options available Guthrie et al 2012 used two common methods of estimating landslide speeds: a theoretical method called superelevation Chow 1959 and a numerical landslide model DAN-W Hungr 1995 Hungr and McDougall 2009 I validated these methods against the more physically based measurement available from the results of this study since the opportunity is not often available for natural landslides As mentioned Guthrie et al 2012 also used features of the raw seismograms to estimate speeds and I include that result in the comparison as well The four methods are plotted for comparison on Figure 2a-11 and were all adjusted to the same path starting point used in this study 2a- 39 The speeds predicted by the numerical model presented by Guthrie et al 2012 are much higher at the start of the debris flow than that determined in this study The initial acceleration in the first 20 seconds was about 4 5 m s2 which should have generated a force an order of magnitude higher than that observed in the force-time function so the speeds cannot have been that high at the onset The exceptionally low coefficient of friction they used in this simulation 0 06 compared to 0 38 determined in this study may partially explain the difference Guthrie et al 2012 chose this value to best fit the runout distance and velocities of the landslide interpreted from the raw seismograms and did not fit the superelevation estimates well This low value for is probably because they were trying to match initial speed estimates that were too high This mismatch highlights the potential of using the force-time functions and other information derived from seismic waves to validate and calibrate numerical models and tie them to the physical world as Moretti et al 2012 did in their study The limitation is that for complicated events - such as this one with subevents of unknown relative masses and a complex path causing opposing forces at times - numerical models may be needed to fully interpret the force-time function So in reality the comparison between numerical models and landslides may be more of an iterative process that may not necessarily have a unique solution The landslide speeds estimated roughly from the raw seismograms in Guthrie et al 2012 also had a much higher estimate of the initial speed Figure 2a-11 This is due to the aforementioned difference in their interpretation of mobilization sequence They assumed that the majority of the landslide mass - the flank of the mountain - did not mobilize until the secondary peak collapsed on it about 45 seconds after the start of the landslide With this interpretation there is very little time between the mobilization of the flank of the mountain and its arrival at the first corner thus resulting in the extremely high initial speeds they report As 2a- 40 explained above the force-time function shows the reverse sequence of events: the flanks of the mountain mobilized first followed by a vertical collapse If they had this information in the initial interpretation of the seismograms the initial speed estimate would have been much closer to the speeds obtained by this study Though the uncertainties are higher the best estimates of the speeds from the raw seismograms are close to those estimated in this study: between 10 and 30% lower but with error bars that overlap The main benefit of using the results of the seismic inversion to estimate speeds is the elimination of most of the guesswork involved in correlating pulses in the seismic record to exact locations of events along the path The speeds determined in this study compare most favorably with the values determined using the superelevation method Chow 1959 a theoretical method of determining speed by how much higher the debris flow reaches on the outside corners of turns than the inside corners The three superelevation measurement points are between 5 and 11% different from the projection of the speeds calculated in this study and are well within the error bars Figure 2a-11 providing a validation of this theoretical method with real data The main discrepancy is the average speed for the path segment between points c and d coming out of the last corner in the valley where the average speed from this study exceeds the projection line between superelevation estimates by 35% However it is not possible to conclude whether this discrepancy is real or not because the superelevation measurements are effectively point measurements at the points before and there is no information in between There is a possibility that the continuous increase in the debris flow speed until point d found in this study could be erroneous However the uncertainties incorporated in the calculation of the error bars of the speeds for this study were conservatively wide The main source of error would have to be a misinterpretation of the force-time function in this study due 2a- 41 to the complexity of flow at this junction This is possible but it is difficult to conceive where the pulse of eastward forces observed in interval 4 would come from if not from the material running up against the adjacent primarily west-facing valley wall point d so I consider this unlikely Assuming this late peak in speeds is real and the other methods are either erroneous or cannot resolve this peak there are a few potential explanations According to field evidence there was very little entrainment of material along the path in fact deposition started immediately below the initiation zone but most material was deposited beyond the Capricorn creek valley Guthrie et al 2012 so the mass was relatively constant during the fastest intervals along the landslide path A landslide of constant mass will continually increase in velocity if the angle of friction tan-1 is shallower than the slope angle Iverson 2012 The apparent coefficient of friction at the base of the rockslide estimated in this study to be 0 38 which translates to an angle of friction of about 21 The slope of the debris flow path is shallower than this averaging around 10 which means the coefficient of friction must have dropped below 0 18 tan 10 during the debris flow in order to still be accelerating along this path A drop in the coefficient of friction of a debris flow can occur due to undrained loading of wet bedded sediments by the overriding debris flow that causes an increase in the pore pressures at the bed Iverson et al 2011 This often also results in an increase in entrainment Iverson et al 2011 but entrainment was not observed in this case possibly because of the exceptionally high speeds which actually make entrainment less likely to occur Iverson 2012 Another contributing factor to the late high peak in speeds estimated in this study could be due to a common behavior of debris flows: the development of surging also referred to as roll waves As explained by Zanuttigh and Lamberti 2007 debris flow surges develop when 2a- 42 smaller flow instabilities grow and form surface waves that overtake each other with growing wavelengths and amplitudes As these instabilities progress downstream and continue to overtake each other they can coalesce into bigger surges often eventually forming one dominant first surge characterized by a concentration of boulders at the front sometimes followed by subsequent smaller surges Debris flow depths are often significantly higher in surge waves and the waves can travel up to three times faster and exert forces more than an order of magnitude higher than the rest of the regularly flowing mass The development of one or more large coalesced surges along the flow path of the Mount Meager debris flow could have moved the speed of the center of mass of the debris flow forward faster than the average flow but the forces exerted by the surges themselves were likely too short period and too low-amplitude to be resolved in the force-time function The timing of the speedup is consistent with the observation that larger coalesced surges tend to preferentially appear further down the flow path because it takes time for the instabilities to grow large enough and overtake each other Zanuttigh and Lamberti 2007 If the surge started to develop prior to reaching point c the speed estimate between b and c could also be higher than the regular nonsurging flow There is even a hint of what could be interpreted as two separate surges visible in the vertical component of the force-time function The vertical component of the force at point d has a shorter duration than the eastward component and is followed by a second smaller upward pulse Figure 2a-7A This could indicate that the bulk of the debris flow material did not run up vertically but was primarily deflected horizontally and it could have been the arrival of these two or three subsequent surges that were faster deeper and higher energy than the rest of the flow that was responsible for the high runup observed in the field The surges do not appear as discrete events on the east component of the force-time function however though this could be 2a- 43 because their masses are not large enough to contrast with the rest of the regular flow being deflected primarily horizontally 5 2 Limitations One major limitation to the application of the methods used in this study to other events is that there is a whole spectrum of landslide types and behaviors Varnes 1978 but these methods can only be used to study the small percentage that generate the required long period waves: exceptionally large and rapid landslides Scaling these methods down to more common shorter duration smaller rapid landslides would require a detailed characterization of the velocity and attenuation structure of the study area and better seismic coverage because they would generate lower amplitude and shorter period seismic waves Even if this can be done it doesn t address the problem of potential overlap in the frequency domain between the coherent pulses from the bulk mobilization of the landslide mass and the signal generated by stochastic smaller scale processes For larger landslides the two sources of seismic radiation are manifested in distinct frequency bands e g Figure 2a-3c but this may not be the case in a scaled down scenario and if they overlap the two can no longer be isolated with simple filtering On the other side of the spectrum slower events that may have large masses but slow accelerations and long durations such as large slumping events may be too slow to generate waves of short enough period to be observed by seismic methods though subevents or smaller scale forcing may be resolvable Another limitation is that the force-time function alone cannot be used directly to estimate useful information about the dynamics of the landslides Other information is required For example even if the landslide under investigation can be approximated as a coherent sliding block equation 6 dictates that the trajectory of the sliding block can only be calculated from the 2a- 44 force-time function if the mass is known Likewise the mass can only be calculated if the trajectory is known However even if neither is known order of magnitude estimates of mass can still be obtained due to physical limitations on acceleration I showed that the methods used in this study can be used to determine the sequence of events and the occurrence of subevents However this can also be a limitation because subevents can complicate the force-time function and thus make straightforward interpretation and calculations from it challenging In this study I was able to get around the fact that the rockslide initiation occurred in two subsequent failures because the two subevents were close enough in time and space that they acted as a single failure mass at the long period limit Care must be taken to correctly assess when and where the rigid sliding block approximation is valid and when it breaks down For example the approximation breaks down if subevents are too far apart in time or space to be considered one failure mass at long periods or when the failure mass is not moving coherently enough such as during the debris flow of this event where the material became elongated in space and internal agitation and complex flow patterns dominated 6 Conclusions In this study I inverted the long period seismic signals generated by the Mount Meager landslide to solve for the forces it exerted on the earth as the failure mass accelerated turned curves along its path and decelerated I used this result the force-time function to track landslide behavior over time This analysis is useful not only for unraveling the sequence of events and facilitating a more direct interpretation than is typically possible between post-slide evidence and what actually happened during the event but can also be used to make first order calculations about landslide dynamics 2a- 45 Using the three component force-time function I was able to identify the directions of the slope collapse and discern that the slope failure was progressive with the massive flank of the mountain starting to mobilize first in two discrete but closely timed subfailures followed by a much smaller nearly vertical collapse that might have been the collapse of part of the gendarme of the secondary peak of Mount Meager left unsupported as the flank mobilized The addition of this new information clarified the sequence of events suggesting that the initial interpretation made by Guthrie et al 2012 where they proposed that the vertical collapse occurred first and caused the flank to mobilize was actually reversed Using the mass of the failure determined from satellite imagery by Guthrie et al 2012 I was able to use the force-time function directly to estimate the trajectory of the center of mass of the rockslide showing that it had an average horizontal acceleration of 0 39 m s2 and estimated the apparent coefficient of friction at the base of the rockslide to be 0 38 a low value that suggests basal fluid pressures were high at least 22% of the normal stresses at the base of the slide assuming a minimum coefficient of friction of 0 6 for dry rocks Following the sequence of forces generated by the rockslide initiation the direction and timing of the primarily horizontal forces were consistent with the debris flow turning two corners in its path and then running up the wall of an adjacent river valley The horizontal forces from these centripetal accelerations were actually the highest forces overall A debris flow is poorly approximated as a sliding block so I could not make calculations or estimate the trajectory directly from the force-time function but instead tied the timing and direction of peak forces to points of peak forcing along the path to estimate the speed of the center of mass of the debris flow I found that speeds increased continuously as the debris flow progressed down the first valley peaking at 92 m s before rapidly decelerating upon reaching the adjacent Meager Creek 2a- 46 valley The speeds I found by this method were very close to the speeds predicted by superelevation providing a physically based validation to that theoretical method The forcetime function also provided a test of other speed estimation methods applied by Guthrie et al 2012 The initial speeds they estimated by numerical modeling were much higher than those estimated in this study and would have required forces an order of magnitude higher than those observed in the force-time function Their estimates of speed from the raw seismograms were close to those estimated in this study though with higher uncertainties but their speed estimates were also too high at the onset of the landslide because of their reverse interpretation of the sequence of initiating events The differences show that the addition of the information provided by the force-time function can significantly clarify landslide characterization Though the calculations I presented in this study are rough and large scale due to the long period nature of the seismic waves used and direct interpretation is difficult due to the complexities of debris flow behavior it is remarkable that using data from five broadband stations 70 to 276 km from the source it was possible to reconstruct details of this event that are unobtainable by other methods but nonetheless important for understanding landslide physics and improving numerical models As there are currently networks of broadband seismometers worldwide for which data are freely available the techniques I described could be applied to study other large landslides that occurred both in the past and to come 7 Acknowledgements Many thanks to Ken Creager who provided indispensable guidance on what started as a project for his Inverse Theory course and to my advisor John Vidale Also to Emily Brodsky Dick Iverson Rick Guthrie John Clague Anne Mangeney and Hiroo Kanamori for helpful 2a- 47 feedback reviews and discussions Nicholas Roberts for helping with some geospatial calculations the Pacific Northwest Seismic Network and Canadian National Seismograph Network for providing the seismic data and Sharon Watson for tolerating frigid fast flowing river crossings and quicksand to accompany me on a field visit of the landslide Additionally reviews by Jackie Caplan- Auerbach Agnes Helmstetter and two anonymous reviewers helped improve the manuscript significantly 8 References Aster R C B Borchers and C H Thurber 2005 Parameter estimation and inverse problems Elsevier Amsterdam Berrocal J A F Espinosa and J Galdos 1978 Seismological and geological aspects of the Mantaro landslide in Peru Nature 275 5680 532-536 Bouchon M 1981 A simple method to calculate Green s functions for elastic layered media Bull Seism Soc Am 71 959-971 Brodsky E E E Gordeev and H Kanamori 2003 Landslide basal friction as measured by seismic waves Geophys Res Lett 30 24 2236 doi:10 1029 2003GL018485 Byerlee J 1978 Friction of rocks Pure and Appl Geophys 116 4-5 615-626 Chow V T 1959 Open-channel hydraulics McGraw-Hill New York Cruden D M 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I Vilajosana G Khazaradze B Biescas G Furdada and J M Vilaplana 2005 Seismic detection and characterization of landslides and other mass movements: Nat Haz And Earth Syst Sci 5 791-798 Varnes D J 1978 Slope movement types and processes in: Landslides analysis and control Transportation Research Board Special Report 176 R L Schuster R J Krizek Eds pp 11-33 National Research Council Washington DC Weichert D R B Horner and S G Evans 1994 Seismic signatures of landslides: the 1990 Brenda Mine Collapse and the 1965 Hope Rockslides Bull Seismol Soc Am 84 5 15231532 Zanuttigh B and A Lamberti 2007 Instability and surge development in debris flows Rev Geophys 45 3 RG3006 doi: 10 1029 2005RG000175 2a- 51 Chapter 2b: The Seismic Story of the Nile Valley Landslide Most of the content of this chapter was presented at: Allstadt K Vidale J Thelen W and Bodin P 2010 The Seismic Story of the Nile Valley Landslide Poster Session presented at: Seismological Society of America Annual meeting 2010 2010 Apr 21-23 Portland OR 2b- 1 Table of Contents Summary 2b-3 1 Introduction 2b-4 2 Background 2b-5 3 Seismic Data 2b-10 4 Discussion 2b-13 5 Conclusion 2b-15 6 Acknowledgements 2b-16 7 References 2b-16 2b- 2 Summary The Nile Valley landslide of October 11th 2009 was one of the largest in recent Washington state history This translational slide involved a volume on the order of 107 cubic meters and destroyed 2 houses a portion of highway and flooded several houses when it partially dammed a stream Residents in the area reported noises and deformation starting 2 days beforehand and evacuated safely The main sliding sequence occurred over about 6 hours and two regional seismic stations 12 and 29 km away captured some of the signals generated by it Distinct seismic pops began to appear about 3 hours before a partial slope failure generated a continuous 2-minute signal with an emergent onset After this the pops became more frequent and evolved into the largest sliding event This appeared as a 13-minute broadband rumble centered on 4 5Hz with an emergent onset and spindle shaped signal Diminishing rumbling followed for another hour After the landslide occurred we installed 12 vertical geophones and 4 three-component seismic stations around the perimeter More than 60 small events were recorded at these stations in the days after the slide and are likely due to settling and continued deformation One particularly large movement 9 days after the main event generated a signal that also appeared on the more distant permanent stations This event had a similar shape to the main event but lasted only 15 seconds with about 25% of the amplitude Smaller events recorded on the seismic stations at the site showed a buildup in amplitude hours before this event This case adds to the body of knowledge on the seismic manifestation of landslides and gives more clues as to what happens before during and after a landslide of this type In addition our observations indicate that landslides may show precursory patterns that seismic monitoring can detect if they can be reliably identified 2b- 3 1 Introduction The Nile Valley landslide of October 11th 2009 Figure 2b-1 located on the east side of the Cascades along Highway 410 was one of the largest in recent Washington State history This translational slide involved a volume on the order of 107 cubic meters of material It destroyed a portion of state highway damaged several houses and diverted a river causing flooding Fortunately no one was injured because the landslide gave warning signals in the days and hours beforehand Figure 2b-1 Location of Nile Valley Landslide in Washington State on Google earth basemap The slopes failed over the course of about 24 hours in a complex series of events of various sizes and velocities Some of the more energetic events generated seismic signals that were captured by the Pacific Northwest Seismic Network PNSN regional stations 12 and 29 km away NAC and ELL Figure 2b-2 This highly precise seismic timeline in combination with detailed eyewitness reports provided to the Washington State Department of Transportation WSDOT and studies of the geology of the landslide conducted by the Washington State 2b- 4 Department of Natural Resources DNR resulted in a detailed account of the unfolding of a landslide unlike any other This study focuses mainly on the seismic manifestation of movements on the slide and how this case study can contribute to the sparse existing body of knowledge on landslide seismology Complementary details from eyewitness accounts and landslide geology are included Figure 2b-2 Location of nearby PNSN stations in relation to Nile Valley Landslide Google Earth basemap 2 Background The Nile Landslide may be related to or occur in deposits of the much larger ancient Sanford Pasture Landslide Figure 2b-3 which covers an area of over 50 square kilometers The Sanford Pasture Landslide is on a southern face of an oversteepened anticline The Nile Thrust fault approaches the surface inside this ridge Weak Ellensburg Formation interbeds siltstone volcaniclastics and sandstone created a perfect failure plane for the landslide The Sanford Pasture landslide is at most 2 million years old but the actual age is not well known The 2b- 5 present-day scar from this slide is apparent on Figure 2b-3 After failure erosion split the Sanford Pasture landslide and formed a river valley between the deposit area and the main body of the landslide now known as the Nile Valley Smaller blocks continued to move at least two major movements flow into the valley area and to the location of the Nile slide Hammond 2009a b Figure 2b-3 The size of the scar of the ancient Sanford Pasture Landslide dwarfs the Nile Valley Landslide circled in red basemap from Google maps A cross-section of the Nile Valley landslide of October 2009 is shown on Figure 2b-4 and a map view showing the different failures adapted based on interpretation by the WSDOT is shown on Figure 2b-5 the timing of the different failures depicted on this map will be discussed in the next section The headscarp of the Nile Valley Landslide formed along the contact with a separate landslide block of basalt beds Movement occurred on two failure planes located on interbeds between basaltic flows The upper failure plane is composed of sandstone and siltstone at an approximate depth of 20 meters Movement along this plane was translational with localized rotational blocks and flows and resulted in the main surface movement that covered 2b- 6 Highway 410 and diverted the Naches River The deeper failure plane was at a depth of around 60 meters and borehole drilling afterwards revealed high confining water pressures in this failure plane most likely confined by a clay-rich sedimentary layer overlying the basalt Badger 2010 pers comm This failure block moved into the valley creating deformation and folding and movement of the soft sediments at the toe of the landslide including shifting an entire intact block with a house on top of it eastern hill of uplifted areas labeled on Figure 2b-5 Figure 2b-4 Simplified cross section through the Nile Valley landslide showing two translational failure planes with rotational surface components Based on borehole data and LiDAR DEM collected by WSDOT and interpretation by WA DNR Location of Cross Section shown on Figure 2b-5 The following account of the sequence of events was compiled by the WSDOT Nile 2010 Signs that slopes were reawakening began up to one month before the main event: A fisherman observed clouds of dust coming from high on the slopes that would later fail Two days before the slide a local couple reported that their driveway was narrowing and occasional 2b- 7 rocks were tumbling down the slope The day before the main event nearby PNSN stations Figure 2b-2 picked up a faint low frequency rumble coming from the direction of the slide area coinciding with eyewitness reports of increased rockfall and thunder-like sounds coming from the ground Later that afternoon a small lobe of talus 10 to 15 meters wide marked initial slide on Figure 2b-5 mobilized This foreshock stopped short of the nearby houses by the late afternoon After this all was quiet and the slide seemed to be over Figure 2b-5 Overview of Nile Valley landslide cross-section A-A shown on Figure 2b-4 Then in the middle of the night: rockfall and rumbling recommenced Rumbling at 46Hz began to appear on the PNSN stations and started to increase in amplitude and the main sliding sequence began The rest of the sequence is illustrated on the timeline Figure 2b-6 2b- 8 2b- 9 Figure 2b- 6 This timeline in UTC shows the spectrograms from 1 to 10 Hz and the corresponding seismograms filtered from 1 to 7 Hz for the nearby vertical component short period PNSN stations NAC Naches WA and ELL Ellensburg WA Their locations relative to the landslide are indicated on Figure 2b-2 The seismic timeline is narrated along the top of this and the corresponding eyewitness timeline paraphrased from the WSDOT compilation Nile 2010 is explained along the bottom 3 Seismic Data Due to attenuation of higher frequencies only signals below 7 Hz appeared at NAC and ELL the two nearby short period vertical component PNSN stations Several early pops and rumbles highlighted in green on Figure 2b-6 coming from the direction of the landslide could not be tied to specific movements of the slide observed by eyewitnesses because it was dark at the time Two clear signals highlighted in red on the timeline on Figure 2b-6 can be tied directly with eyewitness reports of the two separate rapid slope failures The first signal at 14:38 UTC coincides with the rapid failure of the western portion of the slope refer to Figure 2b-5 for location The signal builds slowly up from the background rumbling at 4-6Hz and ends 100 seconds later more abruptly The spectrogram of this part of the signal shows two separate frequency centers and within each of these are discrete peaks of energy indicating multiple small sources within a complex failure sequence The signal at 16:43 UTC corresponds to the rapid failure of the larger eastern slope Figure 2b-5 This builds up from an increasing frequency of pops and rumbles apparent on NAC This signal has a clear center between 4-5Hz on NAC perhaps due to a site amplification effect at that station Eyewitnesses observed 10 to 20 seconds of rapid failure of this eastern portion of the slope Nile 2010 however the signal lasts for 15 minutes This and the fact that uplift began with this signal suggests that much of this signal may be due to the deeper movements on the sliding plane at 60 m depth Due to the shallow nature of the source and their 2b- 10 slower attenuation the seismometers probably recorded mainly surface waves but they are just vertical component instruments so we cannot confirm by looking at particle motions Figure 2b-7 Amplitudes in counts of post-slide landslide-related seismic events as recorded on the three stations closest to the activity Amplitudes are in counts and have not been corrected for station corrections The diurnal pattern is because construction noise drowned out any seismic signals during the day One week after the main sliding event we installed 12 vertical geophones and 4 threecomponent seismic stations around the perimeter to capture the near-source seismic records of any further movements of the slide Station locations are shown on a post-slide DEM of the area on Figure 2b-8 No further widespread movements occurred during the monitoring period but more than 60 small events were recorded at these stations in the days after the slide Figure 2b7 likely due to settling and continued deformation of the slide mass One movement 9 days after the main event generated a strong signal that also appeared on the more distant regional stations Smaller events recorded on the seismic stations at the site showed a buildup in 2b- 11 amplitude hours before this event The locations of these signals and other strong signals located by zero-lag cross correlation Almendros et al 1999 are shown on Figure 2b-8 Figure 2b-8 Location of stations installed after the landslide triangles and best-fit post-slide event locations circles Dashed line outlines approximate slide area The locations are all clustered in the same area located above the headscarp perhaps due to failure of slopes above the newly formed headscarp WTF2 was telemetered in real-time and 3-component stations were left out for two months to assist the WSDOT in monitoring and to ensure that the much larger Sanford Pasture landslide wasn t reawakening Two shallow earthquakes Md 0 7 with all other events in the family Any ungrouped events within each day were discarded This means that in order to be detected a repeating earthquake must repeat at least once within the same day - a condition easily met for the repeating earthquakes we are searching for Next we computed a median stack line all waveforms up in time and take the median at each time interval for each family of events detected in each day to suppress noise and condense the family into a single representative waveform Then we compared the stacks from each day to every other day within that month and grouped them again into larger families Families with more than 5 repeats in a month were saved All event families were visually examined and any false families like calibration pulses data spikes and repeating waveforms from events originating from nearby Mount St Helens were deleted The remaining families were then restacked and compared with all the families detected in the adjacent 3 months on either side and regrouped again At this step because we were comparing stacks and noise is suppressed we used a higher correlation coefficient of 0 8 to combine families These larger families were then restacked again and then each stacked waveform was scanned through the data as a template pulling out any missed detections within one month on either side of the first and last event detection of that family We used a lower cross correlation threshold of 0 6 in order to pull out even noisy events This template search resulted in some 3- 14 individual events being grouped into more than one family if two families were similar enough for that event to have a correlation above 0 6 with both of them so we found any events that were grouped into more than one family and deleted all instances of that event except for the one with the highest correlation Finally once this catalog was completed for both RCS and RCM we compared the two catalogs and families for which at least 10% of the total events overlapped between the two stations were considered to be the same family All these steps except for the visual inspection of waveforms were automated using MATLAB coding The entire search took about a week to run the biggest time limitation was downloading the archived seismic data 3 1 2 Results The results of this search are shown in Figure 3-3 events detected by at least one station are shown in red those detected on both RCS and RCM are shown in blue We only show events with a dominant frequency of less than 8 Hz on this figure We consider 8 Hz a cut-off for a low-frequency repeating earthquake We choose this cutoff because there is a clear clustering of the dominant frequency of repeating earthquakes families below 8 Hz Figure 3-2D and families with a higher dominant frequency typically do not appear on more than the closest station do not repeat at regular intervals and occur just as often or even more often in the summer as in the winter Allstadt et al 2012 suggesting they are related to a different source probably localized crevassing e g Neave and Savage 1970 We do not address these events in this study 3- 15 Figure 3-3 Repeating low-frequency earthquakes detected per hour by stations RCS and RCM Blue indicates detections that occurred on both stations gray shading indicates when at least one station had an abnormal signal RMS i e wasn t functioning properly Black lines indicate the span of select families the thick line delineates the span of 90% of the events in that given family RCS had less downtime and seems to record more repeating earthquakes than RCM probably because it is immediately adjacent to two major glaciers so its catalog is more complete We detected 299 558 repeating earthquakes grouped in 840 families at RCS Of these 3- 16 families 559 families containing 150 271 events had a dominant frequency of less than 8 Hz At RCM we detected 61 772 repeating earthquakes in 372 families 369 of these families had a dominant frequency below 8Hz containing 61 398 events Far fewer higher-frequency crevassing events were detected at RCM probably because it is not as close to major glaciers as RCS 87 families were shared between RCS and RCM The rest of the families that were not shared either were too low energy to appear above the noise on the other station or one of the stations was either not working or saturated with noise for example signals at RCM are often drowned out by high wind noise and RCM was not functioning for significant portions of the study period An initial glance at Figure 3-3 reveals that low-frequency repeating earthquakes have in fact been happening all along we just didn t know to look for them so we didn t find them Individual events often only show up at the three highest stations so the seismic network does not detect them automatically and visual detection is difficult because these high mountain stations are extremely noisy For this reason only the most obvious sequences were noticed in the past Secondly Figure 3-3 shows that though there is always a background level of low-frequency earthquake activity that hovers around 5 events per hour the big swarms of activity like the ones that originally attracted attention to this phenomenon e g Thelen et al 2013 only occur from late Fall to early Spring - essentially the accumulation season Most swarms reach at least 20 events per hour but the repeating earthquake activity sometimes exceeds 50 events per hour meaning there is an event nearly every minute A third conclusion one can make from Figure 3-3 is that there is a secular increase in lowfrequency repeating earthquake activity starting in the autumn of 2009 This cannot be attributed 3- 17 to changes in the seismic stations The changes that have occurred at RCM include a change in the type of sensor from a Kinemetrics Ranger SS-1 to a Mark Products L-4 on 6 Aug 2006 and a replacement of the L-4 on 13 Aug 2010 The gain was halved on 1 April 2008 and then increased by half on 13 Aug 2008 and has stayed stable since RCS has been a Mark L4 sensor since 2003 the only change was that it was replaced with a new one on 7 July 2005 and moved to a quieter location a few meters away on 26 July 2006 The only gain change since 2003 was when the gain was halved on 1 April 2008 None of these changes correspond to obvious changes in the number of repeating earthquakes detected except for a reduction in the outage time staring mid2006 To clarify the complex behavior of these swarms we focus on a time period containing a few consecutive swarms and plot a timeline of repeating earthquake activity Figure 3-4 The swarms are typically composed of more than one dominant family that all start around the same time typically coinciding with an increase in the snow depth recorded at PVC Each family tends to start out with large variability in the correlation between individual events and the stack of all events in the family but after a few hours or days the waveforms become more consistent i e highly correlated Then the correlation and event rate gradually drifts and the family ends When another storm passes through and drops more snow old families tend to shut off though there are some important exceptions like family 681 on Figure 3-4 which will be discussed later and new families appear and follow a similar pattern There are exceptions to these general observations Some event families such as families 704 and 721 on Figure 3-4 do not follow these trends but the families that contribute most to the swarm-like character of the repeating earthquake activity do 3- 18 Figure 3-4 Timeline showing the evolution of repeating earthquake families with at least 100 repeats during two snowstorms Each individual earthquake is a circle plotted on a line corresponding to its event family The family name is labeled at left The number of earthquake occurrences contained in each event family is labeled at right The color of each circle corresponds to the cross correlation between that individual event and the stack of all the events in that family The snow depth measured at Paradise is shown in the background 3 2 Correlation with Weather In order to look more explicitly at the apparent correlation between weather and repeating earthquake swarms we compared temperature and precipitation to low-frequency repeating earthquake activity over several years in Figure 3-5 This figure clearly shows that the start of each swarm of earthquake activity coincides with a period of intense precipitation in almost every case This is particularly apparent in the stormy winter of 2011-2012 each clear step up in the snow level coincides with a clear peak in earthquake activity 3- 19 Figure 3-5 Daily temperatures recorded near seismic station RCM and snow height and precipitation rain & melted snow recorded at Paradise compared with repeating earthquake activity Dotted lines show that peaks in repeating earthquake activity correspond to peaks in precipitation in most cases Figure 3-6 A Normalized cross correlation between daily red and hourly black repeating earthquake activity and precipitation The boxed area is shown on B showing the clear peak that occurs around 1-2 days lag Dashed lines indicate the maximum correlation obtained when the precipitation data was randomized and correlated against earthquake occurrence 10 000 times 3- 20 To quantify this relationship we performed a normalized cross correlation between precipitation liquid equivalent recorded at PVC and repeating low-frequency earthquake activity Figure 3-6 We did this for both hourly and daily time series discretizing the two time series in time exactly the same way To understand the significance of a correlation between these two distinct processes we adopted methods similar to those used by Martini et al 2009 by generating randomized precipitation data and performing the cross correlation between this random data and the vector of repeating earthquakes per day or hour 10 000 times to determine the maximum correlation value that could be obtained if the data were completely random These maxima are shown as dashed horizontal lines on Figure 3-6 We generated the random data by creating a vector of random numbers with the same mean and standard deviation using the lognormal distribution of the actual precipitation data The resulting correlation oscillates with a period of about one year Figure 3-6A because both processes are seasonal though there is a lag in the oscillation of about a month probably because the repeating earthquake activity does not start to appear until a few weeks into the accumulation season as is apparent in Figure 3-5 The most significant correlation is obtained when the repeating earthquake activity lags 1-2 days behind the precipitation indicating a delay time between when precipitation falls and when the repeating earthquake activity appears The peak which far exceeds the correlation value that could be obtained randomly has a broad base particularly on its right side indicating that there is variability in the lag time skewed towards longer times by a few days The correlation is higher for the daily time series comparison than the hourly time series most likely because there is more variability in precipitation on an hourly time scale than in repeating earthquake activity but both are smoother on daily timescales 3- 21 3 3 Locations Knowing the location of these events is crucial to understanding their source Yet locating individual events is nearly impossible because the signals only appear on at most the three edifice stations not enough to determine the location Also precise timing of the first P-wave arrivals required for traditional earthquake location methods is impossible because the signal doesn t emerge from the noise until some time after the first P-wave arrival These limitations are apparent in Figure 3-7 where a record section of the vertical components of an individual event is plotted in the left column Fortunately these earthquakes repeat up to several thousand times so we can line the seismograms up in time and stack the signals to suppress noise and augment the signal We obtained the time lags to apply to data from all seismic stations using the station with the clearest waveforms typically RCS If there were sufficient repeats of an event a clear signal emerges on the three highest stations with essentially no noise and a less clear but still usable signal emerges on the more distant stations where before there was no observable signal whatsoever Figure 3-7 middle column In this study we use the median stack rather than the mean stack to avoid the influence of outliers like spikes in the data The clarification of the signal is such that clear P- and S-wave arrival times are sufficient in number to use traditional location methods for families that have hundreds to thousands of repeats and we were also able to determine the direction of the first motion on the three closest stations The are significantly smaller than the subsequent waves and are not even visible on Figure 3-7 even in the virtual absence of noise unless we zoom in explaining why individual events appear to emerge from the noise Almost all families have mixed first motions on the vertical components though for some families some of the first motions are too small and 3- 22 uncertain to say for sure Unfortunately we cannot go further and estimate the focal mechanisms from these first motions because we only have three stations on which we can reliably recognize first motions if that and cannot estimate take-off angles well-enough in this complex terrain to provide good control of focal mechanisms 3- 23 Figure 3-7 Record section demonstrating that a single occurrence of one of these earthquakes in this case from family 796 only appears above the noise level at the three summit stations left column but when data from hundreds of events are lined up in time and stacked the noise is suppressed and the signal emerges at stations as far as 20 km from the summit This processing allows events to be located and the first motions to be determined on the closest stations First motions are indicated with gray arrows middle column The spectrum of these stacks shows that there is very little energy above 6Hz there aren t clear shared spectral peaks between stations and higher frequencies are more attenuated further from the volcano right column We only attempted to locate families that had enough repeats to clarify the signal sufficiently upon stacking to be locatable We focused on families that had more than 700 repeats and a dominant frequency of 30 at Mount Rainier where at least some of the repeating events are originating When a load of snow falls on the glacier during a storm there are a few immediate effects Figure 3-13B The driving shear stress and the effective normal stress normal stress minus basal fluid pressure are both increased at a ratio depending on the slope angle: 3-4 3-5 where the apostrophe indicates the new value is the density of the new snow g is the acceleration due to gravity hs is the thickness of new snow is the slope angle and k is the fraction of the increase in load that will be offset by an increase in basal water pressure which will be spatially variable because the subglacial water system is poorly connected The increased effective normal stress also results in increased frictional forces that resist the increased driving stresses by an amount proportional to the friction coefficient 3- 47 Figure 3-13 Conceptual model of proposed mechanism for velocity increase triggered by snow loading A Typical winter basal configuration in map view: poorly connected distributed basal cavities filled with water with spatial variability Arrows indicate direction of ice motion B Cross section of steep upper part of alpine glacier after snow added to surface C Change in basal configuration several days after the snow loading begins when stick-slip sliding ensues See text for more detailed explanation In any case the immediate increase in any of these stresses would be just 0 05 - 0 2% assuming slopes of 30 - 45 for the amount of snow that occurred prior to any of the select families This is such a small increase that it could trigger stick-slip sliding only if a particular part of a particular glacier bed was extremely close to a critical state and just a tiny increase in velocity or a tiny increase in effective normal stresses could kick it into an unstable sliding regime In this case the 1-2 day lag between peaks in precipitation rate and peaks in repeating event rates Figure 3-6 could be interpreted as the time it takes for enough snow to build up to push it over the threshold However the sharp peak at a 1-2 day lag time between snow loading and the appearance of repeating earthquakes more strongly suggests that a time-dependent process related to changes in subglacial hydrology is responsible When the additional normal load from the snow is added to the top of the glaciers it also squeezes the fluid filled cavities This increases the fluid pressures 3- 48 pw in each of the isolated basal cavities by the same amount temporarily because they are poorly drained and poorly connected: 3-6 So although the overall shear and effective normal stresses may increase by a fraction of a percent the initial basal fluid pressures in the isolated cavities may be much lower than the effective normal stresses Therefore the fluid pressure could be increased by a larger percentage relative to the initial state and this would occur over a widespread area since snow falls on the entire glacier This has the effect of essentially squeezing the water out of the cavities into adjacent areas resulting in the lubrication of a larger area of bed of the glacier i e reducing the areally averaged effective stresses This could then increase sliding velocities This change in sliding velocities would take time to occur because the movement of water in response to the pressure increase is limited by the hydraulic properties of the system providing a potential explanation for the 1-2 day lag Then as explained earlier a sudden increase in sliding velocities in turn could trigger stick-slip sliding Scholz 1998 at patches of the bed where conditions are favorable to stick-slip sliding i e colder dirtier better drained Zoet et al 2013 This could be for example a patch of fractured bedrock and is most likely a different area than those responsible for the increased velocities because it must be poorly lubricated initially Figure 313C We cannot compute magnitudes because the waveforms are so highly altered and we do not know the scaling laws to apply in this case to estimate the fault size and amount of slip anyway Thelen et al 2013 estimated the size of the seismogenic patch could range from 0 4 to 104 m3 in any case much smaller than the area under any of the glaciers involved meaning just 3- 49 part of the glacier bed is seismogenic the rest may be sliding aseismically The change in event location over time Figure 3-12 could be explained by a particularly dirty ice patch moving over an area that favors stick-slip behavior The family disappearance could occur either when the dirty ice patch moves beyond this area or excess fluid pressures have had sufficient time to drain away and sliding velocities drop back down to previous levels In most cases event families die off in about a week or two which provides a timescale for these processes Basal conditions are highly variable Fountain and Walder 1998 and there are likely to be places that meet conditions favorable to stick-slip sliding at the base of any glacier Zoet et al 2013 If more than one place under a single accelerating portion of a glacier meets the requirements or if more than one glacier responds in this way we can get multiple simultaneous event families as we observed Figure 3-4 The idea that certain parts of certain glaciers are more prone to the observed behavior is supported by the fact that event families with highly similar waveforms reappear years apart Figure 3-14 Of course these are not really the same families but instead stick-slip sliding occurring again in a very similar location to where it occurred before This suggests that some areas of some glaciers are much more prone to this behavior than others over long timescales Hanging glaciers and icefalls in particular may be prone to transient stick-slip sliding because they are less stable to begin with which may make them more prone to increases in sliding velocity from minor changes in the system They also are less likely to have thick layers of deformable basal till beneath them like lower parts of the glaciers might Deformable till may favor aseismic sliding These factors may explain why the locations of at least the select event families occur at hanging glaciers and icefalls as opposed to other areas 3- 50 Figure 3-14 Event families that share similar waveforms to the select families brown text The month in which each family occurred is labeled Waveforms shown are the stack of all events recorded at RCS One may ask why this behavior doesn t also occur in the late spring and summer when there can be rapid and high volume inputs of water from melt water and rain that can cause sliding velocity increases e g Harper et al 2007 Fudge et al 2009 The absence of swarms of repeating low-frequency earthquakes from basal slip in the summer is probably at least in part due to the difference in the configuration of the subglacial drainage system between summer and winter The summer configuration is efficient and well connected and thus less favorable for the buildup of high fluid pressures Fountain and Walder 1998 The absence of repeating earthquake swarms during the spring melts when the basal configuration may still be distributed 3- 51 and there can be rapid influxes of rain and melt water could be in part due to the observation by Zoet et al 2013a that if the bed of a glacier is already well lubricated a minor increase in lubrication from a velocity increase is relatively small and is less likely to result in stick-slip sliding There may just be too much water coming too fast When there is a lot of basal fluid in the system widespread bed separation occurs removing areas of higher drag Mair et al 2001 Stick-slip sliding may be triggered for a short time with the initial influx of water but could quickly be shut off as more and more water enters the system providing more and more lubrication that can t be drained away fast enough to allow stick-slip sliding to continue This is consistent with the observations There are low-frequency repeating earthquakes occurring year round at a background level of about 5 per hour Figure 3-3 Furthermore the larger glacial earthquakes observed at Mount Rainier and other Cascade volcanoes by Weaver and Malone 1979 and also at Mount Baker by Moran et al 2009 were classified as stick-slip events Those events occurred more often in the summer indicating that stick-slip sliding probably occurs at some locations of some glaciers year round just not in the prolonged swarms of repeating earthquakes that seem to rely on winter-like subglacial drainage conditions Another reason these larger stick-slip events in the summer are not as repeatable as the smaller winter earthquakes of this study could be because the fault area and total slip are larger so it may require fewer stickslip cycles for a given patch of entrained debris to move past an area of the bed favorable to stick-slip sliding Precipitation does not tend to trigger swarms of repeating earthquakes early in the accumulation season Figure 3-5 It takes a few weeks of winter conditions for them to start to appear which may be the amount of time required for the subglacial conduits to collapse viscously and for the drainage system to transition from summer to winter conditions 3- 52 There is also the secular trend to explain: the apparent increase in low-frequency repeating earthquake activity over the past ten years Figure 3-3 This may simply be a function of storminess for example the most repeating earthquake activity was detected in the winter of 2011-2012 which also was characterized by fewer storms dropping larger amounts of snow Figure 3-5 Stormier behavior i e large amounts of snow falling in short amounts of time would be more likely to trigger sudden velocity increases by the mechanisms we propose than many small storms depositing snow incrementally 4 3 Broader Implications Beyond proposing a solution to the puzzle of a peculiar seismic source on one mountain the findings of this study and our proposed mechanisms have wider implications both in glaciology and beyond This case adds to the body of knowledge on alpine glacier behavior We show that some parts of some glaciers can be extremely sensitive to minor changes in external loading Our observations suggest that if conditions are right surges in basal sliding velocity can be triggered by surface loading that is a fraction of a percent of the total overburden load at least in the winter months when the subglacial drainage system is composed of isolated and poorly connected cavities Furthermore though stick-slip behavior has been confirmed geodetically for large shallowly sloping ice streams in Antarctica e g Wiens et al 2008 this is the strongest evidence of seismicity resulting from stick-slip glacial sliding at steep temperate alpine glaciers that we know of The long-term year round record of repeating earthquake activity provides a window into seasonal differences in the behavior of alpine glaciers particularly the behavior of the high reaches of alpine glaciers in wintertime an essentially inaccessible environment that is thus difficult to study with other methods The behavior documented here adds to the spectrum of known glacier behavior This may also have ramifications for subglacial morphology as some 3- 53 studies suggest stick-slip sliding may have a connection to erosional processes e g Zoet et al 2012 Our hypothesis that these events are initiated by a surge in the sliding velocity of hanging glaciers and icefalls also may have implications for ice avalanching hazards If a velocity increase were to cause sliding to accelerate critically something we could observe from telemetered seismic data like the accelerating stick-slip seismicity Caplan-Auerbach and Huggel 2007 observe prior to ice avalanches at Iliamna volcano in Alaska the end result could be an ice avalanche The long-term year-round record of repeating earthquake activity also allowed us to show with more confidence that the majority if not all of the observed repeating low-frequency seismicity is not related to volcanic activity This type of behavior is common and occurs every year The catalog we compiled also allows us to characterize what is normal behavior so that when Rainier reawakens we are better equipped to discriminate harmless glacier-quakes from seismicity related to the volcano A near real-time method for monitoring repeating earthquake activity that sends alerts when activity is beyond pre-determined bounds on normal behavior is already under development and testing Allstadt et al 2012 These methods could be customized and applied to other glacier-covered volcanoes that present similar monitoring challenges These repeating earthquakes at Mount Rainier can provide insight into repeating earthquakes and earthquake behavior in other environments provided we understand the limitations of the analogy e g ice melts at a much lower temperature than rocks It is rare to have such an extensive catalog of earthquakes that occur so frequently: nearly 300 000 repeating earthquakes with more occurring every day This allows us to identify certain seismicity patterns that we do 3- 54 not typically have enough data to observe for regular earthquakes For example we showed that these events show slip-predictable behavior on short timescales but even minor changes in external loading such as a tiny increase in the normal load or a gradually decreasing slip rate throw off this relation but in systematic ways Shelley 2010 and Shelly and Johnson 2011 observed similarly abrupt changes in the recurrence intervals of small stick-slip earthquakes and non-volcanic tremor on the San Andreas fault near Parkfield that were brought on by stress changes from nearby earthquakes This is a comparable environment because the repeating earthquakes at this section of the San Andreas are proposed to be sticky spots on a larger plane that is slipping mostly aseismically similar to the sticky patches at the base of a glacier surrounded by areas that continue to slide aseismically proposed for this study Ocean and earth tides and even dynamic loading from seismic waves of distant earthquakes also change the normal and shear stresses in the earth by amounts that are a fraction of the total stresses but have all caused observable changes in the behavior of tectonic events e g Rubenstein et al 2008 Nakata et al 2008 Peng et al 2009 Apparently even minor changes in the stress field can alter fault behavior on a range of scales even for glaciers The mechanism we invoked as a trigger for the swarms of glacier quakes at Mount Rainier fluid redistribution and increased aseismic slip around a sticky patch has been invoked as a trigger for swarms in tectonic environments e g Vidale and Shearer 2005 Vidale et al 2006 Though Vidale and Shearer 2005 suggest tectonic swarms are triggered either by the redistribution of fluids or by accelerated aseismic slip but the mechanism we propose for this study requires both perhaps both mechanisms are involved in such cases in tectonic environments as well 3- 55 5 Conclusions In this study we compiled a complete catalog of repeating earthquake activity that occurred over the past decade at Mount Rainier We found nearly 300 000 repeating earthquakes About half have dominant frequencies below 8 Hz low-frequency and many of these repeat at regular intervals the type of event that motivated this study We found that this type of seismicity has occurred every year for at least the past decade but previously went undetected Though low frequency repeating earthquakes occur year round at a background level of about 5 per hour big swarms of activity occur only in late autumn to early spring We used this catalog to fully characterize this type of earthquake to understand the source and to confirm that the source is glacial and not related to volcanic activity We found that the swarms often are composed of several distinct families occurring at different areas of the mountain simultaneously Swarms correlate strongly with precipitation with a normalized cross correlation coefficient of nearly 0 5 peaking sharply around a 1-2 day lag Within each family we showed that recurrence intervals inter-event correlations and event energy all vary over time often gradually but sometimes suddenly and these sudden changes often correlate with minor changes in loading 30% Transit Highways Arterials Railways A2-3 Figure A2-1 N Landslide Hazard Zones Newmark displacement probability of failure Low 1-3 5cm 0-10% Moderate 3 5-7cm 10-20% High 7-12cm 20-30% Very High 0 1 2 4 km 12cm 30% Transit Highways Arterials Railways A2-2 Appendix 3 Details of Inversion Methods This section details the inversion process used to obtain the force-time function in Chapter 2a The forward problem to obtain the displacement seismograms generated by a single force applied at the source location is: di t Gij t mj t A1 where the seismogram di t at each component of each station i is equal to the Green s functions Gij t for station component i for an impulse force applied at the source location in direction j convolved with the force-time function of the source mj t where j is the directional component of the force Up North East Note that mj t is equivalent to Fe t - the change in notation is for consistency with inverse theory conventions where m refers to model Equation A1 assumes a stationary force vector applied to a single point on the surface of the earth Though the landslide is moving it can be approximated as a stationary point force for the long period wavelengths used in the inversion as explained in the methods section Green s functions are the response of the earth to an impulse source In this study I calculated the Green s functions relating an impulse force at the source location to the response at the distance and azimuth corresponding to each seismic station I computed these using the wavenumber integration method Bouchon 1981 as implemented in Computer Programs in Seismology CPS Hermann 2002 The velocity model used for these calculations was ak135Q Kennett et al 1995 This is a one-dimensional radially stratified global earth velocity model and does not account for regional or smaller scale variations However it was sufficient for this study because the long period waves T 30 150 s used in the inversion are not sensitive to smaller scale variability A3- 1 Using CPS I computed the Green s functions corresponding to each seismic station used in the inversion for a Dirac delta function impulse force applied to the surface of the earth at the location of the landslide Five Green s functions are required for each station used in order to calculate three-component synthetic time histories for a single force mechanism applied in any direction at the source Hermann 2002 The radial component of the seismogram is positive in the direction pointing directly away from the source The transverse component is perpendicular to the radial direction positive in the direction clockwise from north Vertical is positive upwards The five Green s functions are abbreviated as follows: ZVF Vertical component of the seismogram for a downward vertical force RVF Radial component for a downward vertical force ZHF Vertical component for a horizontal force in radial direction RHF Radial component for a horizontal force in radial direction THF Transverse component for a horizontal force in transverse direction The first four Green s functions correspond to the P-SV system while THF corresponds to the SH system The Green s functions calculated for station SHB 118 km from the source are shown on Figure 2a-A1 These illustrate the role of the earth s structure in the waveforms observed at station SHB due an impulse force of 1 N at the source The Rayleigh wave dwarfs the P and S arrivals on the top four Green s functions but has not moved out and dispersed much yet because of SHB s proximity to the source Note that due to the nature of causal filters the relatively compact unfiltered Green s function becomes distorted when filtered the energy is smeared out later in time This is not a problem in the inversion because identical filters are applied to the data so it is distorted in the same way This is confirmed in that a nearly identical force-time function is obtained when a zero-phase acausal filter is used Also note that the A3- 2 duration of the source force-time function is much longer than the Green s functions unlike for most regular earthquakes which is why such a detailed force-time function can be derived from the seismograms These Green s functions can be used to calculate synthetic ground displacement seismograms for any single force vector impulse or time series by: uz f1cos f2sin ZHF f3ZVF A2 ur f1cos f2sin RHF f3RVF A3 ut f1sin -f2cos THF A4 Hermann 2002 where is the source to station azimuth measured clockwise from north The single force f f1 f2 f3 is in a north N east E vertical Z respectively Cartesian coordinate system where Z is positive down note however that Z was switched to positive up in the force-time function plots in this paper to be more intuitive The ground displacement seismograms are in spherical coordinates local to each source-station pair where vertical is positive up uz radial ur is positive in the direction away from the source and tangential ut is positive at a right angle clockwise from ur A3- 3 Figure 2a-A1 Green s functions calculated for this study for station SHB located 118 km from the source for a impulse force of 1 N The functions are shown unfiltered 0 5 Hz sample rate and bandpass filtered between periods of 30 to 150 seconds using the same causal minimum phase butterworth filter applied to the data and Green s functions prior to inversion The amplitude of the filtered Green s functions is amplified by a factor of ten relative to the unfiltered version See text for discussion In order to do the inversion the forward problem equation A1 was rewritten as matrix multiplication rather than a convolution A convolution is equivalent to reversing one of the two signals being convolved in time and passing them by each other multiplying all points and summing them up at each time interval To convolve a Green s function with a force vector via matrix multiplication the Green s functions were reversed in time and staggered by shifting the Green s function by one sample in each successive row to produce a convolution matrix To illustrate this setup Equation A5 shows the convolution via matrix multiplication between a 4sample Green s function g and a 3-sample force-time function m to obtain the seismogram d that is 6 samples long: d1 % g1 d2 g2 d3 g3 d4 g4 d5 0 d6 & 0 0 g1 g2 g3 g4 0 0% 0 m % g1 1 m g2 2 m3 & g3 g4 & A5 Equation A5 illustrates the convolution with just one Green s function for one station and one component of the force-time function The actual Green s function convolution matrix must be set up to include all the Green s functions corresponding to each component of each seismic station used and to incorporate the equations that relate the source to station azimuth to account A3- 4 for the radiation patterns of each type of wave equations A2-A4 This setup can be illustrated for two three-component stations by: d1z % ZVF 1 1 1 d r RVF d1t 0 2 2 d z ZVF d 2r RVF 2 2 d t & 0 ZHF 1 cos RHF 1 cos THF 1 sin ZHF 2 cos RHF 2 cos THF 2 sin ZHF 1 sin % RHF 1 sin m Z % THF 1 cos mN ZHF 2 sin m E & RHF 2 sin THF 2 cos & A6 Each dic in Equation A6 is a column vector that contains the seismogram for the station i and component c z vertical r radial and t transverse The left side of Equation A6 is a column vector consisting of all the data displacement seismograms concatenated end to end Each entry in the G matrix is a Green s function convolution matrix indicated by superscript for the Green s function specified by its abbreviation for each station indicated by the superscript Each mj is a column vector containing the force-time function for each component j of force The sines and cosines come from equation A2-A4 For this study as described in the text I downweighted the noisy data based on the inverse of the root mean squared value of the noise before the signal at each component of each station To include this in the inversion I constructed a weighting matrix W W was built by filling the weights in along the diagonal of W organized so that the correct scalar weight value multiplied the entire seismic signal of the corresponding component of each station when W is multiplied with the data vector For example the weight for the vertical component of the first station d1z fills in the diagonal of W from W11 to Wii where i is the length of d1z W weights both the data vector d and the Green s functions matrix G which when weighted are denoted as dw and Gw respectively because the same processing must be done to both sides of the equation For the same reason the individual Green s functions and the seismograms were bandpass A3- 5 filtered identically as well prior to building the matrix G In this study I used a minimum phase causal Butterworth filter but a nearly identical result is obtained when using a zero phase acausal filter because the same filtering is applied to both sides of the equation The next step was to solve the damped least squares problem to invert for m: m GwTGw 2I 1GwTdw A7 where superscript T indicates the transpose I is the identity matrix and is the regularization parameter chosen as the trade-off between keeping the model small while still fitting the data well The matrix setup of the forward problem using data from five seismic stations with three components of motion each becomes very large but the inversion was still manageable: it took less than a minute to run in MATLAB on a desktop computer An additional step I took in this study was to constrain that all components of the single force must add to zero in the end because the total momentum of the earth must remain stable Fukao 1995 This did not significantly change the solution but is more physically correct To constrain this in the solution I added equations to the forward problem by concatenating matrix A a 3x3N matrix where N is the length of the data from one component of one station to the bottom of the Green s function matrix G A was constructed so that the first third of the first row was ones and the rest was zeros so that it multiplied and added up just the z component of m a corresponding zero is added to the bottom of the data vector d to constrain that these forces add to zero The same was done for the next two rows to multiply and add up the north and east components of m to equal zero The A matrix was scaled up to the same magnitude as the weighted Green s functions so that it influenced the final solution A3- 6
    • Barker, Adam - Ph.D. Dissertation
      Glaciers, erosion and climate change in the Himalaya and St. Elias Range, SE Alaska 2016, Barker,Adam,Adam Barker Glaciers erosion and climate change in the Himalaya and St Elias Range SE Alaska Adam D Barker A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2016 Reading Committee: Bernard Hallet Chair Howard Conway Alan R Gillespie Edwin D Waddington Program Authorized to Offer Degree: Department of Earth and Space Sciences i Copyright 2016 Adam D Barker ii University of Washington Abstract Glaciers erosion and climate change in the Himalaya and St Elias Range SE Alaska Adam D Barker Chair of the Supervisory Committee: Professor Bernard Hallet Department of Earth and Space Sciences The important roles of glaciers in topographic evolution relief development and sediment production are well recognized but understanding remains rather limited largely because of the inherent complexity of glacial erosion in diverse terrains the lack of validated glacial erosion models and the sparse nature of the data available on erosion rates The primary focus of this research is defining and understanding rates of glacial erosion and their spatio-temporal variation at the scales of single glacier basins and entire orogens I study glacial erosion in two tectonically active mountain ranges the Himalaya and the St Elias Range Alaska ideally suited for this study because of the wealth of pertinent data already available and because they represent a broad range of climates and glacier types In the Himalaya study I also examine the impact of the debris produced by glacial erosion that accumulates on the glacier surface on glacier mass balance and the response of the glacier to climate change In the SE Alaska study I model the spatial pattern of erosion rates over an entire glacial cycle and compare the temporally averaged rates to published rates of exhumation to validate and calibrate an erosion model These model results illuminate the source region and temporal aspects of the offshore sediment record that have received iii considerable attention in the context of climate-driven modulation of erosion and sediment production Large data sets on exhumation rates spanning the entire Himalayan arc have documented spatial and temporal variations in erosion rates however data on glacial erosion rates at the heavily glaciated crest of the Himalaya are very sparse In light of this weakness in the knowledge base I integrate several types of field research to investigate rates of erosion for a single glaciated basin at the base of Mt Everest I found that erosion rates for two timescales contemporary 101 yr and over the Holocene 104 yr are similar to published long-term O 107 yr exhumation rates 1 mm yr derived from thermochronometric data in the region The apparent uniformity of erosion and exhumation rates over a large range of time implies a surprising insensitivity to likely variations in climate structural development and relief evolution it also contrasts with recent studies emphasizing the variation of rates over different timescales Moreover measurements of the suspended sediment flux out of the proglacial stream suggest that the fluvial evacuation rate of suspended sediments is 50x less than the contemporary sediment production rate This together with the known time over which sediment has accumulated in the basin the downglacier decrease in sediment flux and evidence that the contemporary glacier is perched on a 20 100 m thick debris edifice implies that most of the eroded debris remains within the basin This result provides new insights into the geomorphic development of the high relief in the Himalaya and the episodic nature of the downstream transfer of sediment from high glaciers iv To investigate links between basin erosion debris transfer and the evolution of debris-covered glaciers during periods of climate change I numerically model the coupled evolution of ice and debris for Khumbu Glacier For the first time I define a relationship between ice-melt rate and debris thickness representative of the thick surface debris characteristic of the Khumbu region and implement it in the model to quantitatively explore the debris-covered glacier anomaly The model simulates the response of a debris-covered glacier to changes in climate forced by variations in the net mass balance represented by vertical shifts in the equilibrium line Model results indicate that despite the thick debris cover Khumbu Glacier has thinned at rates similar to current rates measured by remote sensing averaging 0 4 m w e yr for over a century since the Little Ice Age LIA Even under a constant climate it will continue to thin into the future by about 6 8% by AD2100 largely in the middle part of the glacier with minor changes in the terminus ice thickness and extent In SE Alaska I expand the study region from a single catchment to an entire orogen where I model the spatial distribution of erosion rates on two timescales the present-day and the longer-term The latter represents the past 100-kyr when much larger ice masses covered the study area and underwent large oscillations by inference it represents the Quaternary during which these large oscillations prevailed and much of the orogen was exhumed I hypothesize that the rate of erosion increases with the glacier power the amount of energy available for erosion per unit time and per unit area of the glacier bed which has the advantage of representing the strength of the ice-bed coupling the basal shear stress as well as the sliding rate When averaged over an entire major cycle glacier power accounts for nearly 70% of the variation in the published exhumation rates inferred from v thermochronology data from the entire orogen despite the large range of substrate characteristics expected in the region The strong correlation between exhumation rates and glacier power validates the hypothesis that the rate of erosion scales with power and the numerical erosion model Model results define the zones of rapid exhumation as the zones of steep and rapid glaciers Moreover the results dispel the notion that rapid erosion is spatially coincident with the long-term position of the equilibrium line averaged over the major Quaternary glaciations the position of the equilibrium line is well south of zones of rapid exhumation close to the continental shelf break in the Gulf of Alaska vi TABLE OF CONTENTS LIST OF FIGURES ix LIST OF TABLES x ACKNOWLEDGEMENTS xi Chapter 1: Introduction 1 1 1 Importance of glacial erosion 2 1 2 Glacial erosion and representation in models 6 1 3 Modeling the response of debris-covered glaciers to climate change 8 1 4 Thesis roadmap 9 Chapter 2: Glacial erosion exhumation and debris evacuation over a wide range of time scales in the Mt Everest region Nepal 11 2 1 Abstract 11 2 2 Introduction 12 2 3 Existing and new glaciological and geological measurements 14 2 4 Framework for analyses 15 2 5 Materials and methods 17 2 5 1 2 5 2 2 6 2 7 2 8 2 9 Contemporary erosion rates 17 Holocene erosion rate 19 Results 21 2 6 1 2 6 2 Contemporary erosion rates 21 Holocene erosion rates 24 Discussion 25 2 7 1 2 7 2 The pace of erosion and exhumation of Khumbu Basin 25 Implications for the structural and topographic development of Mt Everest 26 2 9 1 Measurements of fluvial sediment flux 30 Summary 29 Supplement 30 Chapter 3: Climate and debris controls on the evolution of debris-covered glaciers on time scales of 10 to 104 years examined for Khumbu Glacier Nepal 42 3 1 Abstract 42 3 2 Introduction 43 3 3 Khumbu Glacier 46 3 4 Model 48 3 5 3 4 1 3 4 2 3 4 3 3 4 4 3 4 5 Conservation of ice and debris 48 Glacier flow model 51 Boundary Conditions 52 Glacier mass balance in the absence of debris 54 Dependence of surface melt rate on surface debris thickness 55 3 5 1 3 5 2 3 5 3 3 5 4 3 5 5 Large-scale melt rule 57 Modern dynamics at the glacier terminus from GPS 58 Debris Sink 58 LIA and LGM glacier conditions 60 Perturbing the LIA state to achieve modern and potential future states 63 Results 56 vii 3 5 6 3 6 3 7 3 8 Model Sensitivity 65 Discussion 65 Conclusions 69 Supplement 71 Chapter 4: Orogen-wide rates of glacial erosion during major 100-kyr glacial cycles in the St Elias Mountains SE Alaska 88 4 1 Abstract 88 4 2 Introduction 89 4 3 Methods 94 4 4 Results 99 4 5 4 6 4 4 1 4 4 2 Contemporary distribution of glacier power 99 Quantitative glacier power averaged over a full glacial cycle 100 4 5 1 4 5 2 4 5 3 4 5 4 4 5 5 Assessing the erosion model 103 Temporal variation in basin-wide erosion rates through a glacial cycle 106 Is the EL a useful metric of erosion rate 107 Implications for controls on erosion rates 108 Model limitations and caveats 110 Discussion 103 Conclusions 112 Chapter 5: Summary and conclusions 123 5 1 Tempo of erosion at the top of the world 123 5 2 Debris-covered glaciers and climate change 124 5 3 Spatial distribution of erosion rates in SE Alaska 127 5 4 Summary 129 Bibliography 130 viii LIST OF FIGURES 2 1 Composite satellite image of Khumbu Basin 32 2 2 Profiles of elevation and surface velocities of Khumbu Glacier 33 2 3 Downglacier variation in mean thickness of surface debris 34 2 4 Electrical resistivity tomography ERT profiles 35 2 5 Surface and subsurface cross-sections 36 2 6 Surface englacial and total debris fluxes beginning near EBC 37 2 7 Time series of daily-averaged stream discharge and turbidity 38 2 8 Spatial extents of basin areas for erosion rates 39 3 1 Multiband composite satellite image of Khumbu Basin 72 3 2 Components of the conservation of mass equation 73 3 3 Relationships between melt rate and debris thickness 74 3 4 Horizontal and vertical surface speeds 75 3 5 Total debris flux 76 3 6 Debris thickness profiles for debris sink term 77 3 7 Modeled LIA steady-state surface profile 78 3 8 LGM extent 79 3 9 Surface subsidence for melt rules 80 3 10 Debris thickness evolution for melt rules 81 3 11 Spatial and temporal response of glacier after ELA change 82 3 12 Model runs at time-point 150 years 83 3 13 Glacier evolution for both debris and no debris cases 84 4 1 Geologic map of SE Alaska 114 4 2 Modeled ice thickness at maximum glacier extent 115 4 3 Histogram of ice-thickness differences 116 4 4 Distribution of the relative erosion rate based on the glacial power 117 4 5 Comparison of relative erosion rates for Seward Throat 118 4 6 Spatial distribution of the time-averaged glacier power 119 4 7 Glacier power during a complete glaciation 120 4 8 Time-series of glacial power for the three principal glacier basins 121 4 9 Glacier power averaged over 115 kyr versus exhumation rates 122 ix LIST OF TABLES 2 1 Observations of englacial sediment concentrations 40 2 2 Basin-wide debris volume estimates 41 3 1 Summary of differences in surface elevation 85 3 2 Summary of modern glacier variables 86 3 3 Model LIA glacier 87 x ACKNOWLEDGEMENTS I begin by thanking Bernard Hallet whose vast knowledge and broad scientific understanding opened up worlds I never knew existed Thank you to my committee members Howard Conway Alan Gillespie and Ed Waddington who provided essential encouragement and help I especially want to thank Twit for your effort and support My work brought me to locations that are the extremes of this world Thank you to my field assistants Taylor Brugh Lauren Wheeler and Trevor Hillebrand who had to endure the beauty of the Khumbu region and also do work I also thank Peter Koons my Master s advisor and Sean Birkel for their integral assistance and modeling results that went into the SE Alaska project The NSF and the Quaternary Research Center provided financial support I have worked alongside some incredibly smart people far more than I can possibly mention out of fear of leaving anybody out More important I have made some life-long friends at UW most notably Brooke Medley T J Fudge Isaac Larsen and Kristin Poinar I want to thank you for being the wonderful people you are And to my family thank you for your love and support I must also acknowledge Brooke Medley a very special person to me xi 1 Chapter 1: Introduction Rates of erosion and debris production at the crest of the Himalaya the quintessential tectonically active mountain range are poorly known yet it is widely recognized that erosion plays a central role in mountain building and that debris strongly influences the sensitivity of glaciers to climate change In contrast erosion rates averaged over individual glacier basins and over timescales of 10 to 106 years are relatively well defined in the St Elias Range SE Alaska through studies of sediment flux and thermochronology respectively However the link between the pace of erosion and glacier characteristics has received little attention and very little geologic data exist to define empirically the spatial variation of erosion rates within the vast areas of individual glacier systems that reach 5000 km2 Moreover long-term variations in the pattern of erosion driven by growth and shrinkage of glaciers during typical glacial cycles are poorly understood Consequently the relationship between the dynamic glaciers and the rapid exhumation in the St Elias Range remains poorly defined This thesis aims to constrain the temporal variations of glacial erosion rates at the crest of the Himalaya Nepal and their spatial and temporal variation in the St Elias Mountains SE Alaska In the Himalaya I also examine the impact of the debris produced by glacial erosion which accumulates on the glacier surface on the mass balance of a glacier and on its response to climate change This work bears on several topics of considerable current interest within the scientific community and of direct societal relevance Three substantive chapters 2-4 comprise the thesis and are followed by a summary In this chapter I introduce important underlying concepts and 2 provide context for the research reported herein I start by introducing the importance of glacial erosion studies and explaining what is known and is not known about glacial erosion rates I then follow with a primer on how glacier erosion is implemented in numerical models and review modeling studies investigating the influence of debris on glacier evolution in the Mt Everest region 1 1 Importance of glacial erosion Understanding the spatial and temporal variations of glacial erosion rates not only helps define the influence of glaciers on Earth s surface but also helps address topics in diverse disciplines in which glacial erosion plays a vital role 1 Geodynamics: the influence of glacial erosion on mountain building and the interplay between tectonics topography and surface processes e g Molnar and England 1990 Beaumont et al 2001 Zeitler et al 2001 Wobus et al 2003 Tomkin 2007 Berger et al 2008 Scherler et al 2011 Valla et al 2011 Yanites and Ehlers 2012 Herman et al 2013 2015 Enkelmann et al 2015 Herman and Champagnac 2016 Willenbring and Jerolmack 2016 2 Marine geology: offshore glacial sediment sequences record spatial and temporal patterns of sediment production that reveal the influence of climate variability on erosion processes e g Hallet et al 1996 Elverh i et al 1998 Peizhen et al 2001 Molnar 2004 Koppes and Hallet 2006 Gulick et al 2015 Koppes et al 2015 Fernandez et al 2016 3 Glaciology: sediments that underlie ice masses e g the ice streams that drain much of the West Antarctic Ice Sheet may enhance glacier motion and influence the position of ice streams by reducing bed roughness and lowering resistance to flow e g Weertman 1964 Anandakrishnan et al 1998 Tulaczyk et al 2000 Alley et al 2003 Joughin et al 2004 Smith et al 2013 Seigert et al 2016 4 Climate change and sea-level rise: ice ocean interactions have 3 received much attention in part due to the role of offshore sediments in controlling the advance of marine-terminating glaciers into deep water e g Meier and Post 1987 Nick et al 2007 Pollard and DeConto 2009 Love et al 2016 and their retreat that tends to be more rapid e g Benn et al 2007 Nick et al 2007 Straneo et al 2010 2011 Motyka et al 2013 Rignot et al 2016 Despite the importance of glacial erosion rates of erosion are only defined by sparse data and the diversity of rates is not understood Numerous field studies in SE Alaska of sediment accumulation in fjords e g Koppes and Hallet 2002 2006 on the continental shelf Jaeger et al 1998 Sheaf et al 2003 and in the deep sea part of the Gulf of Alaska Gulick et al 2015 have respectively documented spatially averaged erosion rates over multiple timescales for individual glacier systems and regional rates In a comprehensive overview of existing data Hallet et al 1996 reported effective rates of glacial erosion from sediment yields over years or decades reaching or even exceeding 10 mm yr for large and fast-moving temperate valley glaciers in the tectonically active ranges of SE Alaska At Tyndall Glacier in SE Alaska Koppes and Hallet 2006 estimated the long-term basin-wide erosion rate to be 9 2 mm yr after applying a correction factor accounting for glacial retreat and the release of stored sediment On the shelf sediment accumulation rates averaged nearly 8 mm yr over the Holocene corresponding to an average erosion rate of 5 1 mm yr which they attributed to efficient erosion by glaciers Sheaf et al 2003 Over longer time scales drilling of deep-sea sediment deposits shows an acceleration in sediment yields following the onset of 100-kyr glacial cycles the evacuation of eroded crustal material appears to outpace the tectonic influx by 50-80% Gulick et al 2015 Collectively the studies of sediment accumulation in fjords on the shelf and in the deep sea suggest that 4 erosion rates in SE Alaska are some of the highest in the world For glaciers in Patagonia and the Antarctic Peninsula Koppes et al 2015 reported a three order of magnitude difference in basin-averaged erosion rates inferred from 15 outlet glaciers spanning 19 degrees of latitude Their findings which show how glacial erosion rates increase with decreasing latitude suggest that climate and the glacier thermal regime exert more control on erosion rates than do ice cover extent ice flux or sliding speeds However using sediment volumes as a proxy for glacial erosion is not without controversy as the incompleteness of the sediment record and remobilization of previously deposited sediments confound the erosion signal e g Sadler 1981 Sadler and Jerolmack 2014 Cowan et al 2010 Boldt et al 2016 Herman and Champagnac 2016 Ganti et al 2016 Unlike the offshore sediment record thermochronometric methods allow for quantification of local erosion rates for the source regions producing the sediment Specifically low-temperature thermochronology can be used to determine the time since a mineral cooled through a closure temperature window which is generally due to exhumation over million-year timescales Dodson 1973 The cooling age is converted into an erosion rate making the reasonable assumption for convergent orogens that erosion accounts for the exhumation and using estimates of the near-surface temperature gradient however uncertainties in the geothermal gradient lead to corresponding uncertainties in the interpretation of thermochronometric data e g Herman et al 2013 Enkelmann et al 2015 Global compilations of exhumation data reveal an increase in erosion rates in mountain ranges since ca 6 Ma and most rapidly since 2 Ma Herman and Champagnac 2016 the increase in erosion rates has been reported a number of regions including both SE Alaska Berger et al 2008 and parts of the Himalaya Thiede and Ehlers 2013 5 In SE Alaska many thermochronometric studies have documented rapid erosion and deep-seated rock exhumation e g Berger et al 2008 Enkelmann et al 2008 2009 2010 2015 Grabowski et al 2013 Falkowski et al 2014 Detrital zircon fission track FT ages reveal rapid exhumation 2-5 mm yr primarily under the Hubbard and Seward-Malaspina Glacier systems Enkelmann et al 2015 Previous studies have used the spatial correlation between rapid exhumation and the current state of glaciers and equilibrium line EL position as evidence of a link between climate and erosional processes Berger et al 2008 however this general notion fails to take into account specific controls on erosion rates and the large changes in the ice masses through the Quaternary In contrast with SE Alaska very little data exists on erosion rates for Himalayan glaciers Using a method that parallels Chapter 2 of this thesis Heimsath and McGlynn 2008 estimated the headwall retreat rate of 1 3 0 5 mm yr for a debris-covered glacier on the north slope of the Annapurna Range central Nepal Faster contemporary erosion rates of 5 7 mm yr were derived for Raikot Glacier Nanga Parbat Gardner and Jones 1993 In the Marsyandi river catchment modern basin-wide erosion rates of 0 1 to 2 0 mm yr were reported in sparsely glaciated catchments based on suspended sediment flux measurements Gabet et al 2008 Erosion is fast however for at least one major mountain in the Himalaya in the eastern most Himalaya Detrital zircons from a stream draining the cirque glacier incising the north flank of Namche Barwa yielded a population of extremely young ages characterized by a number of peaks the youngest of which is 0 3 Ma and accounts for 35% of the 81 grains analyzed the oldest grain in this entire sample is 3 6 Ma Enkelmann et al 2011 The dearth of information highlights the need for additional studies 6 1 2 Glacial erosion and representation in models The deeply incised valleys of glaciated regions leaves little doubt that glaciers actively erode and efficiently remove rock debris From the early illustrations and descriptive studies by Chamberlain 1885 to sophisticated analog experiments by Iverson and Zoet 2015 a wide range of studies and experiments have improved our knowledge of glacial erosion In this section I outline published theoretical and experimental studies on glacial erosion and review the representations of glacial erosion in past models of landscape evolution Glacial erosion and sediment production occur primarily by two processes: abrasion and quarrying Abrasion is the dominant producer of fine sediments and has received much attention in the literature Glen and Lewis 1961 Boulton 1974 Hallet 1979 1981 Abrasion depends on the flux and lithology of rock fragments in contact with the glacier bed the shapes of the bed and fragments and the effective contact force the rate of abrasion is proportional to the rate at which work is done on rock-to-rock friction on the glacier bed Hallet 1979 Quarrying plucking occurs following cracking and dislodgement of bedrock and supplies rock fragments for abrasion Cracks form due to stress concentrations that tend to be enhanced by variations in basal water pressure Rothlisberger and Iken 1981 Cohen et al 2006 Field observations theoretical considerations and cosmogenic nuclide studies Briner and Swanson 1998 suggest that quarrying dominates over abrasion Mechanistic models of abrasion e g Hallet 1979 and quarrying e g Hallet et al 1996 Iverson 2012 assume that basal sliding is the primary control on the rate of glacial erosion however estimating absolute erosion rates from the models is difficult due to poorly known basal conditions and bed properties 7 In numerical models glacier erosion has been represented over length scales ranging from a single landform Harbor 1992 to an entire mountain range Egholm et al 2009 As summarized by Iverson 2012 bedrock erosion rate is generally represented in models as:: Eq 1 where us is the glacier sliding speed and a and b are constants Harbor 1992 Humphrey and Raymond 1994 Braun et al 1999 MacGregor et al 2000 Tomkin 2007 2009 Herman and Braun 2008 Kessler et al 2008 Egholm et al 2009 Herman et al 2015 The constant a depends on bedrock properties and basal conditions Other forms assume that erosion rate scales with ice discharge: Eq 2 where af is similar to a but with units of m-1 is depth-averaged velocity and H is ice thickness Kessler et al 2008 Herein in chapter 4 the erosion rate is assumed to scale with glacial power the product of the sliding speed and basal shear stress b: Eq 3 where the proportionality factor is with units: Pa-1 Pollard and DeConto 2007 Hallet et al 2011 Melanson et al 2013 The glacial power approach combines the widely recognized importance of glacial sliding with the coupling strength of the glacier and bed Hallet 2011 While modeling the spatial variation in erosion rates for Seward Glacier Headley et al 2012 compared the erosion rate models from Eqs 1-3 they reported that the basin geometry exerted stronger control on the spatial distribution of erosion rates than both the model choice and equilibrium line which is commonly invoked in discussions of patterns of glacier erosion because the ice flux is greatest there 8 1 3 Modeling the response of debris-covered glaciers to climate change The response of glaciers to climate change is of fundamental scientific interest and has important practical consequences including fresh water availability global sea-level change and environmental hazards e g Richardson and Reynolds 2000 Immerzeel et al 2010 A significant threat to Himalayan communities is moraine-dammed lakes that form following glacier recession or subsidence Bolch et al 2008a Benn et al 2012 Thompson et al 2012 Recent studies show that the areal extent of glaciers in the Everest region including many with a thick debris cover decreased 5% during the second half of the 20th century Bolch et al 2008b Salerno et al 2008 The glaciers are also thinning actively For Khumbu Glacier the rate of thinning across the ablation area averaged 0 38 0 07 m yr between 1970 and 2007 Bolch et al 2011 Predicting the future of Himalayan glaciers and hence assessing the societal consequences are especially challenging due to the presence of surface debris which strongly influences glacier mass balance and evolution e g Scherler et al 2011 Anderson and Anderson 2016 To shed light on glacier changes in the Khumbu region and by extension in similar settings along the Himalaya and elsewhere several researchers have used numerical models to examine the current state of Khumbu glacier and its probable evolution Naito et al 2000 coupled mass balance glacier flow to investigate shrinkage of the Khumbu between 1978 and 1999 They predicted that the lowest part of the glacier would stagnate and eventually decouple from the upper glacier which could lead to the development of a large and potentially hazardous glacial lake Shea et al 2015 used a glacier mass balance and ice-flow model to examine historical change of glaciers in the Everest region from 1961 to 2007 and assess future changes They concluded that glaciers may lose between 73 to 96% 9 of their total volume due to sustained warming by the year 2100 Rowan et al 2015 coupled ice flow with debris evolution in a three-dimensional model and focused on interactions between the debris cover and mass balance Model simulations quantified the imbalance of Khumbu Glacier with the current climate which is evident from the current and post-Little Ice Age LIA thinning of the Khumbu They suggest that even without a further change in climate Khumbu Glacier will continue to respond to post-LIA warming until AD2500 In another study Anderson and Anderson 2016 developed a transient 2-D model to investigate debris cover and glacier evolution for generic debris-covered glaciers using Khumbu Glacier as a case example Unlike Rowan et al 2015 they focus on improving understanding of glacier evolution solely in response to changes in debris cover in this initial modeling phase they do not consider the effects of climate change These numerical models provide insight into the response of Khumbu and other debris-covered glaciers to climate change and provide a rich backdrop for this study 1 4 Thesis roadmap In this thesis I address glacial erosion in a glaciated basin in Nepal and over an entire orogen in SE Alaska For the Nepalese glaciated basin I also consider the storage and evacuation of debris and the effect of the eroded rock debris on the response of glaciers to adverse climatic trends in Nepal Chapters 2 and 3 report the findings of several field seasons of measurements and numerical modeling regarding Khumbu Glacier Mt Everest region of Nepal In Chapter 4 I investigate erosion rates in the St Elias Mountains the highest coastal mountain range in the world My thesis addresses the following questions: 10 In Himalaya what is the pace of erosion at the crest of the range and has it changed over time Chapter 2 How does debris influence glacier evolution Chapter 3 How can we improve understanding and predictions of the future behavior of Khumbu Glacier and similar glaciers Chapter 3 In Alaska what is the spatial and temporal variation in erosion rates and what is the link between glacial erosion and exhumation and tectonics Chapter 4 11 Chapter 2: Glacial erosion exhumation and debris evacuation over a wide range of time scales in the Mt Everest region Nepal 2 1 Abstract The pace of erosion in the Himalaya has been studied extensively yet few studies have addressed the glaciated crest of the orogen New and existing data from Khumbu Basin at the base of Mt Everest are used to define erosion rates over two time scales: contemporary and the Holocene O 101 and 104 yr Erosion rates are calculated using field and remote sensing measurements of the flux of rock debris from the basin The underlying premise is that just as the flux of glacier ice is sustained by input of snowfall the flux of debris is sustained by erosion Contemporary and Holocene basin-averaged erosion rates on average 0 6 and 0 8 mm yr respectively are very similar to one another suggesting that erosion of the Khumbu basin has on average maintained a steady pace over time scales up to 104 years Contemporary suspended sediment evacuation is 50x less than the Holocene-averaged sediment production This together with evidence that the contemporary glacier is perched on a debris edifice implies that most of the eroded debris remains within the basin Moreover the basin-averaged erosion rates are similar to published long-term O 107 yr exhumation rates derived from thermochronometric data in the region This similarity contrasts with other studies that suggest exhumation accelerated significantly with the onset of Plio-Pleistocene glaciation our results point to the need for additional studies of erosion in other high regions in the Himalaya 12 2 2 Introduction The rate and spatial pattern of erosion and exhumation in the Himalaya have been studied extensively using diverse approaches largely because of the important role exhumation plays in the development of the range For example in a comprehensive study across the entire Himalaya significant spatial and temporal variations in exhumation rates were inferred from more than 103 mineral cooling ages obtained from in-situ bedrock samples Thiede and Ehlers 2013 Within the range a few basins the Sutlej Thiede et al 2004 Vanney et al 2004 Bookhagen et al 2006 and the Marsyandi Burbank et al 2003 2012 Hodges et al 2004 Pratt-Situala et al 2004 Brewer et al 2006 Huntington et al 2006 Garzanti et al 2007 Godard et al 2012 in particular have been studied in detail while other areas have received sparse attention Beyond the Himalayan arc much work has focused on the two syntaxial regions at the ends of the range: the Nanga Parbat Zeitler 1984 Gardner and Jones 1993 Burbank et al 1996 Zeitler et al 2001 Koons et al 2002 and Namche Barwa massifs Clark et al 2004 Hren et al 2007 Finnegan et al 2008 Stewart et al 2008 Enkelmann et al 2011 Larsen and Montgomery 2012 Lang et al 2013 Zeitler et al 2014 However little is known about erosion rates at the heavily glaciated crest of the Himalaya which spans 2000 km Contemporary erosion rates of 5 7 mm yr derived for Raikot Glacier Nanga Parbat Gardner and Jones 1993 are similar to exhumation rates estimated for the region over time scales of 106 yr Zeitler et al 2001 Comparable but slightly faster exhumation has also been inferred from sediments from a stream draining the steep glacier on the West flank of Namche Barwa Sample H Enkelmann et al 2011 On the other hand relatively slow erosion 1 3 mm yr determined from contemporary headwall 13 retreat rates were reported for a high basin in Nepal Heimsath and McGlynn 2008 and modern basin-wide erosion rates of 0 1 to 2 0 mm yr were reported in sparsely glaciated catchments based on suspended sediment flux measurements Gabet et al 2008 In the latter study it was argued that relatively rapid erosion during periods of glaciation e g Hallet et al 1996 would compensate for the slow erosion now occurring in the High Himalaya Gabet et al 2008 In contrast Rahaman et al 2009 found that sediment yields in the High Himalaya decreased during periods of more extensive glacial cover in the past 105 years The sparse data currently available indicate highly varying erosion rates along the glaciated Himalayan crest ranging from 1 7 mm yr which points to the need for additional studies in those regions Here we synthesize existing data and present new data from Khumbu Basin to constrain erosion rates over two timescales: contemporary and the Holocene O 101 and 104 yr We compare these rates with published exhumation rates over much longer times scales O 107 yr derived from thermochronometric studies in the region Sakai et al 2005 Streule et al 2012 Using field measurements and observations and remote sensing data we i quantify the modern debris flux including suspended sediments flushed out of the basin ii calculate the debris volume within Holocene-aged deposits We also consider temporal changes in the rates of erosion and debris production and implications for the evolution of the highest topography on the planet Other aspects of Khumbu Glacier are considered in Chapter 3 of this thesis which investigates the influence the eroded material has on ice melt The Chapters are linked in many ways with the overall goal in characterizing Khumbu Basin from two perspectives First from the view of a geologist we consider erosion and long-term geomorphic evolution of Khumbu Basin Second from the 14 view of a glaciologist we consider past and future states of the glacier and the important role of eroded debris in the evolution of Khumbu Glacier 2 3 Existing and new glaciological and geological measurements Khumbu Basin in Sagarmatha National Park Nepal extends over an area of 90 km2 that is bordered by several of the world s highest peaks including Mt Everest Fig 2 1 The 18 km-long Khumbu Glacier descends from an elevation of about 7100 m to 4900 m and covers an area 17 km2 Snow and ice avalanches from the steep cliffs that surround the accumulation zone contribute to the mass balance of the glacier Fig 2 1 inset Khumbu icefall a steep heavily crevassed region connects the accumulation zone with the relatively gentle-sloped debris-covered ablation zone Fig 2 2 The modern equilibrium line altitude ELA is within the icefall at 5700 m Scherler et al 2011 Abundant geological and glaciological observations and measurements make Khumbu Basin ideal for our study: 1 Glacier surface and bed profiles: the surface profile along the centerline of the glacier was constructed from a 2003 ASTER DEM and the bed profile was calculated by differencing the surface and the ice-thickness profiles Fig 2 2 Seven ice-penetrating radar profiles from May 1999 show ice thickness decreasing from 450 m maximum thickness near Everest Base Camp EBC to less than 20 m minimum thickness about 2 km from the present terminus Gades et al 2000 To our knowledge ice thickness has not been measured in the upper glacier we estimate it using measurements of surface slope and assuming a constant value 105 Pa for the basal shear stress which is consistent with values we calculate for locations where the ice thickness is known 15 2 Surface velocity profile: velocities derived from repeat measurements using satellite optical and radar sensors Luckman et al 2007 Quincey et al 2009 Casey et al 2012 range from 60 m yr just below the Khumbu icefall to less than 5 m yr in the lower ablation area of the glacier Fig 2 2 3 Distribution of surface debris: previous direct field measurements indicate the present-day thickness of surface debris varies from less than 0 1 m directly below the icefall to more than 2 m near the terminus Nakawo et al 1999 Our measurements over four field seasons during pre- and post-monsoon months in 2010-2012 including electrical resistivity tomography ERT quantified the spatial distribution and variability of surface debris Fig 2 3 2 4 Framework for analyses We begin by considering the contemporary erosion rate from the fluxes of surface and englacial debris and of suspended sediments exiting the glacier through the proglacial stream Calculation of the total volume of Holocene debris deposits in the Khumbu Basin allows us to compare contemporary erosion rates with those over 104 years Excluding transient changes in the volume of debris stored in the basin above the ELA the debris flux at any glacier cross-section represents the product of the spatially averaged erosion rate and the area of the basin upglacier of that section Transient changes are neglected because the very steep slopes preclude significant storage of sediment above the glacier and the rapid ice flow above the ELA is not conducive to appreciable storage under the glacier The debris flux is linked to the ice flux which can be estimated from available field and remote sensing studies: 16 1 Eq 1 where the values of surface velocity thickness of surface debris porosity of the supraglacial debris and the volumetric concentration of debris within the ice are averaged across the glacier width w We assume that the englacial debris concentration is uniformly distributed Here we adopt 0 33 based on measurements from nearby Ngozumpa Glacier Nicholson and Benn 2013 The contemporary area-averaged erosion rate scales with the sum of the glacier debris flux and the suspended sediment flux Qsus in the outlet stream: Eq 2 The density ratio 0 8 accounts for the density difference between sediment s and bedrock Heimsath and McGlynn 2008 and is the area of the contributing basin 26 5 km2 is used to derive the contemporary erosion rate Fig 2 8 Next we consider the Holocene timescale by examining the volume of debris currently residing in the basin Multiple lines of evidence support the notion that debris has been accumulating since the Holocene Near the base of the Khumbu terminal moraine optically stimulated luminescence OSL dating of sediments yield ages at 10 9 2 4 ka Richards et al 2000 Moreover cosmogenic radionuclide CRN 10 Be surface exposure dates 9 2 0 2 ka of glacial deposits at the terminus of other glaciers in the region support the Holocene OSL age Finkel et al 2003 Studies of outwash fans terraces and moraines in the Khumbu region show that glacial debris has been accumulating in the valleys since the last major glacier advance at ca 10 ka Chhukung stage Williams 1983 Nakawo et al 17 1999 Richards et al 2000 Finkel et al 2003 Barnard et al 2006 Hambrey et al 2008 Owen et al 2009 Together the data provide a time scale for Holocene sediment accumulation within the basin The glaciers that correspond to older well-dated moraines which are 16 ka and older Finkel et al 2003 would have filled the entire lower portion of Khumbu Valley rather than only the central portion that is currently occupied by the current Khumbu Glacier We expect that the broader valley had to be excavated during this and similar glacial advances and hence that any unconsolidated debris would have been removed during the extended ice advance over this area Moreover stratigraphic and sedimentology relationships suggest that formation of fans and terraces occurs during glacier retreat Barnard et al 2006 Hence the volume of glacial debris eroded during the Holocene is estimated from all the debris bounded by the Holocene-aged moraines and regions upvalley Therefore the average erosion rate over the Holocene is the sum of the volume of debris and the volume fluvially evacuated from the basin over period t and the area of the Khumbu basin 70 km2 is used to derive the Holocene erosion rate Fig 2 8 : 2 5 Eq 3 Materials and methods 2 5 1 Contemporary erosion rates The contemporary erosion rate for the portion of the basin above the ELA was calculated from the surface and englacial debris fluxes at the uppermost cross-section in Fig 2 1 using Eq 2 The 10 50 yr-timespan represented in the contemporary analysis reflects the period in which the principal characteristics i e glacier thickness and velocity are well 18 documented Near EBC the site of the upper ice-thickness survey the ice surface elevation changed less than 5 m between 1970 and 2007 Bolch et al 2011 To determine the debris flux we used published and our new measurements of surface ice velocity glacier thickness and width surface debris thickness and englacial debris concentration The debris flux cross-sections shown in Fig 2 1 correspond to locations of measured ice thickness Gades et al 2000 Horizontal surface velocities were derived from feature tracking of distinct surface features using TerraSAR-X imagery between January and May 2008 Courtesy of M Braun depth-averaged velocities were estimated by accounting for the decrease in velocity with depth Cuffey and Paterson 2010 Surface velocities were used to calculate surface debris flux and depth-averaged velocities were used to calculate the englacial flux The thickness of surface debris was measured pre- and post-monsoon in 2010 2011 and 2012 Fig 2 3 The spatial variation of debris thickness was determined from 125 direct field measurements over the entire ablation region using hand measurements and at the top of ice cliffs using a Laser Range Finder To augment these measurements we used ERT in the lower few kilometers of the glacier The ERT surveys used an IRIS Syscal Kid system with 36 electrodes spaced 10 m apart Because the glacier surface is very rough the maximum survey line-length was 300 m The output current was adjusted automatically to optimize measurement quality Both Wenner and Dipole-Dipole configurations were tested in the field during processing it became evident that the Wenner array was more effective in identifying the relatively flat ice debris interface Electrode contacts were maintained by watering the electrodes in the debris with a saline solution The data were filtered and processed using commercially available software Res2D 19 The ERT surveys clearly distinguished glacial ice which includes englacial debris domains with resistivity 106 m Reynolds 1985 Haeberli et al 1988 from surface debris or moraine deposits 1 5 x 104 m Nakawo et al 1999 The most complete section Line B-B that runs N-S Fig 2 4 shows that the ice-debris contact is nearly horizontal The internal consistency of the surveys was excellent where it could be assessed at the cross-over point X in lines A-A and B-B here the debris thickness over a substantial part of the domain is 5 m In several surveys notably line D and parts of A and B the electrode coupling with the debris was poor limiting acquisition of useful data Fig 2 4 Nevertheless we show data from all surveys to highlight the challenges of surveying glaciers covered with loose dry debris 2 5 2 Holocene erosion rate Holocene sediment volumes were estimated from field measurements and DEM analysis Parabolic functions were used to approximate the geometries of 25 U-shaped valley cross-sections Mey et al 2015 a DEM of the bedrock surface was constructed by simply interpolating between the cross-sections Fig 2 5 shows three representative cross-sections for the upper middle and lower parts of the glacier and the approximation of the bedrock and sediment glacier interface Additional cross-sections not shown used to calculate deposit volumes include cross-sections for the tributary glaciers that likely fed the Khumbu during the Little Ice Age and other periods of the Holocene These tributary glaciers are included in calculation of the Holocene contributing-basin area Fig 2 8 Sediment volumes for the Holocene analysis were split between two domains: Khumbu Glacier and Khumbu Basin Khumbu Glacier includes surface englacial and subglacial debris described above Khumbu Basin includes Khumbu Glacier and the massive 20 lateral and terminal moraines bordering the glacier and the tributary glaciers as well as the total volume of sediment evacuated in the proglacial stream during the Holocene The volume of the lateral and terminal moraines was estimated using DEMs composite images of VNIR visual near-infrared bands from an ASTER image collected in April of 2003 and thickness measurements from a laser-range finder gathered during field seasons The transverse profile of the massive terminal moraine is rounded and tapers downvalley we estimated its volume by abstracting this edifice as a half-cone with a range of sizes Tributary glacier volumes were estimated using corresponding data from Khumbu Glacier and the surface thickness was assumed to be identical to that at the same elevation on the Khumbu In addition to stored debris the amount of debris evacuated fluvially during the 104 year period was determined by assuming that the modern fluvial flux averaged over two years of suspended sediment monitoring in the proglacial stream is representative of the Holocene Likely the value represents a lower bound due to episodic high-discharge events that were not captured in our suspended sediment study We monitored the suspended sediment flux in the principal outlet stream during the 2011 and 2012 monsoon season We used two nearby sites: 1 0 5 km upstream from the small settlement of Thukla where the stream forms a single channel directly beyond the moraine and where we felt confident the equipment would remain undisturbed Fig 2 1 and 2 just upstream from Thukla At site 1 we monitored stage water temperature and turbidity continuously measurements were automated at 15-minute intervals with stage and water temperature recorded using a HOBO water level logger and turbidity averaged over five measurements monitored using a Campbell Scientific OBS 3 At site 2 we measured stage visually and photographically we also collected water samples periodically to determine the suspended sediment concentration SSC 21 Additional information about our SSC measurements is in supplementary section 2 9 2 6 Results 2 6 1 Contemporary erosion rates Surface debris: Debris emerges from the glacier at the surface in patches that coalesce to form a nearly continuous monolayer about 2 km down glacier from the ELA near EBC Our 30 evenly spaced point measurements roughly parallel to glacier flow near EBC showed debris thickness ranging from 0 008 to 0 08 m averaging 0 03 0 03 m A few kilometers down glacier debris thickness across the top of an ice cliff varied from 0 85 to 2 5 m in just 10 m Measurements at other locations down the glacier showed both increasing debris thickness and increasing local variability Fig 2 3 summarizes the surface debris thickness data thickness was most variable near the terminus where the ERT measurements augment ice-cliff-top measurements In nearly all cases the ice-cliff-top measurements which are included in Fig 2 3 were less than those from the ERT resulting in asymmetric error bars Fig 2 3 Englacial debris: We are unaware of any measurements of englacial-debris concentration for Khumbu Glacier but data exist for other temperate alpine glaciers Table 2 1 Here we select a range of values based on Table 2 1 centered on 2 kg m3 which is similar to the mean value for Raikot Glacier in the Punjab Himalaya Gardner and Jones 1993 The two glaciers have similar configurations: a high elevation accumulation basin surrounded by steep slopes which transitions through a steep icefall to a low-gradient ablation zone 22 Debris Flux: At the uppermost cross-section in Fig 2 1 the total debris flux both surface and englacial was used to estimate the contemporary erosion rate for the upper Khumbu catchment Eq 2 Near EBC the englacial contribution dominates the total debris flux erosion rate for the upper catchment Fig 2 6 uncertainty in the englacial-debris flux is calculated using the range of debris concentrations measured on other glaciers Table 2 1 We also calculate uncertainty in surface-debris thickness based on our new spatially distributed measurements Using these values in Eq 2 the contemporary upper basin-wide erosion rate is 0 6 0 3 mm yr For all cross-sections in Fig 2 1 surface and englacial debris fluxes are summarized in Fig 2 6 While englacial transport dominates in the first two cross-sections most of the debris in the lower five sections is advected along the surface The flux of surface debris increases for about 3 5 km down glacier from EBC further down glacier it remains relatively constant Fig 2 6 The surface flux profile reflects spatial variations in debris thickness and the glacier velocity For example with a constant debris thickness the flux of surface debris would be proportional to the ice velocity The nearly constant flux suggests a balance between diminishing ice speeds and the dynamic thickening of the surface debris that is caused by the slowdown of the ice Fig 2 2 and the active surface melting The relationship between the surface melting and the lowering as well documented from satellite data Bolch et al 2011 is discussed elsewhere Chap 3 In general the total debris flux decreases steadily down glacier except near the terminus which implies active loss of debris from the glacier along the length the ablation zone the debris is evidently transferred to the glacier base as it is not accumulating elsewhere off the glacier Along the glacier sides the steep inner slopes of the moraines 23 would more likely function as sources of surface debris than sinks of debris Moreover leakage of debris out of the confines of Khumbu Glacier is unlikely because sediment evacuation rates in the proglacial stream are insignificant Section 2 9 This discovery that debris is currently lost from Khumbu Glacier along the length the ablation zone and accumulating below the glacier is supported by evidence that the modern glacier is perched on a thick valley fill of debris that accumulates over time Near the terminus ice is at most 20 m thick Gades et al 2000 yet the crest of the glacier terminus rises more than 200 m above the modern valley surface This debris flux analysis which is developed in the next paragraph also provides an opportunity to assess the rate of formation of thick subglacial debris edifice for other Himalayan glaciers which have been illustrated in the literature Benn and Evans 2000 Westoby et al 2014 From mass conservation the rate of change in the total debris thickness can be quantified from the divergence of the total flux of debris Fig 2 6 and was approximated as the ratio of the change in debris flux measured at two adjacent cross-sections to the distance between the defining sections x Fig 2 1 is the upglacier location Thus the deposition rate of debris beneath the glacier is: 1 Eq 4 For the analysis the glacier was subdivided into six zones defined by seven icethickness profiles across the width of the glacier Gades et al 2000 Glacier variables at each profile include the depth-averaged glacier velocity the average glacier thickness width across the glacier defined by surface velocities ice flux and distance between each flux gate For all zones the rate at which debris is lost from the glacier and presumably accumulating at the bed ranges from 0 6 to 5 0 mm yr average 1 7 mm yr The rate of 24 basal deposition is highest in the three upper zones and steadily decreases down glacier to a minimum value near the terminus The analysis is presented in greater detail in Chap 3 2 6 2 Holocene erosion rates In contrast to the accumulation area the lower part of Khumbu Glacier is surrounded by sediment accumulations lateral and terminal moraines and subglacial deposits that have formed through the Holocene Richards et al 2000 The volume of debris stored or evacuated within the Khumbu Basin is summarized in Table 2 2 and estimates range from 0 5 to 0 9 km3 The range of volumes shown in Table 2 2 reflects the uncertainty in the measurements The bulk of the debris 0 3 to 0 6 km3 is stored in the terminal moraine and debris edifice lateral moraines and tributary glaciers In fact the massive terminal debris edifice contains about half the volume of the 8 km long lateral moraines which are evident in the southernmost cross-section in Fig 2 5 along with the depressed glacier surface Near EBC it is likely that the glacier is sliding over bedrock and eroding it whereas near the terminus the glacier is perched on 150 m of debris Overall debris on top of within and beneath the glacier ranges from 0 1 to 0 3 km3 The wide range especially for the englacial subglacial and tributary glacier domains reflect the considerable uncertainties in the analysis Using Eq 3 we estimate the Holocene basin-wide erosion rate is between 0 8 0 2 mm yr This rate is 50 times higher than that needed to sustain the measured suspended sediment fluxes from the basin 0 015 mm yr This result indicates that much of the debris eroded over the last 104 years still resides in the basin and implies that measurements of sediment flux in proglacial streams can lead to substantial under-estimates of erosion rates 25 2 7 Discussion 2 7 1 The pace of erosion and exhumation of Khumbu Basin Results suggest that on average erosion of Khumbu Basin has maintained a steady pace over time scales ranging from 102 to 104 years Our estimated basin-averaged erosion rates are similar to exhumation rates derived from thermochronometric data in the region which include both erosional and tectonic exhumation over timescales of 106-107 years Rates of exhumation since the mid Miocene 9 Ma derived from apatite and zircon fission track data on samples from the high slopes of Everest average 1 0 0 2 mm yr Streule et al 2012 Nearly uniform erosion and exhumation rates over a large range of time scales for the Khumbu Basin imply a surprising insensitivity to likely variations in climate structural development and relief evolution For example in terms of expected climate effects frost cracking that likely affects headwall retreat rates is sensitively dependent on temperature Scherler 2014 Furthermore an ice-core sample from the north side of Everest showed significant variations in mean annual snow accumulation related to changes in the south Asian monsoon Kaspari et al 2007 Our findings contrast with results of other studies that commonly report exhumation accelerating in the Himalaya and other regions worldwide with the onset of Plio-Pleistocene glaciation Shuster 2005 Thomson et al 2010 Herman et al 2013 Thiede and Ehlers 2013 Herman and Campagnac 2016 Our findings also contrast with a number of studies in diverse settings reporting a dependence of erosion rates on the duration of the period under study For example Kirchner et al 2001 suggested that erosion rates measured over short timescales are lower than those over longer timescales in part because the shorter measurement periods tend to miss large but ephemeral erosional events On the other hand 26 short-term sedimentary records often suggest faster erosion than longer-term records which are more likely to reflect significant depositional hiatuses Sadler 1981 Finnegan et al 2014 Moreover erosion rates from glaciated basins decrease with the length of the period over which they are averaged Fernandez et al 2011 2016 Yet based on our work in the Khumbu we see little if any temporal variation at least within a factor of 2 We note that our estimates of erosion rates integrate all processes operating in the Khumbu Basin not just those associated directly with glacial erosion we do not address the relative efficiencies of erosional systems: glacial periglacial or hillslope processes They simply imply constant rates of erosion over time despite climate change structural activity and relief evolution 2 7 2 Implications for the structural and topographic development of Mt Everest The wealth of structural metamorphic and geochronological data from the Mt Everest region provides insight into the evolution of the highest region on Earth One of the principal Himalayan faults the South Tibetan Detachment fault STD is exposed in the region it consists of 1 the upper brittle Qomolangma detachment QD and 2 the lower ductile Lhotse detachment shear zone LD Searle et al 2003 2006 Cottle et al 2011 The two strands merge into one large-scale ductile shear zone to the North in the Rongbuk valley Cottle et al 2007 Streule et al 2012 Collectively they separate un- metamorphosed Ordovician limestone that extends to the peak of Mount Everest in the upper plate from high-grade metamorphic rocks of the Greater Himalayan Sequence GHS below The GHS rocks beneath Everest were at high temperatures during a metamorphic event that lasted from 39 Ma to 17 Ma while brittle faulting on the QD is likely younger than 16 Ma Searle et al 2003 Since the main phase of melting and metamorphism in the 27 GHS during the Miocene from ca 21 to 16 Ma Searle et al 2003 Cottle et al 2007 Hodges et al 2000 Simpson et al 2000 Cottle et al 2009 Streule et al 2010 the exhumation rate due to both tectonic extension and erosion in the Khumbu and nearby regions has averaged 1 0 mm yr Sakai et al 2005 Streule et al 2012 This exhumation probably switched from being driven by tectonic processes to erosion at 11 13 Ma when movement on the STD in the Everest area ceased Streule et al 2012 Meanwhile paleoelevation estimates based on hydrogen isotope ratios of hydrous minerals deformed in the STD during the Early Miocene suggest that mean surface elevations in the Everest region at that time were similar to modern ones G belin et al 2013 The history of the extreme relief of the Everest region with several of the world s highest peaks and deep glacial valleys remains essentially unconstrained The deep glacial incision probably started when glaciers first developed at the crest of the range before the global Quaternary glaciation Sustained erosion of bedrock even at the relatively low rate of 1 mm yr would exhume 10 km of crustal material over 107 years the time scale since cessation of the STD movement Hence the absence of long-term surface uplift suggested by the paleoelevation study requires a close balance between bedrock uplift and erosion at the crest of the Himalaya despite substantial changes in climate during the onset of Pliocene-Pleistocene glaciation and major changes in monsoonal circulation This result is consistent with recent global datasets of sediment accumulation rates and weathering rates suggesting that rates of landscape change have remained surprisingly constant over the last 10 Ma Willenbring and Jerolmack 2016 The total debris flux for Khumbu decreases steadily downglacier which indicates a progressive loss of debris along the length of the debris-covered ablation zone and deposition 28 subglacially Fig 2 6 Our estimates of basal deposition reveal that the highest rates are near EBC however the subglacial debris thicknesses in Fig 2 5 reveal that much of the subglacial debris resides beneath the lower part of the glacier where basal deposition rates are at a minimum Conceptually we hypothesize that a fraction of the surface debris actively falls into crevasses tarns moulins or other englacial conduits Gulley et al 2009 progressively migrates to the glacier bed and is transported subglacially to the terminus likely by meltwater An important consequence of the debris transfer is that the surface of the glacier now has less debris and hence less insulation which promotes more ice melt In Section 2 6 1 we determined that contemporary subglacial deposition rates range from 0 6 to 5 0 mm yr along the glacier Assuming these values represent the range of rates that can be sustained through the Holocene 104 years the average thickness of debris beneath the glacier would range from 6 to 50 m Previously in our analysis of Holocene deposits we estimated the volume of subglacial debris for Khumbu Glacier to be 0 04 to 0 095 km3 Table 1 which corresponds to a width-averaged subglacial debris thickness of 12 to 40 m The similarity between the subglacial debris thicknesses based on the topographic analysis Fig 2 5 and the thickness based on basal deposition rates suggests that debris is currently accumulating under Khumbu Glacier and doing so at a rate that is similar to the Holocene average Before the Holocene extensive valley glaciation corresponding to the Periche stages e g Finkel et al 2003 efficiently transported eroded material downvalley and the absence of upvalley fans terraces and moraines older than the Holocene can be attributed to rapid sediment transfer characteristic of large glaciers Richards et al 2004 Following retreat to the current position tributary and debris flow fans and moraines were deposited as the smaller glacier and lower-runoff rates could not keep pace with 29 sediment production Note that contemporary suspended sediment evacuation is 50x less than the Holocene-averaged sediment production This together with evidence that the contemporary glacier is perched on a debris edifice implies that most of the eroded debris remains within the basin 2 8 Summary In view of the structural complexities as well as major climatic changes through the last few million years including the onset of glaciations and several glacial cycles two surprises emerge from our study: exhumation rates are similar to erosion rates and they show no significant changes over time periods ranging from 10 to 107 years Taken together with the paleo-elevation evidence our results suggest a self-organized balance achieved as the surface and tectonic systems mutually adjust to remove rock mass from the crest of the range at roughly the same rate as the rock uplift Over the last 104 years the bulk of debris produced by erosion remains under and in the vicinity of Khumbu Glacier suggesting that although erosion rates of the basin do not vary appreciably over time debris evacuation and transfer down valley is likely be highly variable in time and peak during major glacial advances The current accumulation of debris beneath the glacier that curtails the accumulation of debris on glacier surfaces is likely widespread in the region and hence has important implications for estimates of ice volumes and predictions of future glacier evolution and fresh water resources 30 2 9 Supplement 2 9 1 Measurements of fluvial sediment flux We established rating curves to convert stage measurements to water discharge by measuring depth profiles of flow velocity We also surveyed repeat topographic profiles of the streambed covering both the stream bank and channel in order to estimate rates of higher discharge using the Manning equation with values for bed roughness guided by our measurements During monsoon periods stage and turbidity were monitored continuously at site 1 while stage and suspended sediment concentrations SSC were measured twice daily at site 2 Fig 2 1 Locals were hired and trained to collect water samples from the stream surface at periods of near minimum early morning and maximum evening discharge and to photograph the stream to document stage The measurements of SSC were used to calibrate the turbidity data which were collected over a longer period and with higher temporal frequency The suspended sediment discharge Qss is calculated from the product of the SSC and water discharge We do not account for the increase in sediment concentration with depth which could be as much as 30% e g Riihimaki et al 2005 and nor do we account for the fluvial flux of solutes and corresponding chemical erosion In another study the cation denudation rate for catchments occupied by alpine glaciers was greater than the global mean rate but did not exceed rates in nonglacial catchments with similar water discharge suggesting that water flux exerts the primary control of chemical erosion by glaciers Anderson et al 1997 During colder periods such as the Last Glacial Maximum LGM chemical erosion rates determined from LGM sediments were an order of magnitude lower than that measured from youngest sediments Anderson et al 2000 A third more significant loss of material that is also not considered is the evacuation of 31 sediments during glacial outburst floods our estimates should therefore be considered as a lower bound Fig 2 7 summarizes the discharge SSC and turbidity measurements Measurements vary widely each summer and year-to-year In 2011 discharge steadily increases until it peaks in late July and then steadily decreases In contrast in 2012 the discharge peaks early in the monsoon season and subsequently varies around a relatively constant value in early Sept SSC also peaks in mid-June and then slowly decreases over the rest of the measurement period SSC measurements in 2011 yielded a mean concentration of 0 10 g L with a standard deviation of 0 04 g L In 2012 the mean concentration was 0 14 g L with a standard deviation of 0 05 g L Assuming little sediment is removed before or after the measurement period in 2011 and 2012 570 and 840 m3 of debris respectively were evacuated or 106 and 1 5 x 106 kg assuming a density of 1800 kg m3 The amount of sediment evacuated is averaged over the year for the erosion rate however we only measured sediment fluxes when they are likely to be significant during the monsoon The corresponding erosion rate 0 01 and 0 02 in 2011 and 2012 respectively from the suspended sediment flux in this study may miss episodic but high-discharge events and hence is a lower bound of both suspended sediment fluxes and erosion rates 32 Figures for Chapter 2 Figure 2 1 Visual and near infrared band composite satellite image of Khumbu Basin Aster 3 Oct 2003 Solid and dashed yellow lines outline the drainage basin and the glacier respectively Transverse white lines locate the ice-thickness radar surveys Gades et al 2000 Red dotted line is the centerline and location of the longitudinal elevation profile in Fig 2 2 The orange line near Everest Base Camp EBC is the start of the longitudinal velocity profile in Fig 2 2 and the red line is the equilibrium line altitude ELA near 5700 m in the icefall Scherler et al 2011 Red square over the lower ablation zone defines area covered in Fig 2 4 The blue star shows where suspended sediment flux was determined in the proglacial outlet stream Inset shows the massive headwalls surrounding the accumulation zone of the glacier and extreme relief above the glacier Image courtesy of A Gillespie 33 Figure 2 2 Longitudinal profiles of the surface and bed elevation profiles and surface velocities right-hand axis of Khumbu Glacier In the lower half of the glacier shown as dotted line between 8-16 km the glacier bed is interpolated between 7 cross-profiles of ice thickness Gades et al 2000 and between 0-8 km the dash-dot line it is modeled using profiles of surface slope and velocity derived from remote sensing data and by assuming basal shear stress of 1 bar Surface velocities are derived by using intensity feature tracking over a period of 4 5 months courtesy of M Braun The vertical lines at km-8 and km-15 7 are the start and end positions of Figs 2 3 and 2 6 34 Debris Thickness m 12 8 4 0 0 2 4 6 8 Distance from EBC km Figure 2 3 Downglacier variation in mean thickness of surface debris The horizontal axis distance down glacier starts at Everest Base Camp where debris begins to accumulate at the surface Error bars represent the range in debris thicknesses where measurements are available binned into 250 m increments along the glacier surface 35 Fig 2 4 Electrical resistivity tomography ERT profiles along survey lines shown in the top image the location of which is shown in Fig 2 1 Horizontal and vertical axes are in meters All images use the same color scheme blue colors denote very high resistivity Resistivity values of 106 m marked by white lines likely correspond to the boundary between surface debris and glacial ice below Solid green lines above each survey indicate regions where electrode coupling with the surface debris was adequate dashed green lines indicate regions of high uncertainty regions with no line are those where electrode-debris coupling was inadequate and data are uninterpretable 36 Fig 2 5 Surface and subsurface cross-sections from which the volume of sediment stored within the basin was estimated In the cross-sections which run West to East the solid black line is the current surface blue line is the glacier bed solid are measurements Gades et al 2000 and dashed are extrapolated shaded brown region represents subglacial sediment debris 37 Fig 2 6 Surface englacial and total debris fluxes downglacier beginning near EBC the uppermost radar profile in Fig 2 1 The shaded regions represent uncertainties in the data The flux calculation at 7 7 km corresponds to the radar profile 2 km up from the terminus Near EBC total debris flux is dominated by the englacial flux but at 2 2 km contributions from the englacialand surface-debris fluxes are similar By 4 5km the surface-debris flux dominates the englacialdebris flux is small because of the combination of low depth-averaged velocities
    • Chiao, Chester - M.S. Research Paper
      THE ROLE OF LARGE WOODY DEBRIS AND RIPARIAN FOREST IN CHANNEL AVULSION IN THE CARBON RIVER, MOUNT RAINIER NATIONAL PARK, WA 2016, Chiao,Chester,Chester Chiao The role of large woody debris and riparian forest in channel avulsion in the carbon river mount rainier national park wa Chester Chiao A report prepared in partial fulfillment of the requirements for the degree of Master of science Earth and Space Sciences: Applied Geosciences University of Washington May 2016 Project mentor: Paul Kennard Mount Rainier National Park Reading committee Brian Collins Steven Walters MESSAGe Technical Report Number: 037 Abstract A specific type of natural log jam in the upper alluvial reach of the Carbon River was found to influence secondary channel avulsion causing flooding hazards to the adjacent Carbon River Road in the northwest quadrant of Mount Rainier National Park Washington The fence-like natural log jam was characterized by large woody debris buttressed horizontally against standing riparian trees i e fence rails and fence post The objectives of this report are two-fold First physical characteristics and spatial distribution were documented to determine the geomorphic controls on the fence-like log jams Second the function and timing of the natural log jam in relation to channel avulsion was determined to provide insight into flooding hazards along the Carbon River Road The fence-like log jams are most abundant in the upper reaches of the Carbon River between 3 0 and 5 5 kilometers from the Carbon Glacier terminus where longitudinal gradient significantly decreases from about 0 06 to 0 03 Sediment impoundment can occur directly upstream of the fence-like log jam creating vertical bed elevation difference as high as 1 32 meters and can form during low magnitude high frequency flood event 3 5-year recurrence interval In some locations headcuts and widening of secondary channel were observed directly to the side of the log jams suggesting its role in facilitating secondary channel avulsions Areas along the Carbon River Road more prone to damages from avulsion hazards were identified by coupling locations of the log jams and Relative Water Surface Elevation map created using the 1-meter 2012 Light Detection and Ranging Digital Elevation Map Ultimately the results of this report may provide insight to flooding hazards along the Carbon River Road from log jam-facilitated channel avulsion i Contents Introduction 1 Carbon River Road and flood damage 1 Geologic history and a melting glacier 2 An aggrading river 4 Role of natural log jams in channel avulsion 6 Study Area 9 Methods 10 Log jam survey 10 Relative cross-sectional profile at WF-13 12 Historical aerial photograph 12 2012 LiDAR DEM 13 Hydrology 14 Results and Discussion 15 Characteristics of fence jam 15 Spatial distribution along the Carbon River 15 Fence post and fence rails 18 Role of fence jams in channel avulsion 19 Implications of flooding hazards to the Carbon River Road 20 Classification of fence jam 23 Conclusion 24 References 25 Figures 28 Tables 48 Appendices 49 ii List of Figures Figure 1: Geographic location map of study area 27 Figure 2: Extent of study reach of the Carbon River 28 Figure 3: Flood damage from 2015 winter storm 29 Figure 4: Nisqually Glacier recession from 1974 to 2004 30 Figure 5: Elevation change in the Carbon River from 1994 to 2008 30 Figure 6: Aggradation rates along the Carbon River from Knoth 2013 31 Figure 7: Longitudinal profile of various river 32 Figure 8: Orientation of woody debris placement 32 Figure 9: Picture showing measurement of bed-surface elevation change 33 Figure 10: Schematic of fence jam 34 Figure 11: Picture of fence jam with headcut 35 Figure 12: Picture of fence jam with avulsion 35 Figure 13: Location of mapped fence jams 36 Figure 14: Longitudinal profile of the Carbon River 37 Figure 15-20: Cross-sectional profile at Upper Reach 38 Figure 21: Main channel migration between 2006 and 2015 40 Figure 22: Log Pearson III distribution 41 Figure 23: Distribution of fence post diameter 42 Figure 24: Distribution of vertical bed-surface elevation change 42 Figure 25: Vertical bed-surface elevation change in the Queets River 43 Figure 26: Cross section of fence jam-facilitated channel avulsion 43 Figure 27: Fence jam causing channel avulsion 44 Figure 28: Relative water surface elevation map 45 Figure 29-30: Secondary channel avulsions caused by fence jams 46 iii List of Tables Table 1: Summary of GIS data aquired 47 Table 2: Comparison of bench jam 47 Table 3: List of fence jams causing channel avulsion 47 iv Introduction The Carbon River a rapidly aggrading proglacial river in the northwest quadrant of Mount Rainier National Park has increasingly caused flooding hazards and significant damages to the adjacent Carbon River Road in the past decade Figure 1 In the winter of 2006 the largest flood event on record washed away sections of the road near Falls Creek Green Lake Trail and the Ipsut Creek Campground vicinity Figure 2 To this day low magnitude high frequency floods continue to damage road structure through channel avulsion and overbank flooding rendering the road inaccessible to motor vehicle and even foot pedestrian further upstream Figure 3 The National Park Service has observed that channel aggradation and a certain type of natural log jam may be acting in concert to facilitate channel avulsion and overbank flooding The purpose of this study is to determine whether this specific type of log jam is promoting or preventing channel avulsion in an aggrading unconfined river system In order to answer this question I examined historical aerial photographs to determine main channel migration pattern conducted field investigation to map locations and describe functionality of the log jams and used remote sensing to identify areas more prone to potential log jam-facilitated avulsion Carbon River Road and flood damage On November 6th and 7th 2006 a narrow strip of very wet air mass the so-called atmospheric river hit Mount Rainier National Park dropping nearly 45 centimeters of rain over the course of 36 hours Neiman et al 2008 Peak precipitation intensity during the storm was measured at 2 0 centimeter hour at the National Resource Conservation Service NRCS Paradise Snowpack Telemetry SNOTEL station Legg et al 2014 The Carbon River USGS gauging station near Fairfax WA USGS Gauge 12094000 measured a greater than 70-year recurrence interval discharge Flood stage measurement rose from 4 meters at noon to 5 meters at about 18:00 on November 6th Overbank flooding caused significant damage and led to 6 months of park closure the single longest closure since the park was established in 1899 Several locations along the Carbon River Road were significantly damaged Specifically sections of the road near Falls Creek Green Lake Trail and the Ipsut Creek Campground vicinity were washed away In the fall of 2015 a 3 5-year recurrence interval flood event additionally caused several bank failures and 1 tread damage between Falls Creek river-kilometer 11 6 and Chenuis Falls river-kilometer 8 Figure 2 3 Today visitors are able to reach Ipsut Creek Campground on bike or foot and only foot traffic is allowed above Ipsut Creek Campground The condition of the road as of the time of this writing is hazardous and any kind of access terminates at the lower bridge crossing at river-kilometer 3 0 Figure 2 The Carbon River Road corridor was first established in the 1920 s for logging and mining access Today the corridor provides recreational access to unique habitat in the northwest quadrant of Mount Rainier National Park The Carbon River Road corridor was established as a National Register of Historic Places which is part of the Mount Rainier National Historic Landmark District NHLD In addition to its cultural significance the Carbon River provides critical fish habitat to bull trout Salvelinus confluentus as well as other species that are federally listed resources under the Endangered Species Act of 1973 Fish and Wildlife Services 2011 Recent studies in Mount Rainier National Park have suggested interaction between instream woody debris and riparian old-growth stands can have significant impacts on local aggradation secondary channel avulsion and floodplain development Entrix 2010 Kennard et al 2011 For the Carbon River these effects can have managerial implications on the Carbon River Road an easy access for the Mowich Lake hiking areas and the Carbon glacier in the northwest corner of Mount Rainier National Park Figure 2 Geologic history and a melting glacier The Carbon Glacier on Mount Rainier is a major source of sediment production for the Carbon River Located in western Washington Mount Rainier is a stratovolcano that rises to 4400 meters 14 410 feet above sea level and contains the largest volume of glacial ice in the contiguous United States Krimmel 2002 Mount Rainier is situated along the Cascade Range volcanic arc as a result of the subduction of the Juan de Fuca Plate under the North American Plate Though volcanism in the Cascade Range has been active since the Oligocene 27 Ma the modern edifice of Mount Rainier has only been assembled during the last half-million years from a series of andesitic and dacitic lava flows pyroclastic flows and lahars Fiske 1963 2 The present day U-shaped valley of the Carbon River valley was formed through a series of alpine glaciation during the Pleistocene Waitt and Thorson 1983 The Puget Lobe of the continental Cordilleran Ice Sheet did not reach its maximum extent until 15 to 14 ka and stopped just north of Mount Rainier Nevertheless alpine glaciations such as the Hayden Creek 170 to 130 ka and the Evans Creek glaciations 22 to 15 ka spread down valley onto the margins of the Puget Lowland and repeatedly scoured the landscapes Several minor neoglacial advances occurred during the last 10 000 years as well reaching its maximum between 2 8 and 2 6 ka Crandell 1969 As glaciers retreat the valley experiences sedimentation of glaciofluvial drift such as till and outwash Waitt and Thorson 1983 Evolution of the Carbon River valley following alpine glaciation occurred during the Holocene Kennard 2011 The Carbon River continuously incised into the valley bottom to form terraces that represent relic fluvial surfaces not inundated by high flow events Over time encroachment of maturing vegetation occupies the alluvial terraces to form old-growth forest stands along the margins of the valley bottom Today these old-growth riparian forests seen throughout the Carbon River are currently experiencing higher mortality from burial of sediments during the recent aggradational trends governed by glacial recession Beason et al 2014 Czuba et al 2012 Glacial recession affects sediment inputs into river valleys and can have significant implications to geologic hazards in Mount Rainier National Park Beason et al 2014 Mountain-wide glacier volume loss has been estimated at 14% from 1970 to 2008 Sisson et al 2011 Although no publication was found for the recession of the Carbon Glacier Reidel et al 2015 has been monitoring two of the major glaciers from 2003 to 2011 Emmons 11 6 square-kilometer and Nisqually 6 9 square-kilometer Cumulative net volume loss in the eight years is 89 4 million cubic-meter for Emmons Glacier and 58 1 million cubicmeter for Nisqually Glacier Figure 4 Similar volume recession is expected for the Carbon Glacier 3 An aggrading river Geologic hazards such as flooding and channel avulsion can be caused by channel aggradation when sediment production overwhelms the stream s ability to transport the sediment downstream Recent studies have shown that glacial recession is increasing sediment inputs into rivers that radially drain Mount Rainier and limiting channel conveyance over the past 15 years Beason et al 2014 Czuba et al 2012 The Carbon River is showing aggradation in certain segments of the study reach as well Knoth 2013 Entrix 2008 In these aggradational areas the valley cross sections show convexity where the active channel is perched as high as 6 meters above adjacent floodplain Kennard et al 2011 The rivers are expected to respond by either changing its channel planform its location in the valley bottom or both this has significant implications to many of the park infrastructures that are built along the adjacent floodplain For example the perched active channel above adjacent floodplain has been attributed to be the dominant factor in channel widening and avulsions during the 2006 storm event in the Carbon River as well as in the White River and Tahoma Creek Entrix 2008 Entrix 2010 Beason et al 2014 Mount Rainier rivers have been experiencing aggradational trends for the past 15 years Beason et al 2014 In the Nisqually River and the White River aggradational trends occurred in all of the surveyed cross sections between 1997 and 2012 with the exception of the 2007-2008 period For example at the Sunshine Point Reach in the Nisqually River average aggradation rates range from 0 04 0 15 meter year 2005-2006 to 0 36 0 15 meter year 2006-2008 In the White River aggradation rates of 0 04 0 15 meter year and 0 05 0 15 meter year occurred in periods 2005-2007 and 2008-2011 respectively Similar to the Nisqually River and the White River the Carbon River is also showing aggradational trend in some sections of the river between 1994 and 2012 Entrix 2008 Knoth 2013 Reference cross sections near the Ipsut Creek Campground showed elevation difference ranges from 0 5 to 1 5 meters with an uncertainty of 0 6 meters between 1994 and 2008 Figure 5 This equates to an aggradation rate of 0 04 to 0 1 meters year suggesting a similar aggradation rate to certain sections on the Nisqually River and the White River Entrix concluded that aggradational trends between 1994 and 2008 extend throughout the study reach and aggradation could occur even at low magnitude high frequency flood 2-year 4 recurrence interval In a similar study Knoth observed aggradational trend in the Carbon River between the Carbon Glacier and Mother Mountain between 2008 and 2012 through LiDAR DEM differencing Figure 6 Highest aggradation rate of 0 25 meters year was seen between river-kilometer 2 5 and 3 0 Figure 2 6 Despite aggradation in the Carbon River close to the Carbon Glacier Knoth 2013 observed no significant bed elevation change in the Ipsut Creek Campground vicinity and even incisional trends close to the Park entrance Figure 6 Sediment input that is contributing to aggradation in the Carbon River is first initiated by rockfalls and debris avalanches in the surrounding hillslopes and glacier terminus Czuba et al 2012 Sediment is then transported downstream through debris flow and fluvial processes Debris flows consisting of both sediment and water efficiently transport large sediment loads downstream Czuba et al 2012 observed debris flows in the Carbon River to have traveled as far as 2 kilometers downstream from the glacier terminus within the past 10 years Debris flows in the upper reach of the Carbon River have become more active when compared to historical rate increasing sediment inputs and exacerbating aggradation Czuba et al 2012 Legg et al 2014 Throughout Mount Rainier at least 12 separate debris flows initiated in six different drainages were recorded in 2001 2003 2005 and 2006 all of which occurred in recently deglaciated areas Beason et al 2014 Debris flows efficiently promote the overall delivery processes of sediment from the steeper section of the fluvial network near the glacier to the fluvial reaches at lower elevation where flow competence and stream power is sufficient to mobilize larger particles into river sediment load 5 Role of natural log jams in channel avulsion Natural log jams created by accumulation of wood and sediment play an important role in floodplain development and channel avulsion Numerous studies have shown significant effects of natural log jams in the morphology of alluvial river valleys in the Pacific Northwest Abbe and Montgomery 2003 Collins et al 2012 For example lateral channel migration in the Queets River is strongly influenced by vertical channel adjustment due to some types of log jams such as those created by valley-spanning wood accumulation Brummer et al 2006 Up to 2 meters of vertical change in water surface and thalweg elevation was linked to the channel-spanning log jams Sediment impoundment behind stable log jams initiates positive feedback when aggradation in the upstream channel bed reduces transport capacity resulting in further sediment deposition and slope reduction On the one hand stable log jams have the potential to create hardpoints where channel bars and banks are protected against erosion to allow revegetation and floodplain development Abbe and Montgomery 2003 Collins et al 2012 On the other hand the processes of wood accumulation and sediment impoundment can end when the log jam is breached by overtopping or channel is forced to migrate laterally into surrounding floodplain In the White River natural log jams can prevent migration of the main channel but the resulting aggradation in the main channel can promote secondary channel avulsion Entrix 2010 Kennard 2011 The specific type of log jam created by instream wood horizontally buttressed against standing oldgrowth forest effectively retain the main channel in place by creating stable surface for revegetation along the floodplain As the White River remain in its historic channel aggradation can result in an elevated bed surface Entrix 2010 observed increasing lateral channel migration from 1957 to 2009 in some sections of the White River by mapping floodplain changes using historical orthoimageries The two factors influencing secondary avulsions in the White River were the negative elevation of adjacent floodplain relative to main channel and the proximity of wetted channel to forest margins Entrix 2010 Kennard et al 2011 Slope of valley cross sections from the main channel to the adjacent floodplain 7-20% greatly exceed downstream gradient 0 01-1 3% Entrix 2010 Furthermore secondary channel avulsion was found to be independent of flood magnitude a small magnitude high frequency flood as little as 2-year recurrence interval can cause secondary channel to laterally migrate into adjacent floodplain 6 The specific type of natural log jam created by instream large woody debris and standing old-growth stands as seen in the White River may be unique to the proglacial alluvial rivers that radially drain Mount Rainier where old-growth riparian forest exist Its distribution functionality and stability are not completely understood Field investigation conducted in the spring of 2016 suggests that the log jam is a result of the interaction between instream woody debris and standing riparian forest manifesting itself into a fence-like feature i e fence post and fence rails Therefore this specific type of log jam will be mentioned as fence jam hereafter In the Carbon River aggradation and channel widening increases mortality of adjacent old-growth forests Beyeler 2013 providing an abundant input of large woody debris as fence rails to be buttressed against riparian trees that are still standing fence posts The purpose of this study is to characterize fence jams in the Carbon River by evaluating its role in channel avulsion and floodplain development through literature review remote sensing and field mapping This report will attempt to answer the following questions: 1 where in the Carbon River are fence jams located 2 What are the physical characteristics of fence jams that render its uniqueness to the Carbon River 3 Do fence jams facilitate or prevent channel avulsion Ultimately understanding the role of fence jams in the Carbon River may provide information on flooding hazards for the Carbon River Road In order to answer these questions the project was divided into three phases First I compiled geospatial information system GIS data to help constrain geomorphic characteristics of the Carbon River Table 1 Bare-earth light detection and ranging LiDAR digital elevation maps DEM from 2012 was used to create hillshade base map visualize longitudinal profile and cross-sectional topography to determine the control of channel slopes on fence jam formation In addition I compared repeated years of U S Department of Agriculture s USDA National Agriculture Imagery Program NAIP orthoimagery to observe historical channel migration in the past decade NAIP imageries from 2006 2009 2011 and 2015 were used to map main channel migration This allowed me to determine changes in Carbon River main channel along the valley bottom in relation to the formation of fence jams 7 Second I conducted field mapping of log jams along the Carbon River and characterized the fence jams Data collected in the field included number of individual woody debris and standing tree involved in the log jam diameter at breast-height DBH of standing tree diameter at midpoint of woody debris standing tree spacing spatial extent of log jam flow geometry during formation vertical height difference between stream bed and floodplain channel and spatial distribution of log jams This data serves as the basis to determine physical characteristics log jam stability and role of fence jams in channel avulsion The project concluded by determining the role of fence jams in potential avulsion hazards along the Carbon River-left This is achieved by creating a Relative Water Surface Elevation RWSE map using the 2012 one-meter LiDAR DEM and comparing with the mapped locations of fence jams RWSE maps help visualize areas that are more prone to flooding and coupling with fence jam locations determines whether the fence jams are related to channel avulsion that pose flooding hazard to the adjacent Carbon River Road 8 Study Area For the purpose of this study I focused on the southern margin of the Carbon River on river-left where the Carbon River Road is located Figure 2 The study area spans throughout the 15-kilometer reach between the Carbon Glacier and park entrance However due to flood damages that occurred in the winter of 2015 I was only able to reach to river-kilometer 3 0 during field survey of the fence jams The study reach is characterized by a braided stream with a concave longitudinal profile Figure 7 Czuba et al 2012 Slope in the headwaters decrease from 0 1 to 0 06 near the Carbon Glacier and gradually decreases from 0 02 near Mother Mountain to 0 015 at the park entrance channel width typically ranges from 150 to 300 meters One-quarter of the bed material within 3 kilometers of the glacier terminus consists of boulders Grain size distribution generally decreases downstream becoming predominantly cobbles with 10-20% of sand in the bed material Czuba et al 2012 The Carbon River is split into three sections Upper Reach Ipsut Creek Floodplain and Lower Reach Figure 2 First the Upper Reach ranges from the Carbon Glacier terminus at river-kilometer 0 to riverkilometer 5 0 The Upper Reach is dominated by debris flow processes and shows steeper longitudinal profile Czuba et al 2012 During field reconnaissance I observed mostly large boulders in poorly-sorted matrix in exposed cutbanks and midchannel bars upstream in the Upper Reach Second the middle section Ipsut Creek Floodplain is located at the Ipsut Creek Campground river-kilometer 5 to 6 This section of the Carbon River shows transitional characteristics between debris flow-dominated to fluvialdominated processes J Beyeler personal communication 2015 Third the Lower Reach stretches from the downstream extent of Ipsut Creek Floodplain to park entrance river-kilometer 6 to 15 where fluvial processes dominate suggesting a different longitudinal gradient cross-sectional width and different aggradational trends Entrix 2008 Knoth 2013 9 Methods Log jam survey In order to determine spatial distribution of fence jam along the Carbon River I conducted field investigation on 2 19 2016 3 25 2016 3 30 2016 and 4 07 2016 Geographic locations of these features were collected using the Trimble R10 global navigation satellite system GNSS unit paired with a TSC3 controller and was collected in Universal Transverse Mercator UTM coordinate system Zone 10N Using the Fast Static method I recorded the GPS position of log jams by occupying the locations for approximately 7 minutes at each site To understand the characteristics of fence jams field measurements were collected where they were identified For each site I catalogued the number and size of standing trees and woody debris involved in the log jam Additional quantitative information includes the spacing of standing trees spatial extent and bed-surface elevation Definition of data collected is summarized as the following: Standing tree count: number of standing tree acting as fence post in riparian forest that is supporting accumulation of woody debris and resulting local aggradation on the upstream bed-surface Standing tree diameter: diameter of standing tree is measured at breast height DBH while standing on the downstream bed-surface Circumference was measured in the field with a 50-feet measuring tape and was later converted to diameter Diameter of standing trees helped determine if fence jams were limited to old-growth stands Standing tree spacing: showed the horizontal distant at breast height between two fence posts Multiple post spacing were collected when more than two posts were identified This determined whether there was a minimum requirement for tree spacing to create fence jams 10 Woody debris count: number of horizontal large woody debris acting as fence rails that is buttressed against the standing trees In some cases where there were overabundances of small woody debris accumulation that may be buried an estimated count was recorded Key member was identified as the largest horizontal wood that was directly in contact with the fence post Woody debris key member diameter: diameter of the key member horizontal WD buttressed against the standing trees that was supporting aggradation on the upstream end Key members were identified as the largest horizontal woody debris that was buttressed against standing tree and allowed accumulation of smaller woody debris and facilitate sediment impoundment in the upstream bed-surface Woody debris diameter helped determine whether only old-growth debris was involved in the formation of fence jam Spatial extent: the fence-like log jam is recorded either discrete or continuous Discrete extent indicated that multiple log jams were not interconnected throughout the floodplain Whereas continuous extent entailed multiple log jams that were interconnected throughout the floodplain This provides information on the scale at which fence jams could occur Woody debris accumulation orientation: measurement to indicate orientation of log placement relative to flow This is categorized into quadrants based on wood survey method by Bilby and Ward 1991 Figure 8 shows whether the log jam can be parallel A perpendicular B or askew C and D to the current flow direction of the main channel Bed-surface elevation change: measurement of the vertical drop from the locally aggraded bed-surface upstream to bed-surface downstream of the fence jam Figure 9 A height difference was recorded at the point along the fence jam where bed-surface elevation change was at its maximum 11 A total of 28 fence jams were identified along the 15 kilometer reach of Carbon River Out of the 28 fence jams I collected quantitative data as described above for 25 of the features and measured geographic locations for 15 of the features I collected additional descriptive information such as presence of alder and size distribution changes in sediment grain size from upstream of the fence jam to downstream bed-surface and presence of headcut or evidence of avulsed channel associated with the fence jam Relative cross-sectional profile at WF-13 I surveyed two cross-sectional profiles at fence jam location WF-13 to show relative elevation of floodplain below the wetted main channel Fence jam at this specific location is particularly interesting because it was formed between field reconnaissance in the summer of 2015 and field mapping in the spring of 2016 Thus this was a fairly new feature that may be linked to the 2015 winter storm Measuring a relative elevation change from adjacent floodplain to the wetted channel provided information on channel avulsion facilitated by the fence jam The elevation profiles were measured using a hand level a stadia rod and a 50-feet measuring tape The horizontal distance extended from an arbitrary datum control point set at the valley wall to the edge of the wetted main channel Cross section 1 is located at the initial control point 46 967869 -121 819176 Cross section 2 is located 50 meters downstream from the control point Historical aerial photograph The Carbon River channel migration was analyzed using a series of historical aerial photographs 2006 2009 2011 2013 and 2015 orthophotos were obtained from the US Department of Agriculture USDA National Agriculture Imagery Program NAIP online database Dates of publication of each NAIP imagery is shown in Table 1 Changes in main channel location along the valley bottom was associated with particular storm events that may have caused avulsions channel widening and timing of fence jam formation NAIP imagery tiff files was imported into ArcMap to digitize changes in thalweg position identify channel avulsion and potential widening of floodplain channel facilitated by fence jams 12 2012 LiDAR DEM The 2012 LiDAR one-meter DEM was obtained from Scott Beason a Park Geologist in Mount Rainier National Park The 2012 DEM was imported into ArcMap to create hillshade map longitudinal gradient cross-sectional profile and a Relative Water Surface Elevation RWSE map A hillshade map was created mainly to be used as basemap and visualize topographic relief in the alluvial valley The longitudinal profile was plotted at 0 5-kilometer increments to show downstream variation in channel gradient Meanwhile cross-sectional profile was plotted at 10-meter interval at several locations on the Carbon River RWSE map was used to determine locations that were well below the perched wetted channel and served as a flood hazard map to the Carbon River Road Methods of RWSE analysis was based on Model 2 developed by Jerry Franklin of Washington State Department of Ecology which was included in a compiled report by Patricia Olson 2012 First crosssectional cutlines were drawn at an evenly spaced interval along the thalweg using River Bathymetry Toolkit developed by ESSA Technologies Ltd Second elevation of surface water was defined at the intersection between cross-sectional cutlines and thalweg line This elevation data was then added to each cross sections Third a triangulated irregular network TIN model was then created using the cross sections that contained elevation value The TIN model could then be converted into a raster Finally a Relative Water Surface Elevation map was created by subtracting the raster TIN from the bare earth LiDAR 13 Hydrology In order to understand magnitude and frequency of flood events that may be associated with fence jam formation or channel avulsion I analyzed historical annual peakflow data using the Log Pearson LPIII statistical analysis Peakflow data for the Carbon River was downloaded for the USGS gauge 12094000 near Fairfax WA The stream gauge is located outside of the study reach about 10 kilometers from the park entrance and at approximate river-kilometer 26 on the left bank 2 kilometers from State highway 165 Fairfax bridge Thus peakflow statistics at this location used to determine flood patterns within the study reach would generate some degree of uncertainty due to factors such as difference drainage areas Data was available from water years 1930 to 2014 with a data gap between 1978 and 1991 Log Pearson LPIII statistical analysis was used to analyze flow rates at various recurrence intervals This was analyzed on a Microsoft Excel spreadsheet with written macros that was developed by the Natural Resource Conservation Service http: go usa gov KS6 14 Results and Discussion Characteristics of fence jam A typical fence jam consists of fluvial-transported large woody debris as fence rails that are horizontally buttressed against standing trees or stump as fence post Figure 10 Usually a key rail member is identified to be the most stable that causes additional woody debris accumulation and sediment deposition creating a steep vertical elevation drop from upstream channel bed to surrounding floodplain Figure 11 Grain size generally ranges from cobbles to boulders upstream of the fence jam to coarse sand and cobbles downstream of the wood fence Figure 12 The wood accumulation and subsequent sediment impoundment directly upstream of the fence jams effectively dissipate boundary shear stress by promoting spill resistance Throughout the Carbon River fence jams can occur at discrete locations where one or two standing trees can cause wood accumulation and sediment impoundment it can also occur continuously where multiple fence jams are interconnected along the margins of the floodplain Spatial distribution along the Carbon River A total of 25 fence jam were surveyed throughout the 15 km reach of Carbon River Figure 13 Appendix 1 Fence jams along the Carbon River are pervasive especially in the Upper Reach and Ipsut Creek Floodplain river-kilometer 3 0 to 5 7 Although field investigation did not include the right side of the active channel more fence jams are expected to be present on river-right between river-kilometer 3 0 and river-kilometer 5 0 At this location on the river-left however no fence jams were observed because the wetted channel borders bedrock outcrop where riparian forest does not exist The high frequency zones of fence jams in the Upper Reach and Ipsut Creek Floodplain are associated with three factors changes in longitudinal gradient Figure 14 cross-sectional profiles Figure 15-20 and lateral channel migration of the main channel between 2006 and 2015 Figure 21 15 In the longitudinal profile there is a sudden decrease in slope at river-kilometer 4 0 Figure 14 From river-kilometer 0 5 to 2 0 the slope decreased from 0 093 to 0 055 The Carbon River meanders almost 90 into the southern margin of the active channel at this location Slope increased to 0 070 at riverkilometer 3 0 before decreasing again to about 0 058 at river-kilometer 4 0 At this location gradient decreased significantly again from 0 05 to 0 03 This break in slope is hypothesized to be the transition point between debris-flow-dominated processes and fluvial-dominated processes J Beyeler personal communication 2016 This is supported by field observations of cobbles- to boulder-sized material supported by poorly-sorted fine-grained matrix exposed in the cutbanks and mid channel bars in the Upper Reach which suggest debris flow deposits Upstream of river-kilometer 4 0 the two concavities in longitudinal gradient river-kilometer 2 0 and 3 5 coincide with changes in the cross-sectional profiles in this section of the river Figure 15-20 At riverkilometer 1 6 the channel cross section is generally flat neither convex nor concave At river-kilometer 2 1 the cross-sectional profile begins to tilt to the river-right This becomes more apparent as the point of lowest elevation deepens on the river-right at river-kilometer 2 5 At river-kilometer 3 2 the channel cross section returns to a flat bottom with an apparent channel bank on river-left At river-kilometer 4 0 and 4 3 the lowest point of elevation in the active channel evidently shifted river left The higher elevations in the seesaw pattern of the cross-sectional profile between river-kilometer 1 6 and 4 3 likely indicates the transient alluvial storage mentioned by Czuba et al 2012 and Beason et al 2014 High frequency of fence jams occurred in the vicinity where the largest lateral migration occurred in the main channel between 2006 and 2015 Figure 21 The 2006 main channel green in Figure 21 shows historical position of the Carbon River prior to the 2006 storm event The Carbon River flowed along the river-right as it meanders around Mother Mountain In 2009 and the subsequent years the main channel of the Carbon River migrated dramatically into the river-left inundating the former Carbon River Road J Beyeler personal communication 2016 The cause for the 2009 channel migration is linked to either the 2006 2008 flood events or both According to the Log Pearson III flow statistics the 2006 flood event have a recurrence interval of 67 5 years with an exceedance probability of 1 48% and the 2008 flood 16 event have a recurrence interval of 26 4 years with an exceedance probability of 4 32% Figure 22 In 2011 gray in Figure 21 the main channel further migrated into the southern floodplain on river-left possibly occupying secondary channels created during the 2006 flood event The 2011 channel migration is linked to a relatively smaller flood event earlier in the same year that has a recurrence intervals of 4 8 years Figure 22 The changes in longitudinal gradient cross-sectional profiles and main channel migration discussed above likely show that fence jams in the Upper Reach and Ipsut Creek Floodplain are due to the combination of factors between increased aggradation and proximity of the wetted channel to riparian forests First higher gradient in the longitudinal gradient showing increased sediment deposition in riverkilometer 3 0 coincide with fence jams in the Upper Reach shaded yellow in Figure 14 Meanwhile fence jams in the Ipsut Creek Floodplain vicinity at river-kilometer 5 5 shaded green is at the same location of higher aggradation rate of about 0 1 meters year between the years 1994 and 2008 Figure 5 Entrix 2008 Second active channel migration occurred between 2006 and 2015 due to flood events at various recurrence intervals shifting the Carbon River closer to the southern floodplain on river-left Figure 21 Thus deposition of sediment onto adjacent floodplain during high flows results in buried riparian forests and creates the so-called ghost forests Knoth 2015 Increased tree mortality creates a positive feedback when large amount of instream wood is readily available to be transported downstream and deposited along channel margins The large woody debris are then buttressed horizontally against oldgrowth trees that remain standing creating fence-like log jams In the Lower Reach of the Carbon River fence jams generally become relatively older when compared to those mapped upstream I observed young alder stands not observed in the upper reaches approximately 1-3 years in age above developed floodplain caused by fence jam in the Lower Reach dashed and shaded blue in Figure 14 The alders occupying armored bank surfaces have a maximum height of approximately 3 meters and an average diameter of 3 centimeter The relative stability of fence jams at the Lower Reach may be due to its distance from the main channel The Lower Reach fence jam zones are approximately 250 to 500 meters from the wetted channel whereas the zones in the Upper 17 Reach were in close proximity to the wetted channel Figure 13 The absence of developed floodplain with revegetation from fence jam upstream suggests that these features are unstable compared to other types of natural log jams Abbe and Montgomery 2003 The oldest fence jams found in the Lower Reach where 1-3 year-old alders stands suggest the fence jams fail regularly and cannot support long-term revegetation of floodplain However I was unable to determine the mechanism of failure Fence post and fence rails Riparian forests in the Carbon River involved in providing fence posts mostly consist of a variety of conifers including Douglas firs Pseudotsuga menziesii western hemlock Tsuga heterophylla western red-cedar Tsuga heterophylla I did not observe any alder Alnus that served as fence post Forest age structure ranges from young stands less than 100 years-old to old-growth stands 1000 years-old or more NPS 2011 There is not enough evidence to show that fence jam formation is dependent of riparian tree age even though the Upper Reach does include more old-growth tree stands maximum diameter 1 80 meters when compared to Ipsut Creek Floodplain Figure 23 The average post diameter is 0 53 meters and 0 58 meters for the Upper Reach and Ipsut Creek Floodplain respectively Furthermore percentage of three size intervals shows majority of fence posts found in the Carbon River range between 0 20 m to 0 50 m and only 15% in the Upper Reach and 5% in the Ipsut Creek Floodplain exceeds 1 0 m Figure 24 Thus fence jams found in the Carbon River does not require old-growth stands to act as fence post for accumulation of large woody debris and local aggradation 18 Vertical bed elevation change due to sediment deposition from fence jams varies throughout the Carbon River Distribution of vertical bed elevation ranges between 0 40 meters to 1 32 meters with a median of 0 75 meters Figure 24 The ratio of key piece diameter to vertical bed elevation change is predominantly greater than 1:1 Figure 24 Out of the 16 comparative ratios 12 75% are plotted between the 1:1 and 3:1 range This suggest the amount of the sediment impoundment is in direct relationship to the size of the log jam and aggradation height is generally within 2- or 3-fold of the diameter of fence rail key member Furthermore the plotted ratio resembles tree diameter to bed elevation change plot for valley-spanning jams in the Queets River WA Figure 25 Brummer et al 2006 even though vertical bed elevations found in fence jams are relatively smaller Role of fence jams in channel avulsion For several mapped fence jams along the Carbon River I observed active or relic secondary channel created by redirection of flow into adjacent floodplains Table 2 At these locations flow is directed by running parallel along the fence rails and spills around the corners of the log jams to create secondary channel avulsions Figure 12 Through field mapping I observed that fence jams can affect channel avulsion in a two-step process: First the redirection of flow effectively localized overbank flow to the side of the jam and incise into the secondary channel while continuing to build up bed elevation of the main channel directly above the fence jam through wood accumulation and sediment impoundment This resulted in the formation of headcuts at the downstream corner of the fence jams Figure 11 creating a negative gradient from the main channel to the floodplain This cross-sectional trend is seen at WF-13 Figure 26 where the floodplain channel is incised behind and beyond the defined bank approximately 100 meters from the wetted channel at the headcut and continues to widen downstream Width of the secondary channel widened from 10 meters to 60 meters within 50 meters of downstream distance Figure 26 In other locations WF-17 WF-28 WF-26 WF-28 where two discrete fence jams are adjacent to each other orientation of the fence rails can cause flow to be concentrated in between Figure 27 At these locations headcuts can be much steeper creating a more defined secondary channel that flows into the floodplain 19 Second channel avulsion occurs when the secondary channel around the fence jams described above continues to incise into the floodplain as flood events wanes separating secondary flow from main channel flow The resulting floodplain incision thus becomes an easier pathway for secondary channel to flow into the floodplain for future flood events Theoretically there is also a higher potential for main channel avulsion though I did not observe evidence of main channel avulsion in the presence of fence jams Overall despite local armoring of floodplain directly upstream of the fence jams redirection of flows suggests fence jams in the Carbon River promote secondary channel avulsions which creates flooding hazards to the adjacent Carbon River Road Implications of flooding hazards to the Carbon River Road Flooding hazards in the Carbon River may be exacerbated by receding glaciers increasing aggradation and presence of fence jams at certain locations With the current state of climate change the Carbon River Road has the potential to experience higher frequency of flood damage Between summer of 2015 and spring of 2016 I observed the newly-formed fence jam that is the direct result of the 2015 winter flood event at WF-13 Figure 11 Timing of the fence jam at WF-13 suggests formation of these natural log jams only requires low magnitude high frequency flood events 3 5-year recurrence interval Figure 22 This suggests avulsion of secondary channel facilitated by fence jam can occur more frequent especially in the Upper Reach and Ipsut Creek Floodplain vicinity The interaction between sediment instream large woody debris and standing riparian trees may be creating a positive feedback in these areas where aggradation promotes tree mortality providing woody debris that are readily available for creating fence jams Sediment impoundments creates further increase bed elevation reducing flood conveyance and creating more frequent and larger secondary channel avulsion In the White River Entrix 2011 and Kennard et al 2011 observed floodplain channels can develop easily during low recurrence interval floods while the mainstem stays relatively stable I observed similar process in the Carbon River where secondary channels initiated at an upstream fence jam WF-28 are still actively conveying water at medium to low flow 20 Throughout the study reach many surrounding floodplains are well-below the main channel water surface which pose significant flooding hazard to the Carbon River Road Figure 28 Relative Water Surface Elevation RWSE map visualize valley bottom that is under the water surface as blue and areas above water surface as yellow and green Relative elevation in the valley bottom ranges between 7 meters below and more than 10 meters above the main channel water surface Four major locations shows a negative elevation height below water surface of more than 6 meters These areas pose potential flooding hazards to the Carbon River Road and surrounding floodplain on river-left At river-kilometer 3 2 the lower elevation on river-right coincide with the seesaw trend of cross-sectional profiles Figure 15-20 as well as the significant decrease in longitudinal gradient In addition the 2009 and 2011 channel migration into the former Carbon River Road also occurred at this meander The area immediate downstream of the low-lying area is a landform that is more than 10 meters above main channel surface river-kilometer 4 Figure 28 Historical images suggest this area was part of the active channel that was abandoned after 2003 resulting in floodplain development Secondary channel avulsion facilitated by fence jam may not be considered a hazard because the main channel is already adjacent to bedrock outcrop on river-left At river-kilometer 5 5 RWSE shows secondary channel that avulsed into the Ipsut Creek during the 2006 flood event Figure 28 This section of the Carbon River is extremely at risk for inundation during high flows because the Carbon River Road and the Ipsut Creek Campground are located on the floodplain at 5 to 6 meters below main channel water surface I observed fence jams throughout the margin that facilitates small scale avulsion into the Ipsut Creek floodplain Figure 29 21 At river-kilometer 9 3 there is another low-lying floodplain Figure 28 RWSE map shows several secondary channels that flows into Ranger Creek before returning back to the Carbon River main channel This section of the river saw several proposed flood control measures by GEOMAX in 2008 including bank barbs cross-valley dike flood dike and road humps Due to the proximity of the main channel to the Carbon River Road and valley wall erosional hazards have caused significant damages since 2006 In 2015 the Carbon River continues to erode the road away Figure 3 At river-kilometer 11 5 fence jam-facilitated channel avulsion can cause serious damage to the adjacent Carbon River Road Figure 28 RWSE shows a tributary sourcing from Falls Creek runs parallel to the Carbon River in close proximity to the Carbon River Road I observed evidence of numerous avulsed secondary channels facilitated by fence jams that are directing flow into the tributary causing further incision Figure 30 Some mitigation measures have taken place since 2006 as well including road humps and drainage culverts Entrix 2008 However with increasing aggradation and the potential for more frequent low magnitude flood events the section of the Carbon River Road may face more frequent flooding hazards from channel avulsion facilitated by fence jams 22 Classification of fence jam Field observation shows that fence jam found in the Carbon River have different physical attribute than the 10 other archetypal natural log jams identified by Abbe and Montgomery 2003 because fence jams require live standing trees as fence posts Out of the 10 types of log jams described these log jams found in the Carbon River most resembles bench jams Thus I proposed to classify the fence jam as a sub-type of bench jam Bench jam is classified as an allochthounous jam where woody debris is transported downstream through fluvial processes and deposited along the margins of the active channel Key members are wedged against irregularities in streams such as bedrock or outcrop to cause natural revetment Orientation of key member can either be oblique or parallel to the flow Accumulation of more woody debris and fine sediment creates floodplain-like feature upstream of the jam Bench jams in the Queets River occurs mostly in the headwaters where longitudinal gradient ranges between 0 06 and 0 20 Similarly fence jams involves woody debris that are transported by fluvial processes and key members can be deposited at any orientation Furthermore it occurs only on the margins of active channel where riparian forest exists and have the potential to create floodplain-like features where aggradation occur on the upstream bed-surface which armor parts of the floodplain Despite these similarities several physical characteristics and functionality still differ from the described bench jam Table 3 First bench jams do not require standing riparian trees to act as fence post Key members in fence jam key members are buttressed against standing trees and pinned by subsequent deposition of sediment and woody debris Second although fence jams observed in the Carbon River show some armoring due to aggradation directly upstream no long-term revegetation was observed Fence jams that causes floodplain development did not stay in place for more than 2 or 3 years with the exception of WF-24 This is supported by relatively young alders with a maximum height of approximately 3 meters and an average diameter of 3 centimeter Average growth rate of red alders in the Pacific Northwest is estimated at 1 8 meters year 6 feet year for highly productive sites Niemeic et al 1995 Third fence jams have the potential to redirect flow into adjacent floodplain Thus fence jam deserves its own definition that may be unique to aggrading unconfined forest rivers 23 Conclusion Interaction between instream woody debris and standing old-growth riparian forests have shown significant effects on secondary channel migration in the aggrading Carbon River These natural log jams manifest into fence-like features i e fence post and fence rail thus being named fence jams In the Carbon River a fence jam is formed when one or more key members of woody debris acting as fence rails is buttressed horizontally against one or more standing riparian trees acting as fence post Figure 12-14 This causes aggradation of coarse sediment and impoundment of additional woody debris directly upstream of the fence jams Flows are then diverted around the natural log jam causing headcuts and incisions into the adjacent floodplain At numerous locations along the Carbon River I observed avulsion pathway as wide as 60 meters facilitated by fence jams WF-13 The spatial distribution of fence jams along the Carbon River is mainly associated with the significant changes in the longitudinal gradient and cross-sectional profile between river-kilometer 2 0 and 5 0 This section of the river is the most upstream meander of the Carbon River where the main channel migrated dramatically to river-left after the 2006 flood event Future flood events of low magnitude high frequency peak flow is expected to create potential avulsion hazards to the Carbon River Road Specifically areas around riverkilometer 5 5 and 11 5 have the most potential to cause flood damage to the adjacent road due to fence jam-facilitated avulsions The product of this report serves as an initial findings of fence jams found in one Mount Rainier river Future field investigation and constrains on geomorphic characteristics can further expand the understanding of this type of natural log jam throughout other proglacial rivers Specifically due to the relatively young floodplain development caused by fence jams I hypothesized these unstable log jams may fail regularly Further study on the understanding of the mechanisms and conditions required to breach the fence jams can provide valuable information on modes of channel avulsion in the Carbon River providing further insight to flooding mitigation for the National Park Service 24 References Abbe T B Montgomery D R 2003 Patterns and geomorphic effects of wood debris accumulations in the Queets River watershed Geomorphology 51 81 107 Beason S R 2007 The environmental implications of aggradation in major braided rivers at Mount Rainier National Park Washington Thesis University of Northern Iowa Cedar Falls Iowa USA Beason S R L C Walkup and P M Kennard 2014 Aggradation of glacially-sourced braided rivers at Mount Rainier National Park Washington: Summary report for 1997-2012 Natural Resource Technical Report NPS MORA NRTR 2014 910 National Park Service Fort Collins Colorado Beyeler J D Rossi R K Kennard P M and Beason S R 2013 Extreme river response to climate-induced aggradation in a forested montane basin Carbon River Mount Rainier National Park Washington United States: American Geophysical Union Fall Meeting v 2013 p AbstractEP51C-06 Bilby W E and j W Ward 1991 Characteristics and function sf large woody debris in streams draining oldgrowth clear-cut and second-growth forests in southwestern Washington Can Fish Aq eat Sci 48: 2499-2508 Brummer C J Abbe T B Sampson J R Montgomery D R 2006 Influence of vertical channel change associated with wood accumulations on delineating channel migration zones Washington USA Geomorphology 80 295 309 Collins B D Montgomery D R Fetherston K L Abbe T B 2012 The floodplain large wood cycle hypothesis a mechanism for the physical and biotic structuring of temperate forested alluvial valleys in the North Pacific coastal ecoregion: Geomorphology v 139-140 p 460-470 doi: 10 1016 j geomorph 2011 11 011 Crandell D R 1969 Surficial geology of Mount Rainier National Park Washington U S Dept Inter Geological Survey Bull 1288 U S Govt Printing Office Washington D C p 41 Czuba J A Magirl C S Czuba C R Johnson K H Olsen T D Curran C A Kimball H K Gish C C 25 2012 Geomorphic analysis of the river response to sedimentation downstream of Mount Rainier Washington: U S Department of Interior U S Geological Survey Report 1242 Entrix Inc 2008 Topographic survey hydraulic modeling and design assessment of proposed Carbon River Road flood damage reduction measures Prepared for National Park Service Project :4194803 Entrix Inc 2010 Avulsion risk assessment Technical memorandum prepared for Sven Leon PE p 21 Fiske R S Hopson C A Waters A C 1963 Geology of Mount Rainier National Park Washington: U S Geological Survey Professional Paper 444 93 p 1 plate Gibling M R Bashforth A R Falcon-Lang H Allen J P Fielding C R 2010 Log jams and flood sediment buildup caused channel abandonment and avulsion in the Pennsylvanian of Atlantic Canada: Journal of Sedimentary Research v 80 p 268-287 doi: 10 2110 jsr 2010 024 Jones J L 2006 Side channel mapping and fish habitat suitability analysis using LiDAR topography and orthophotography: Photogrammetric Engineering and Remote Sensing November issue p 1202-1206 Kennard P M Abbe T Ericsson M Bjork J Beason S R 2011 The role of riparian forests in river avulsion and floodplain disequilibrium in aggrading pro-glacial braided rivers a newly recognized model in fluvial geomorphology: Abstracts with Programs - Geological Society of America v 43 p 164-164 Knoth E F 2015 Aggradation in the Carbon River : a case study at Mount Rainier Washington Thesis Murray State University Kentucky USA Krimmel R M 2002 Glaciers of the conterminous United States Glaciers of the western United States in Williams R S Jr and Feffigno J G eds Satellite image atlas of glaciers of the world North America: U S Geological Survey Professional Paper 1386 J p J329 J381 Legg N T Meigs A J Grant G E Kennard P 2014 Debris flow initiation in proglacial gullies on Mount Rainier Washington: Geomorphology v 226 p 249-260 26 Mount Rainier National Park Service 2011 Floodplains statement of findings: Carbon River area access management environmental assessment Neiman P J Ralph F M Wick G A Kuo Y H Wee T K Ma Z Taylor G H Dettinger M D 2008 Diagnosis of an intense atmospheric river impacting the Pacific Northwest: storm summary and offshore vertical structure observed with COSMIC satellite retrievals Mon Weather rev 136 43984420 Niemiec S S Ahrens G R Willits S Hibbs D E 1995 Research Contribution 8 Oregon State University Forest Research Laboratory Olson P 2012 Quality assurance project plan for channel migration assessments of Puget Sound SMA streams Prepared for U S EPA Region 10 Publication no 12-06-006 Washington Department of Ecology Olympia WA Riedel J M A Larrabee 2015 Mount Rainier National Park glacier mass balance monitoring annual report water year 2011: North Coast and Cascades Network Natural Resource Data Series NPS NCCN NRDS 2015 752 National Park Service Fort Collins Colorado Sisson T W Robinson J E and Swinney D D 2011 While-edifice ice volume change A D 1970 to 2007 2008 at Mount Rainier Washington Based on LiDAR surveying Geology 39 639-642 Trimble Navigation Limited 2015 Trimble R10 GNSS receiver user guide v 1 10 rev c: Trimble Navigation Limited Geospatial Division Westminster Colorado USA Waitt R B Jr Thorson R M 1983 The Cordilleran ice sheet in Washington Idaho and Montana In Porter S C editor The late Pleistocene Volume 1 of Wright H E Jr editor Late-Quaternary environments of the United States: University of Minnesota Press p 53-70 Washington Fish and Wildlife 2011 Biological Opinion for the Carbon River Access Management Plan: National Park Service Report 13410-2010-F-0488 27 Figures Legend Mount Rainier National Park MORA boundary MORA glaciers Study Site - Carbon River 0 2 5 5 10 Kilometers 1:170 000 Basemap: USDA NAIP 2013 Orthoimagery Figure 1: Site location of study area in Mount Rainier National Park Washington The Carbon River is located on the northwest corner of the park boundary 28 k ee Carbon River River km Fa lls Tributaries 11 6 9 3 8 7 4 Chenuis Falls 5 1:38 500 1 1 3 2 1 Mother Mountain 3 2 2 km Projection: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto 0 4 Ipsut Creek Campground 6 3 Carbon River Mt Rainier National Park Washington Figure 2 Extent of study site Green Lake 10 1 Chester Chiao Earth and Space Sciences University of Washington Seattle WA Ra 12 5 ek Cre nge r Cr POI k Figure 2: Extent of study location with points of interest Total length of study reach is 15 4 kilometers River-kilometer is measured from the Carbon glacier The Carbon River flows from the Carbon glacier bottom right to the park entrance top left Legend 15 4 13 3 u Ip s 14 3 ek re 29 tC June Cree Figure 3: Flood damage from the 2015 winter storm event This is located at 8 5 river-kilometer which is just downstream of Chenuis Falls Red arrow in the lower figures show same location before bottom left and after bottom right the flood event Photographs obtained from Paul Kennard 2015 30 Figure 4: Nisqually glacial retreat from 1974 to 2004 Red line indicates same position of the 1974 extent of glacier Photographs obtained from Paul Kennard Figure 5: Estimated elevation difference between 1994 and 2008 at Ipsut Creek campground cross sections The Carbon River flows from figure-right to figure-left Entrix 2008 31 Figure 6: Results from DEM differencing from 2012 and 2008 LiDAR for three sections of the Carbon River within the Park boundary Knoth 2013 32 Figure 7: Longitudinal profile of various rivers that radially drains Mount Rainier Yellow shaded area indicate studied reach modified from Czuba et al 2012 Figure 8: Orientation of log placement relative to flow based on Bilby and Ward 1991 33 Figure 9: Double arrow line show the bed-surface elevation change at a fence jam 34 B A A B Cross-sectional surface profile A A B B Figure 10: Schematic of an archetypal fence jam at various viewpoint: a Planview of fence jam showing standing riparian trees acting as fence post black circle with x keymember large WD acting as fence rails black additional stacked and loose WD gray Underlying shading shows coarse bed material dark gray to fine bed material light gray Arrow suggests avulsion pathways facilitated by the fence jam Headcut is located directly to the right of the fence jam b Upstream-view of a fence jam c Cross-sectional view of a fence jam Notice the bed-elevation change from upstream figureleft to downstream figure-right 35 Headcut Figure 11: Picture of fence jam at WF-13 where a large WD is buttressed against two variously-sized standing trees Mainstem of the Carbon is located behind PhD student Jonathan Beyeler Notice that Jon Beyeler is standing on top of the aggraded bed upstream of the fence jam which is significantly higher than elevation downstream Headcut is formed directly to the left of fence jam figure-right Figure 12: Picture of fence jam at WF-21 showing changes in bed material Red dashed line shows avulsion pathway around the fence jam 36 A WF-10 WF-11 WF-9 WF-1 Mother Mountain B Figure 17-1 Mapped wood fence in the Upper Reach Legend POI Tributaries Mapped wood fence Carbon River Carbon River Mt Rainier National Park Washington 0 0 2 1:7 500 Chester Chiao Earth and Space Sciences University of Washington Seattle WA 0 4 km Projection: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto WF-21 Ipsut Creek Campground WF-20 WF-19 WF-17 WF-16 WF-14 k WF-13 Ips u tC r ee C Figure 17-2 Mapped wood fence in the Ipsut Creek floodplain Legend POI Tributaries Mapped wood fence Carbon River Carbon River Mt Rainier National Park Washington 0 0 2 1:7 500 Chester Chiao Earth and Space Sciences University of Washington Seattle WA 0 4 km WF-27 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto Projection: NAD1983 WF-28 WF-26 WF-25 ek Chenuis Falls Cre WF-24 R an ger Cree k Fall s Figure 17-3 Mapped wood fence in the Lower Reach Mapped fence jams Legend POI Tributaries Mapped wood fence Carbon River Carbon River Mt Rainier National Park Washington Chester Chiao Earth and Space Sciences University of Washington Seattle WA 0 0 25 1:17 000 0 5 km Projection: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto Figure 13: Locations of 25 fence jam for A the Upper Reach B the Ipsut Creek floodplain and C the Lower Reach 37 38 Elevation m 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 0 11 0 12 500 600 700 800 900 1000 1100 0 0 0 0 1 0 1 0 2 0 2 0 3 0 3 0 4 0 4 0 5 0 5 0 6 0 6 0 8 0 9 0 8 0 9 0 Distance Downstream km 7 0 Slope Distance Downstream km 7 0 Elevation 10 0 10 0 11 0 11 0 12 0 12 0 13 0 13 0 14 0 14 0 15 0 15 0 16 0 16 0 Figure 14: Longitudinal profile of the Carbon River from the Carbon glacier figure-left to the Park entrance figure-right Average slope is sampled at 500-meter intervals River bed slope m m rk 1 6 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 900 Distance m Figure 15: Cross-sectional profile sampled at river-kilometer 1 6 Orange arrow approximates position of thalweg rk 2 1 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 900 Distance m Figure 16: Cross-sectional profile sampled at river-kilometer 2 1 Orange arrow approximates position of thalweg rk 2 5 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 Distance m Figure 17: Cross-sectional profile sampled at river-kilometer 12 5 Orange arrow approximates position of thalweg 39 900 rk 3 2 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 900 Distance m Figure 18: Cross-sectional profile sampled at river-kilometer 3 2 Orange arrow approximates position of thalweg rk 4 0 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 900 Distance m Figure 19: Cross-sectional profile sampled at river-kilometer 4 0 Orange arrow approximates position of thalweg rk 4 3 1050 Elevation m 1000 950 900 850 800 750 0 100 200 300 400 500 600 700 800 900 Distance m Figure 20: Cross-sectional profile sampled at river-kilometer 4 3 Orange arrow approximates position of thalweg 40 6 3 5 Ips ut C ree k Ipsut Creek Campground 4 3 2 Mother Mountain 2 1 Legend Tributaries Historical Main Stems Year 2015 Carbon River Road 2013 River-kilometer 2011 Fence jam zone 2009 2006 Figure 21 Historical migration of main channel and fence jam zones in the Upper Reach and Ipsut Creek Floodplain Carbon River Mount Rainier National Park WA Chester Chiao Earth and Space Sciences University of Washington Seattle WA 0 0 25 1:17 000 0 5 km Projection: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto Figure 21: Mainstem migration from 2006 to 2015 Map showing areas around river-kilometer 3 which is located at the upstream meander of the Carbon River 41 USGS 12094000 CARBON RIVER NEAR FAIRFAX WA 2 100000 10 20 50 100 10 5 2 1 500 80000 60000 50000 40000 30000 flow cfs 20000 10000 8000 6000 5000 4000 3000 2000 1000 99 99 99 8 7 090 99 98 95 90 80 70 60 50 40 30 exceedance probability 20 5 2 1 05 01 plot position: Weibull recurrence interval 100 probability Figure 22: Annual maximum series determined using Log Pearson III distribution Dashed line shows 2015 winter flood event that created the fence jam at WF-13 42 70% 60% 50% 40% Upper Floodplain 30% Ipsut Floodplain Lower Floodplain 20% 10% 0% 0 05-0 20 0 20-0 50 0 50-1 0 1 0-2 0 Diameter intervals Figure 23: Normalized percentage of standing tree diameter at breast height DBH for the three sections of the River A 1 5 B 1 5 1 4 1 4 1 3 1 2 1 2 1 1 1 1 1 0 9 0 8 0 7 0 6 0 5 Difference in bed elev m Difference in bed elevation m 1 3 1 0 9 0 8 0 7 0 6 0 5 0 4 0 4 0 3 0 3 0 2 0 2 0 1 0 1 0 0 Mother Moutain Ipsut Creek CG and downstream 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 1 1 1 2 1 3 1 4 1 5 Rail keypiece diameter m Figure 24: a Distribution of vertical bed-surface elevation change throughout all of the mapped fence jam b Ratio of keymember WD fence rail diameter to the difference in bed elevation 43 Figure 25: A Distribution of vertical bed-surface elevation change for valley-spanning log jams on the Queets River Washington Brummer et al 2006 B Ratio of keymember WD fence rail diameter to the difference in bed elevation Elevation relative to wetted channel cm 150 Headcut of avulsed channel 50 -50 -150 -250 Distance from control point on m Elevation relative to wetted channl cm 0 150 20 40 60 80 100 120 140 160 avulsed channel widens 50 -50 -150 -250 Distance from control point m Figure 26: Cross sections measured at WF-13 a Cross section taken from valley wall figure-left to wetted channel figure-right b cross section taken 100 meter downstream from a 44 180 Figure 27: Two distinct fence jams red and blue Flow directed in between yellow at WF-20 45 meters -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9 - 10 10 RWSE 12 5 Fa Legend k ee 11 6 9 3 8 7 4 6 3 5 0 4 3 2 1:30 000 0 75 1 5 km 2 1 Projection: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto Chester Chiao Earth and Space Sciences University of Washington Seattle WA Carbon River Mount Rainier National Park WA Figure 28: Relative Water Surface Elevation RWSE map 10 1 Figure 28: Relative height of water surface elevation map of the study reach 2011 main channel Carbon River Trail River-kilometer Fence jam zone Cr lls 13 3 k ree Ra nge rC Ip k ee Cr su t 46 7 4 6 3 5 4 3 2 Figure 29: Potential avulsion pathway red arrow of secondary channel at Ipsute Creek Campground 2 1 13 3 12 5 11 6 elative Water Surface Elevation RWSE map River Mount Rainier National Park WA 0 h and Space Sciences University of Washington Seattle WA 10 1 0 75 1:30 000 1 5 km 9 3 tion: NAD1983 UTM Zone 10N meters Basemaps: 2012 1 meter LiDAR DEM hillshade USDA NAIP 2011 orthophoto Legend RWSE meters Figure 30: Potential avulsion pathway red arrow at Lower Reach ee Cr ls al 9 - 10 k 10 47 Tables Table 1: Summary of GIS data acquired for this project Data Type LiDAR DEM LiDAR DEM NAIP Orthoimagery NAIP Orthoimagery NAIP Orthoimagery NAIP Orthoimagery Year Publication Date 2008 n a 2012 n a 2006 10 15 2009 10 15 2011 10 5 11 11 2015 Agency NPS NPS USDA USDA USDA USDA Resolution 1-meter 1-meter Table 2: List of fence jam with coordinate system that shows evidence of channel avulsion ID WF-9 WF-11 WF-13 WF-17 WF-20 WF-21 WF-26 WF-28 Latitude Longitude 46 962951 -121 800385 46 963057 -121 803256 46 967869 -121 819176 46 970614 -121 824550 46 972333 -121 826522 -121 827252 46 974144 46 995500 -121 855917 46 995556 -121 881944 Flooding hazard to Carbon River Road No No Yes Yes Yes Yes Yes Yes Table 3: Comparison of bench jam observed in the Queets River Abbe and Montgomery 2003 and fence jam observed in the Carbon River Types Bench jam Channel gradients 0 06-0 20 Fence jam 0 02-0 1 Distinguish characteristics Key members wedged along channel margin forms bench-like surface Can support forested floodplain development Key members buttressed against standing riparian trees to create bench-like surface Relatively unstable 48 Source Abbe and Montgomery 2003 This study Appendices 49 Appendix A: Data collected for fence jams surveys in the Carbon River ID WF-1 Zone 1 Fence Post Fence Post Fence Post Fence Rail Fence Rail Count Circumference Diameter Count Diameter Extent 0 34 Discrete 2 1 3 4 0 1 0 87 Placenment Orientation B Vertical bedsurface elevation change Post Spacing Notes 0 83 WF-2 WF-3 1 3 1 7 3 9 2 5 1 5 0 6 1 2 0 8 0 5 1 6 0 5 Discrete 0 42 Discrete 0 12 0 29 0 28 0 43 C C 0 63 1 2 WF-4 1 1 3 0 4 1 0 24 Discrete C 0 77 WF-5 2 1 3 0 5 0 4 0 2 1 0 41 Discrete B 0 78 WF-6 8 3 5 1 1 10 Continuous C 0 84 Continuous A B C WF-7 not sampled 2 WF-8 11 14 WF-9 5 20 WF-10 2 1 4 2 7 0 4 0 9 3 0 52 Discrete WF-11 3 0 8 0 6 2 0 0 3 0 2 0 6 20 1 2 Discrete WF-12 20 0 76 0 73 0 42 0 86 0 242 0 232 0 134 0 274 3 0 77 B 0 72 measurement taken for one main fence post Active lots of debris Continuous B C 0 34 Continuous A 0 58 0 27 1 32 6 2 2 5 6 1 4 4 3 3 7 2 3 0 7 1 8 0 4 1 4 1 2 0 7 20 WF-14 2 3 5 1 5 1 1 0 5 1 0 5 Continuous B-1 0 4 WF-15 2 2 6 1 4 0 8 0 5 1 0 37 Continuous B-1 0 6 WF-16 3 1 21 1 46 2 80 0 39 0 46 0 89 3 WF-17 6 0 82 0 99 0 80 0 85 0 26 0 32 0 25 0 27 WF-18 4 0 65 1 00 0 80 0 21 0 32 0 25 3 0 3 Discrete 0 55 C WF-19 2 0 35 1 20 0 11 0 38 1 0 35 Discrete B-2 WF-20 4 1 17 1 15 0 90 1 50 0 37 0 37 0 29 0 48 WF-21 3 1 65 1 65 0 95 0 53 0 53 0 30 WF-22 2 1 15 0 98 WF-24 2 WF-25 WF-26 6 7 A C WF-13 4 5 20 Continuous A 3 15 1 15 6 9 Continuous C 0 78 3 4 lots of debris Continuous C 0 85 2 2 unmeasurable degrated wood 2 3 3 2 0 7 1 8 lots of debris 1 2 1 0 82 3 2 lots of debris Continuous C 0 76 1 9 no identifiable key member lots of debris 3 7 7 2 1 15 Continuous A 1 2 1 2 9 4 2 8 0 37 0 31 2 0 25 Continuous C 0 69 0 95 1 30 2 28 0 41 0 73 1 0 52 Discrete B2 0 72 3 55 2 1 75 1 67 0 56 0 53 1 0 26 Discrete B2 0 54 1 46 3 0 26 1 78 1 38 0 08 0 57 0 44 A 1 5 8 Discrete 50 Appendix B: Known GPS coordinates of fence jams Name WF-1 WF-9 WF-10 WF-11 WF-13 WF-14 WF-16 WF-17 WF-19 WF-20 WF-21 WF-26 WF-24 WF-27 WF-28 Latitude Longitude 46 963003 -121 799378 46 962951 -121 800385 46 963099 -121 801624 46 963057 -121 803256 46 967869 -121 819176 46 969475 -121 822861 46 969694 -121 823018 46 970614 -121 824550 46 971544 -121 825680 46 972333 -121 826522 46 974144 -121 827252 46 995500 -121 855917 46 988867 -121 842567 46 997217 -121 864383 46 995556 -121 881944 51
    • DeWitt, Chelsey - M.S. Research Paper
      Geomorphic Impacts of the 2013 Colorado Front Range Flood on Black Canyon Creek and North Fork Big Thompson River 2016, DeWitt,Chelsey,Chelsey DeWitt Geomorphic Impacts of the 2013 Colorado Front Range Flood on Black Canyon Creek and North Fork Big Thompson River Chelsey DeWitt A report prepared in partial fulfillment of the requirements for the degree of Master of Science Earth and Space Sciences: Applied Geoscience University of Washington March 9th 2016 Project mentor: Sandra Ryan United States Forest Service Internship coordinator: Kathy Troost Reading committee: Brian Collins Steven Walters MESSAGe Technical Report Number: 032 Executive Summary In September 2013 the Colorado Front Range experienced a five-day storm that brought record-breaking precipitation to the region As a consequence many Front Range streams experienced flooding leading to erosion debris flows bank failures and channel incision I compare the effects that debris flows and flooding have on the channel bar frequency frequency and location of wood accumulation and on the shape and size of the channel along two flood impacted reaches located near Estes Park and Glen Haven Colorado within the RMNP and the ARNF: Black Canyon Creek BCC and North Fork Big Thompson River NFBT The primary difference between the two study areas is that BCC was inundated by multiple debris flows whereas NFBT only experienced flooding Fieldwork consisted of recording location and size of large wood and channel bars and surveying reaches to produce cross-sections Additional observations were made on bank failures in NFBT and the presence of boulders in channel bars in BCC to determine sediment source The debris flow acted to scour and incise BCC causing long-term alteration The post-flood channel cross-sectional area is as much as 7 to 23 times larger than the pre-flood channel caused by the erosion of the channel bed to bedrock and the elimination of riparian vegetation Large wood was forced out of the stream channel and deposited outside of the bankfull channel Flooding in NFBT caused bank erosion and widening that contributed sediment to channel bars but accomplished little stream-bed scour As a result there was relatively little damage to mid-channel and riparian vegetation and most large wood remained within the wetted channel ii Contents Statement of the Problem 1 Study Area 2 Black Canyon Creek BCC setting 2 North Fork Big Thompson NFBT setting 3 Peak flow estimates for BCC and NFBT 4 Study Background 5 Previous studies of the 2013 Colorado Front Range Flood 5 Debris flow and flood effects on river channels wood and sediment 5 Scope of Work 7 Methods 8 Characterizing position and extent of large wood 8 Characterizing channel bar deposition 9 Describing channel geometry and slope data for BCC and NFBT 9 Results 10 Large wood accumulation and deposition 10 Large clasts accumulation and deposition 11 Channel morphology 11 Discussion 13 Debris flow and flood effects on wood and sediment accumulation 13 Debris flow and flood effects on channel morphology 14 Future studies 14 Conclusion 15 References 16 APPENDIX A: Survey data information 39 APPENDIX B: Channel Cross-Sections 41 iii List of Figures Figure 1 Watershed Location Map 19 Figure 2 Longitudinal profile of BCC and NFBT study area 20 Figure 3 Images of Black Canyon Creek 21 Figure 4 Debris flow and river confluence images for Black Canyon Creek 22 Figure 5 Scour images for Black Canyon Creek 23 Figure 6 Before and after flood image at North Fork Big Thompson 24 Figure 7 Black Canyon Creek Study Area 25 Figure 8 North Fork Big Thompson River Study Area 26 Figure 9 Large Wood Jam Field Data Sheet 27 Figure 10 Criteria for channel zone identification of LW deposition 28 Figure 11 Debris line examples in Black Canyon Creek along the right bank 29 Figure 12 Large wood deposition by zone for BCC and NFBT 30 Figure 13 Large wood jams along Black Canyon Creek 31 Figure 14 Large wood jams along North Fork Big Thompson 32 Figure 15 Width-to-depth ratio normailized by drainage area for BCC and NFBT 33 Figure 16 Cross-sectional area normalized by drainage area for BCC and NFBT 34 List of Tables Table 1 Reach lengths and number of cross-sections per reach in BCC and NFBT 35 Table 2 Frequency of LW per 100 meters in each reach in BCC and NFBT 35 Table 3 Frequency of channel bars per 100 meters in each reach in BCC and NFBT 36 Table 4 Pebble count results for BCC 37 Table 5 Drainage area and dimensions at each cross-section along BCC and NFBT 38 iv Acknowledgements I would like to thank Dr Sandra Ryan and the United States Forest Service for the opportunity to assist in the foundational work of the Geomorphic Impacts of the Northern Colorado Flood of 2013 on Black Canyon Creek and North Fork Big Thompson River I value the skills and problem solving strategies learned during this internship I would also like to thank Aaron Blair my fellow GeoCorps intern for obtaining and constructing our field sites post-flood LiDAR and for his time and tutorials on ArcGIS and GPS Pathfinder Office v Statement of the Problem In September 2013 the Colorado Front Range experienced a five day storm event that dropped a record-breaking cumulative rainfall of 20-45 centimeters Anderson et al 2015 September is usually much drier with average total precipitation of about 4 centimeters Scott 2013 The storm lasted from September 9th through September 15th falling most intensely between September 11th and September 13th This storm caused landslides debris flows bank failures and channel incision Gartner et al 2015 Gorchis et al 2015 noted property damage and infrastructure along the length of the Front Range including areas within the Rocky Mountain National Park RMNP and the Arapaho-Roosevelt National Forest ARNF I compare the effects that debris flows and flooding have on the channel bar frequency frequency and location of wood accumulation and on the shape and size of the channel along two flood impacted reaches located near Estes Park and Glen Haven Colorado within the RMNP and the ARNF: Black Canyon Creek BCC and North Fork Big Thompson River NFBT Figure 1 The primary difference between the two study areas is that BCC was inundated by multiple debris flows whereas NFBT only experienced flooding In the past 60 years fifteen other rain events have occurred that exceeded the total annual precipitation for the region NCAR 2007 The most deadly flood occurred in the summer of 1976 just downstream of Estes Park Colorado In 4 hours 12 inches of rain fell in Big Thompson Canyon a seventy square mile area The rain entered the Big Thompson River and was channelized by the canyon creating a flash flood that claimed 144 lives National Park Service 2014 Colorado s flood history calls to the importance in understanding the in-stream impacts of flooding and debris flows and the potential dangers these impacts pose for us Thus improved 1 understanding of landscape response to increased precipitation and subsequent landslides and debris flows is essential for the improvement of future resiliency of flood prone areas Study Area Both field sites are within the boundaries of RMNP and ARNP with rivers flowing southwest from the Mummy Range The areas studied in BCC and NFBT are both largely free of infrastructure with a few exceptions including a children s summer campground along NFBT a water treatment plant in BCC and a few cabins and various hiking trails within both study areas Vulnerable infrastructure including private residences a ranch and roads are located downstream of both reaches The town of Estes Park lies in the lower part of BCC s watershed and the town of Glen Haven lies below the NFBT watershed Black Canyon Creek BCC setting The 22 5 km2 BCC basin originates from Mummy Ridge between Mummy Mountain and Hagues Peak BCC flows into Fall River and drains into Big Thompson River in Estes Park Colorado The study reach is 2 2 river kilometers long and the elevation ranges from 2511 meters at the most upstream reach Reach 1 to 2398 meters at the most downstream reach Reach 5 Figure 2 The study reaches range from 78 to 177 meters long Slope values vary throughout the study area from shallower more uniform segments to sharp slope breaks seen at small bedrock cliff waterfalls The slope at Reach 1 just downstream of where the debris flow enters BCC is 0 02 Table 1 The average slope increases to 0 04 and then 0 06 moving downstream as bedrock and waterfalls are expressed Reach 5 has the shallowest slope of 0 01 Figure 2 The study area makes up about 10% of the entire stream which is 20 2 river kilometers long Before the flood and subsequent debris flow BCC had a diverse riparian zone of grasses shrubs aspen Populus tremuloides ponderosa pine Pinus ponderosa and lodgepole pine 2 Pinus contorta Figure 3 The upper portion the first 11 5 kilometers shows little flood impact lacking evidence of bank failures and lateral erosion on 2001 Google Earth imagery The middle portion of the watershed was inundated in 2013 by a total of three debris flows Ryan 2015 Figure 2 The longest and more destructive debris flow Debris Flow 1 appears to originate from a colluvium hollow failure along MacGregor Mountain and travelled 1 8 kilometers before reaching the main stem of BCC from the right bank Deposition at the confluence of the debris flow and BCC includes a mixture of wood debris and boulders as well as adjacent scour Figure 4 The channel portion just below the debris flow appears to be scoured up to 10 meters Ryan 2015 Scour and deposition continues throughout the entire study area Figure 5 North Fork Big Thompson NFBT setting NFBT basin is about 46 km2 above Glen Haven Colorado Soule 1976 It originates between Rowe Peak and Hagues Peak and flows in a general southeast direction Clausen 2012 The study area is composed of 5 4 river kilometers and has an elevation change from 2475 meters at the most upstream segment to 2312 meters at the most downstream segment Figure 2 The study reaches range from 55 to 251 meters long The slope at Reach 1 is 0 01 Table 2 Most of the study area has a similar slope throughout but at Reach 5 the slope increases to 0 04 due to valley narrowing caused by adjacent bedrock hillslopes Figure 2 Overall the study area in BCC has a steeper slope than the NFBT study area The study area makes up about 8% of the entire stream which is 38 river kilometers long Channel widening and re-working of floodplains is not readily apparent in the headwaters of the NFBT on 2011 Google Earth imagery until about two-thirds of the way downbasin and about two kilometers upstream of the study area Ryan 2015 The more readily-apparent disturbance begins at approximately the lower end of the glacial drift area suggesting a geologic control on 3 channel response here Ryan 2015 Landsliding is not prevalent on the 2011 Google Earth imagery along this reach but there are noticeable bank failures from channel widening and loss of riparian forest along the lower portion Figure 6 Peak flow estimates for BCC and NFBT Using peak flow data obtained from the U S Geological Survey USGS and the Natural Resources Conservation Service NRCS Yochum and Moore 2013 estimated peak flow discharges for over a dozen rivers impacted by the 2013 Front Range Flood They applied the critical depth method using a single cross-section implementing high water marks at each location and replicating flow estimates for several adjacent cross-sections to confirm consistency in the estimations High-intensity rain events in mountainous topography commonly occur at elevations below 2300 meters in the Colorado Front Range However high discharges were computed at some locations with higher elevations like Estes Park and Glen Haven areas both within my study areas Yochum and Moore 2013 Yochum and Moore 2013 did not estimate peak flow discharge for BCC but they did estimate peak flow discharge for Fox Creek which is located three kilometers north of BCC and has a similar catchment area of 18 6 kilometers squared Flow data were taken at three adjacent locations in Fox Creek with an average peak flow of 99 cubic meters per second cms Yochum and Moore 2013 Using Fox Creek as a reference for discharge the estimated minimum peak discharge in BCC was 119 cms an estimated 38 times the bankfull discharge Ryan 2015 estimated pre-flood bankfull discharge to be 2 5 cms The NFBT basin received about ten times its monthly precipitation during the 2013 storm Average September precipitation for Glen Haven Colorado is 4 centimeters but 43 centimeters fell in September 2013 WeatherDB 2015 Yochum and Moore 2013 measured discharges at 4 three adjacent section on the NFBT upstream of Glen Haven Colorado with an average peak flow of 48 cms an estimated 11 times greater than bankfull discharge Ryan 2015 estimated pre-flood bankfull discharge to be 4 5 cms Study Background Previous studies of the 2013 Colorado Front Range Flood The landscape response to the 2013 flood was so unique in that in an otherwise inactive landscape over 1 100 landslides and debris flows occurred along the Front Range Anderson et al 2015 Anderson et al 2015 concluded debris flows dominate sediment transport and channel erosion for canyons along the Front Range and that the total amount of sediment removed by these landslides and debris flows is equivalent to hundreds to thousands of years of sediment accumulation Another study characterizing debris flows after the 2013 storm was by Coe et al 2014 The debris flows initiated in response to high precipitation and all recorded slides began as colluvial soil failures that liquefied and moved rapidly downslope Coe et al 2014 Their inventory reveals that seventy-eight percent of the failures initiated on south-facing slopes thirty-eight percent of the headscarps occurred within Proterozoic Granite and ninety-seven percent of the failures occurred in open slopes and swales Similar conditions are seen along the failure location of Debris Flow 1 in BCC Debris flow and flood effects on river channels wood and sediment Debris flows are infrequent compared to other natural disasters such as flooding but cause significant long-term effects on stream channel morphology Eaton et al 2003 In forested mountain drainage basins debris flows scour steep headwater channels Montgomery et al 2003 as the BCC study area The erosive force of a debris flow scours sediment and wood out of 5 stream channels and mobilizes and deposits large clasts within the channels promoting a cycle between channel degradation and channel aggradation Benda 1990 Channel degradation results in mixed bedrock and boulder bed morphology and channel aggradation resulting in a gravel bed morphology Benda 1990 Debris flow deposition has also been characterized by the deposition of isolated boulder and tree levees Cenderelli and Kite 1998 In addition to tree levees wood also accumulates as log jams Montgomery et al 2003 Abbe 2000 found that no debris flow formed jams were found in channels with log jam frequencies of greater than 20 jams per kilometer This indicates that debris flow formed log jams are less frequent within a stream channel than log jams formed by other processes Flooding acts to widen stream channels and promotes bank erosion Channel widening is the most common geomorphic response to floods Magilligan et al 2015 Channels widen in response to increases in channel conveyance Magilligan et al 2015 Banks that are saturated and high flow velocities that are adjacent to banks contribute to channel widening Magilligan et al 2015 Another reoccurring impact is the entrainment and transport of extremely coarse clasts including the deposition of gravel bars Floods in the Big Thompson River in Colorado promote both deposition of coarse sediments in the stream channel as well as coarse and fine sediment along the floodplain Jarrett 1990 Unlike debris flows previous studies on flooding do not report substantial amounts of scour to stream channels Sediment and debris are transported and deposited within the stream by accumulating along stream banks and in-stream vegetation Jarrett 1990 6 Scope of Work In cooperation with Dr Sandra Ryan a research geomorphologist for the Rocky Mountain Research Station within the USFS I surveyed current conditions of two flood-impacted streams BCC and NFBT and assisted in establishing reference areas for monitoring natural recovery following large-scale widespread floods To ensure the field portion of this project was completed within the summer months five reaches within each study area were chosen to map in more detail rather than mapping each study area in its entirety These reaches were chosen with the guidance of Dr Ryan based on how well they characterized the overall flood impacts seen throughout the study area Selected reaches were either characterized generally which consisted of documenting channel bar extent and LW position and extent or characterized in greater detail with the addition of multiple cross-section surveys Five reaches along the BCC and NFBT are a combination of general and more detailed characterization Figure 7 Figure 8 In addition to the five reaches in BCC a cross section was taken along the river above the debris flow confluence and is referred to as the reference cross-section in this study Figure 7 After further reconnaissance upstream in the reference reach I concluded that the single cross-section surveyed is representative of the reach walked To compare the consequences from flooding and debris flows I compared the spatial patterns of sediment and wood accumulation in the two streams I also compared the erosional effects of flooding and debris flows by comparing the post-flood channel widths and areas in the two streams Based on previous studies I expect BCC to show evidence of channel bed scour and incision boulder deposition and wood debris accumulation along channel banks In NFBT I 7 expect to see channel widening and the accumulation of wood and sediment deposition mostly instream Methods I combined field observations and field collected global positioning system GPS coordinates with GIS analyses to characterize and count the wood and sediment accumulation along both streams Before going in the field I used aerial photographs from Google Earth dated October 2013 at a 0 6 meter resolution and aerial LiDAR flown October 2013 at a resolution of 0 75 meters USGS 2015 of each stream to compare and locate erosional features such as bank failures and lateral widening scars The areas identified in the desk review were verified through field visits to determine Reaches 1-5 Fieldwork consisted of characterizing the position and extent of LW channel bars and channel geometry using TerraSync on a Trimble GeoXH unit Data points collected with the GPS unit were processed and corrected to improve the accuracy of the field data georeferenced and transferred into ArcMap Characterizing position and extent of large wood Adapting the work of Montgomery 2008 and Schuett-Hames et al 1999 for surveying LW I produced a field data sheet to characterize LW jams Figure 9 For LW jams estimates of jam dimensions height width and length were recorded by visual approximation or using a TerraSync on a Trimble GeoXH unit Four zones were used to characterize LW jam deposition locations Figure 10 The jam key piece if present size and position within the jam were noted In addition evidence of bank scour or imbedded sediment were also recorded After fieldwork was complete I used ArcGIS to digitize line segments connecting the points to trace LW jam boundaries and produce polygons I compiled the data for depositional location and the number of LW jams in each of the five reaches along both streams 8 Much of the deposited wood in BCC collected as one elongated mass of debris parallel to the stream referred to here as a debris line and is seen throughout the upper half of the study area Figure 11 Because I did not consider debris lines to be jams I did not include them in my data collection Characterizing channel bar deposition To see the channel bar frequency per 100 meters I counted the number of channel bars in each of the five reaches along both streams using GPS and ArcGIS To highlight boulder deposition along BCC a pebble count was conducted for channel bars within Reaches 1-5 using a gravelometer and measuring tape A pebble count was performed along the upstream middle and downstream section of the bar Grain size data was collected in NFBT using a digital grain size method This method proved to be ineffective in measuring cobble to boulder size grains and is not presented in this study Describing channel geometry and slope data for BCC and NFBT I surveyed eleven cross-sections along BCC and seven cross-section along NFBT From each cross-section bankfull width and average depth are measured Bankfull was identified as the point in which the gradually sloping floodplain changes to an abrupt bank edge In some cases this criteria was only visible along one bank due to the other bank being eroded In these cases bankfull estimations were made at the height where bare alluvium and vegetation met Bankfull width and average depth were used to obtain width-to-depth ratios and cross-sectional areas which were then normalized to the respective drainage area Lastly I used ArcGIS to obtain the average river bed slope for each reach In addition I used a level and stadia rod to produce channel cross-sections along selected reaches Locations were chosen by Dr Ryan that characterized the spatial variation of the channel and flood deposits in that reach 9 Drainage area was calculated using ArcGIS I used a 10-meter DEM of Colorado to approximate the flow network based solely on topography From this network I extracted points at each cross-section and stream line intersection I then used these as pour points to derive estimated drainage area contributing to flow at each cross-section I calculated mean channel bed slope estimates for each reach using ArcGIS Figure 2 The slope raster was made from the 10-meter Colorado DEM Longitudinal profiles are produced based on the blue stream line in Figure 7 and Figure 8 The profile for BCC starts at the debris flow and stream confluence to the most southern extent of the watershed a total of 3005 river meters The profile for NFBT starts at Reach 1 and ends just downstream of Reach 5 a total of 4500 river meters Results Large wood accumulation and deposition Large wood in BCC was predominantly deposited outside of the bankfull channel Zone 4 whereas in NFBT large wood accumulated within the wetted channel Zone 1 Figure 12 All LW jams in BCC are recorded outside of the bankfull channel except one located within the bankfull channel Zone 2 Zone 4 jams accumulated behind alive and upright trees on the adjacent upland zones terraces and eroded riparian zone Figure 13 Half of the LW jams recorded in NFBT are located within the wetted channel Zone 1 The remaining LW jams in NFBT are found within the bankfull channel Zone 2 directly above Zone 3 and outside the bankfull channel Zone 4 In NFBT wood located in the wetted channel accumulated behind stable upright trees on mid-channel bars or trail bridges Figure 14 Some jams were comprised of a mixture of trail bridge infrastructure and transported wood 10 Comparing the wood in each reach BCC has more LW jams per 100 meters than NFBT The frequency of LW jams per 100 meters in BCC ranged from 0 08 to 3 0 Table 2 In NFBT the frequency ranged from 1 1 to 3 1 On average BCC has 1 3 times the amount of LW jams per 100 meters than NFBT Results from both study areas show an increase in LW jam deposition moving downstream Large clasts accumulation and deposition Comparing the channel bars in each reach NFBT has more channel bars per 100 meters than BCC Table3 Average channel bar frequency for NFBT was 1 5 per 100 meters and 1 1 for BCC The frequency of channel bars per 100 meters in NFBT ranged from 0 06 to 2 2 Table 3 In BCC the frequency ranged from 0 05 to 2 4 Along NFBT many channel bars accumulate along the opposite bank of bank failures Coarse grained sediment and boulder size clasts are recorded throughout the channel bars in BCC Table 4 In Reach 1 the channel bar surface was mostly fine to medium gravel 5-11 millimeters From Reaches 2 4 and 5 the dominant sediment size observed was very coarse gravel 45-65 millimeters Small cobbles 64-128 millimeters are the dominant grain size in Reach 3 The largest clasts recorded are in Reach 5 with deposition of small to large boulders one measured almost 2 meters in height Channel morphology BCC has a greater mean and wider range in width-to depth ratio normalized by drainage area Figure 15 The mean value is almost double in BCC than in NFBT at 0 9 versus 0 5 and the data set for BCC ranges from 0 3 to 1 8 and from 0 3 to 0 9 in NFBT These results are connected to the variance in channel cross-section widths as cross-section depth were a similar value throughout the study area In BCC two cross-sectional widths in Reach 5 are much greater than 11 the rest of the study area at widths of 32 times greater than the corresponding depths Table 5 The average cross-sectional width is only 12 times greater than the corresponding depth in BCC Standard deviation for BCC is 0 5 and 0 3 for NFBT two-sample t-test p 0 04 The normalized cross-sectional area mean and range in data is greater in BCC than NFBT Figure 16 On average the normalized cross-sectional area for BCC was 2 5 times greater than values for NFBT at 0 5 versus 0 2 and the data set for BCC ranges from 0 2 to 1 5 and from 0 1 to 0 3 in NFBT Most of the values for normalized cross-sectional area in BCC concentrate around 0 4 but is greatest at the debris flow and stream confluence with a value of 1 5 Table 5 The crosssectional area at the confluence was approximately three times greater than the areas at the other cross-sections Standard deviation for BCC is 0 4 and 0 1 for NFBT two-sample t-test p 0 01 Comparing the single reference cross-section in BCC surveyed upstream of the debris flow to the cross-sections in the debris flow reach suggests that the debris flow widened the downstream reach by 4 to 11 times the pre-debris flow condition The reference cross-section was 1 3 meters wide by 0 9 meters deep with a cross-sectional area of 1 1 square meters The average width for the entire study area from Reach 1 to Reach 5 was approximately 10 7 meters the average depth was similar to the study area at 0 8 meters with cross-section areas averaging around seven square meters but was as high as 23 square meters at the debris flow confluence Table 5 12 Discussion Debris flow and flood effects on wood and sediment accumulation Past research shows that debris flows scour sediment and debris from a channel Results of this study are consistent with this expectation in that in BCC 1 all large wood jams that could accumulate did so outside of bankfull channel and 2 by the overall lower frequency of channel bars per 100 meters compared to NFBT Throughout the upstream half of the study area wood accumulated as levees or what I called a debris line As wood is recruited from the debris flow source and the riparian zone it is pushed towards the front and sides of the flow Johnson et al 2012 The upstream portion can be summarized by a steeper slope with wood levees lining the adjacent hillslope and a low amount of LW jam deposition This portion of the study area is inferred to be the transport driven portion of the debris flow rather than the depositional zone of the debris flow As the slope in BCC becomes shallower downstream wood and large clasts are deposited and accumulate as jams and isolated boulders Wood debris was eroded by the debris flow from the adjacent hillslopes and vegetated riparian zones The wood debris was transported along BCC and contributes to the high frequency in LW jams per 100 meters The floodwaters of the NFBT were less erosive than the debris flow in BCC Instead of sediment and wood being scoured from the channel deposition happened along and within the stream channel Observation at NFBT support this by 1 half of the LW jams accumulated within the wetted channel 2 the higher frequency in channel bars per 100 meters and 3 lower frequency of LW jams per 100 meters I speculate that the lower average frequency of LW jams per 100 meters can be attributed to less scour and incision of the river bed and less erosion of the riparian zone By NFBT not being entrenched the flow had more opportunities to overtop banks 13 and deposit wood Similarly by the preservation of some streamside vegetation wood snag opportunities existed for wood accumulation within the bankfull channel Debris flow and flood effects on channel morphology Debris flow and flooding differently scoured and reshaped the two stream channels With a larger watershed area we expect and observe NFBT to have greater cross-section dimensions than BCC due to the accommodation of a greater influx of water but normalized cross-section dimensions are larger in BCC than NFBT because of the effects the debris flow had on BCC This is also the case for normalized width-to-depth ratios again due to the effects the debris flow had on BCC For both the normalized width-to-depth ratio and the normalized cross-sectional area plots BCC had a larger distribution and overall greater average than NFBT This is due the scouring of the stream bed and lateral erosion of the stream banks by the debris flow in BCC Using photos and cross-sectional data from the reference cross-section for BCC as a proxy for pre-debris flow conditions the extent to which the debris flow impacted the downstream reach is substantial The debris flow acted to remove streamside vegetation and entrench the stream If the data from the reference cross-section is similar to pre-debris flow cross-sections downstream the debris flow did a considerable amount of incision and lateral erosion The change is so great from pre to post-debris flow conditions that the channel impacts are likely to be more long-term Future studies The study of geomorphic impacts of BCC and NFBT could be furthered by conducting a complete inventory on large wood accumulation and grain size distribution from the headwaters to the floodplain This inventory would provide a detailed report on the spatial distribution of degradation and aggradation produced during these two events In addition an interesting 14 investigation would be to use the large clasts and levee positions to estimate height velocity and stream competency of the debris flow and flooding This information could be used with flood reoccurrence intervals to predict when the recently deposited boulders might be reworked again By doing studies such as these a better understanding of the short and longterm effects to which these two channels have been altered can be obtained Conclusion This study compared the effects that debris flows and flooding have on the channel bar frequency frequency and location of wood accumulation and on the shape and size of the channel along BCC and NFBT The channel entrenchment and widening has left BCC unrecognizable compared to pre-flood stream conditions All wood has been pushed out of the channel and deposited as levees and jams outside of bankfull channel The debris flow widened and incised BCC Current channel conditions of BCC are up to 11 times the original width with cross-sectional areas 7 to 23 times larger than pre-flood dimensions Many portions of the stream are scoured to bedrock Compared to NFBT BCC is occupied by fewer channel bars made up of large clasts and in-stream and streamside wood and vegetation have been ripped away Flooding in NFBT caused bank erosion and widening that fed numerous channel bars but did little scour the stream bed This preserved mid-channel and riparian vegetation allowing wood to accumulate within the stream 15 References Anderson S Anderson S and Anderson R 2015 Exhumation by debris flows in the 2013 Colorado Front Range storm: Geology v 43 no 5 p 391-394 doi: 10 1130 G36507 1 Andy 2013 Hiking Rocky Mountain National Park: http: www hikingrmnp org 2013 01 macgregor-mountain-via-lumpy-ridge-th html accessed September 2015 Benda L 1990 The influence of debris flows on channels and valley floors in the Oregon Coast Range USA: Earth Surface Processes and Landforms v 15 no 5 p 457-466 Brummer CJ Abbe TB Sampson JR Montgomery DR 2006 Influence of vertical channel change associated with wood accumulations on delineating channel migration zones Washington USA Geomorphology 80: 295-309 Cenderelli D A and Kite J S 1998 Geomorphic effects of large debris flows on channel morphology at North Fork Mountain eastern West Virginia USA in Earth Surface Processes and Landforms p 1096-9837 doi: 10 1002 SICI 10969837 199801 23:13 0 CO 2-3 Clausen E 2012 Cache la Poudre River-Big Thompson River Drainage divide Area Landform Origins in the Colorado Mummy Ridge USA: Geomorphology Research: http: geomorphologyresearch com 2012 12 20 cache-la-poudre-river-big-thompsonriver-drainage-divide-area-landform-origins-in-the-colorado-mummy-range-usa accessed October 2015 Coe J A Kean J W Godt J W Baum R L Jones E S Gochis D J and Anderson G S 2014 New insights into debris-flow hazards from an extraordinary event in the Colorado Front Range: GSA Today v 24 no 10 doi: 10 1130 GSATG214A 1 Collins BD Montgomery DR Fetherston KL Abbe TB 2012 The floodplain large-wood cycle hypothesis: a mechanism for the physical and biotic structuring of temperate forested alluvial valleys in the North Pacific coastal ecoregion Geomorphology 139-140: 460470 Dickinson W R Klute M A Hayes M J Jancke S U Lundin M A McKittrick M A and Olivares M D 1988 Paleogeographic and paleotectonic setting of the Laramide sedimentary basins in the central Rocky Mountain region: Geoloical Society of America Bulletin v 100 p 1023-1039 doi: 10 1130 00167606 1988 1002 3 CO 2 Eaton L S Morgan B A Kochel R C Howards A D 2003 Role of debris flow in long-term landscape denudation in the central Appalachians of Virginia Geology v 31 p 339-342 doi: 10 1130 0091-7613 2003 0312 0 CO 2 16 Gochis D Schumacher R Friedrich K Doesken N Kelsh M Sun J Ikeda K Lindsey D Wood A Dolan B Matrosov S Newman A Mahoney K Rutledge S Johnson R Kucera P Kennedy P Sempere-Torres D Steiner M Roberts R Wilson J Yu W Chandrasekar V Rasmussen R Anderson A and Brown B 2015 The Great Colorado Flood of September 2013: Bulletin of American Meteorological Society no 96 p 1461 1487 doi: http: dx doi org 10 1175 BAMS-D-13-00241 1 Great Outdoors Colorado 2015 Colorado Flood recovery: One Year Later: http: www goco org blog colorado-flood-recovery-one-year-later accessed February 2016 Griffin K 2012 Geology Teacher Guide to Rocky Mountain National Park: National Park Service: http: www nps gov romo learn education upload Teacher_Guide_to_RMNP_Geology pdf accessed August 2015 Hines S 2014 Science You Can Use Bulletin US Forest Service Rocky Mountain Research Station Issue 10: http: www fs fed us rm science-applicationintegration docs science-you-can-use 2014-03 pdf accessed May 2015 Jarrett R D 1990 Paleohydraulic techniques used to define the spatial occurrence of floods: geomorphology v 3 p 181-195 Johnson C G Kokelaar B P Iverson R Logan M LaHusen R G & Gray J M N T 2012 Grain size segregation and levee formation in geophysical mass flows: Journal of Geophysical Research: Earth Surface v 117 doi:10 1029 2011JF002185 Klaar MJ Hill DF Maddock I Milner AM 2011 Interactions between instream wood and hydrogeomorphic development within recently degraded streams in Glacier Bay National Park Alaska: Geomorphology v 130 p 208-220 Magilligan F J Buraas E M Renshaw C E 2015 The efficacy of stream power and flow duration on geomporphic responses to catastrophic flooding: Geomorphology v 228 p 175-188: http: dx doi org 10 1016 j geomorph 2014 08 016 McCain J F Hoxit L R Maddox R A Chappell C F and Caracena F 1979 Storm and Flood of July 31-August 1 1976 in the Big Thompson River and Cache la Poudre River Basins Larimer and Weld Counties Colorado: U S Geological Survey National Oceanic and Atmospheric Administration Cooperating Organization: Colorado Geological Survey: United States Geological Survey Professional Paper 1115: http: pubs usgs gov pp 1115a-b report pdf accessed October 2015 McCreary J 2004 Colorado Geology Overview: http: www cliffshade com colorado geo_overview htm accessed October 2015 Montgomery D R 2008 A Simple Alphanumeric Classification of Wood Debris Size and Shape: Stream Notes 17 Montgomery D R Abbe T B Buffington J M Peterson N P Schmidt K M and Stock J D 1996 Distribution of bedrock and alluvial channels in forested mountain drainage basins: Letters to Nature v 38 p 587-589 Montgomery D R Collins B D Buffington J M Abbe T B 2003 Geomorphic Effects of Wood in Rivers: American Fisheries Society Symposium National Park Service 2014 U S Department of Interior Rocky Mountain National Park Front Range Floods Teacher Guide: http: www nps gov romo learn education upload Floods-final pdf accessed September 2015 NCAR 2007 Colorado Flood Summaries by Location: http: www assessment ucar edu flood fld_sum_loc html accessed September 2015 Runnells D D 1976 Boulder: A Sight to Behold: Guidebook: Self-Guided Tours of the Historic City Geology and Scenery University of Colorado: Estey Printing Co: http: bcn boulder co us basin natural geology historic html accessed August 2015 Ryan S 2015 The impacts of the 2013 Colorado Flood on portions of the Arapaho-Roosevelt National Forest and Rocky Mountain National Park: USFS Rocky Mountain Research Station Schuett-Hames D Pleus A E Ward J Fox M and Light J 1999 TFW Monitoring Program Method Manual for the Large Woody Debris Survey Prepared for the Washington State Department of Natural Resources: TFW-AM9-99-004 DNR 106 Soule J M 1976 Damage Caused by Geologic Processes during Flood Producing Storms: United States Colorado Geological Survey: United States Geological Survey Professional Paper 1115: http: pubs usgs gov pp 1115a-b report pdf accessed October 2015 United States Geologic Survey 2015 USGS Lidar Point Cloud CO SoPlatteRiver-Lot2a 2013 13TDE457480 LAS 2015 WeatherDB 2015 Glen Haven Colorado Average Rainfall: http: rainfall weatherdb com l 10165 Glen-Haven-Colorado accessed October 2015 Western Regional Climate Center 2001 Estes Park Colorado Period of Record Monthly Climate Summary: http: www wrcc dri edu cgi-bin cliMAIN pl coeste accessed October 2015 Wohl E Bestgen K Bledsoe B Fausch K Gooseff M and Kramer N 2015 Management of Large Wood in Streams of Colorado s Front Range: A Risk Analysis Based on Physical Biological and Social Factors: Colorado State University Yochum S E and Moore D S 2013 Colorado Front Range Flood of 2013: Peak Flow Estimates at Selected Mountain Stream Locations: United States Department of Agriculture: http: water state co us DWRIPub Documents PeakFlowEstimates_NRCS_12-162013 1 %20 1 pdf accessed August 2015 18 Figure 1 Location of the Black Canyon Creek and North Fork Big Thompson River watersheds Study areas are outlined in blue 19 Longitudinal Profile BCC and NFBT 2550 Reach 1 0 05 2500 Reach 2 0 04 Reach 1 0 01 Reach 1 0 06 0 03 Elevation m 2450 Reach 2 Reach 1 2400 0 02 Reach 4 0 02 0 01 Reach 5 2350 Reach 4 0 02 Reach 5 0 04 2300 0 500 1000 1500 2000 2500 3000 3500 4000 Lonitudinal Distance Moving Downstream m Figure 2 Longitudinal profile of BCC and NFBT study area highlights the location and mean slope of Reaches 1-5 in both streams 20 4500 A B Figure 3 Images of Black Canyon Creek A Black Canyon Creek in January 2013 before debris flow inundation Andy 2013 B Black Canyon Creek above the debris flow confluence at the reference cross-section as of August 2015 21 A B Debris flow Stream flow C Figure 4 Debris flow and river confluence images for Black Canyon Creek taken August 2015 A Taken from the left bank looking across BCC towards the debris flow channel B Looking upstream at BCC at the large clasts and wood accumulation at the stream and debris flow confluence C Taken from the right bank of BCC at the stream and debris flow confluence facing towards the left bank 22 Stream flow A B D C Figure 5 Scour images for Black Canyon Creek taken August 2015 Examples of the types of effects on BCC from the flood and debris flow A Bank erosion and boulder bar deposition 280 meters downstream of Reach 1 B An example of incision to bedrock above blue arrow and bank erosion 280 meters downstream of Reach 1 C Riparian vegetation removed by the flood on the left bank and accumulation of LW on the right bank between Reach 2 and Reach 3 D Deposition of large boulders and channel widening in Reach 4 23 A B Figure 6 Before and after flood image at North Fork Big Thompson An example along NFBT between Reach 2 and 3 of channel widening and erosion of streamside vegetation Yellow arrow highlighting the base of a tree used as a reference point A Before the flood in 2012 http: hikingcoloradotrails com trails north-fork-trail php B Photo taken during my internship in August 2015 24 Figure 7 Black Canyon Creek Study Area Boxes show study reaches White lines show cross-sections Three debris flows occurred within BCC watershed Debris flow 1 initiated during September 2013 The confluence of the debris flow and creek noted with a red dot The upstream section above Reach 1 showed little evidence of flood impact and is the reference crosssection for pre-flood conditions 25 Figure 8 North Fork Big Thompson River Study Area Boxes show study reaches White lines show cross-sections 26 LWD Jam Data Sheet Stream Name:_________________________________________ Date:_______________________________ Page __ of ________ Recorder:______________________________________________Crewmembers:_________________________________________________ GPS ID Stability Zone Wo o d diameter numeric co de and classes m A 0-1 1 0-0 1 B 1-2 C 2-4 D 4-8 E 8-16 F 16-32 G 32 2 0 1-0 2 3 0 2-0 4 4 0 4-0 8 5 0 8-1 6 6 1 6-3 2 7 3 2 Length m General composition Width m R B P U Broken or building Crea ted Jul y 2015 Stability Genera l Compos i ti on Wo o d Length letter co de and classes m Height above surface m Root system is attached to piece Greater than 50% diameter buried at some point along length Piece is pinned between vertical live or dead structures Unstable Chel s ey DeWi tt Comments Additional Notes: _________ ______________________________ Zone system Zone 1 Within wetted portion of channel ______________________________ Zone 2 From water surface to a line connecting the bankfull edges Zone 3 Directly above Zone 2 to infinity ______________________________ Zone 4 Outside of bankfull channel Figure 9 Large Wood Jam Field Data Sheet An example of the LW Jam Data Sheet used in the field to characterize individual LW jams Adapted ______________________________ from Montgomery 2008 and Schuett-Hames et al 1999 27 Figure 10 Criteria for channel zone identification of LW deposition Zone 1 is defined as the portion of the bankfull channel that is wetted at the time of the survey Zone 2 is defined as the area between the bankfull channel edges on both banks above the wetted channel surface and includes areas such as dry gravel bars Zone 3 is defined as the area directly above Zone 2 and typically includes pieces that extend out over the bankfull channel that provide cover Zone 4 is defined as the area outside of the bankfull channel and Zone 3 and typically includes the floodplain terrace and or riparian areas Schuett-Hames et al 1999 28 Stream flow Figure 11 Debris line example in Black Canyon Creek along the right bank Yellow arrow highlights elongated pattern of LW deposition that is parallel to the stream flow Photo taken from left bank at Reach 1 29 LW Deposition by Zone NFBT BCC Zone 4 21% Zone 1 0% Zone 3 7% Zone 2 6% Zone 3 0% Zone 1 50% Zone 4 94% Zone 2 22% Zone 1 Zone 2 Zone 3 Zone 4 Zone 1 Zone 2 Zone 3 Zone 4 Figure 12 Large wood deposition by zone for BCC and NFBT Zone criteria defined in Figure 11 30 A B Figure 13 Large wood jams along Black Canyon Creek Photos show a range of extent in the accumulation behind stable upright trees A A LW jam in Reach 4 5 A LW jam in Reach 5 31 A B Figure 14 Large wood jams along North Fork Big Thompson Photos show a range of extent in the accumulation behind stable upright trees along and in the stream A A LW jam in upstream of Reach 4 5 A LW jam in Reach 5 32 2 0 width-to-depth ratio drainage area 1 8 1 6 1 4 1 2 1 0 mean 0 8 0 6 0 4 0 2 0 0 BCC NFBT Figure 15 Width-to-depth ratio normalized by drainage area Whiskers represent the range of data from maximum to minimum value The box shows the interquartile range of the data The upper box is 75th percentile and the lower box is the 25th percentile The line within the box is the median 33 1 6 1 4 Cross-sectional area drainage area 1 2 1 0 0 8 mean 0 6 0 4 0 2 0 0 BCC NFBT Figure 16 Cross-sectional area normalized by drainage area Whiskers represent the range of data from maximum to minimum value The box shows the interquartile range of the data The upper box is 75th percentile and the lower box is the 25th percentile The line within the box is the median 34 Table 1 Reach lengths and number of cross-sections per reach in the BCC and NFBT Length m Distance from Debris Flow Confluence m Elevation Range m Number of Cross-Sections in Reach 1 2 3 4 5 129 124 5 78 7 139 3 177 8 10 457 891 1601 8 1950 2508-2511 2479-2485 2446-2451 2407-2411 2398-2400 4 0 2 0 5 1 2 3 4 5 88 55 168 112 5 251 n a n a n a n a n a 2475 2442-2444 2356-2359 2322-2324 2312-2323 1 3 1 0 2 Study Reach Area BCC NFBT Table 2 Frequency of LW per 100 meters in each reach in BCC and NFBT Study Area Reach LW Frequency per 100 meters 1 2 3 4 5 0 8 1 6 3 8 3 5 3 1 2 3 4 5 1 1 1 8 1 7 n a 3 1 BCC NFBT 35 Table 3 Frequency of channel bars per 100 meters in each reach in BCC and NFBT Study Area Reach Channel Bar Frequency per 100 meters 1 2 3 4 5 0 8 2 4 1 3 0 7 0 5 1 2 3 4 5 2 2 1 8 0 6 0 9 1 9 BCC NFBT 36 Table 4 Pebblecount results for BCC Grain size Sand VF Gravel VF Gravel Fine Gravel Fine Gravel Med Gravel Med Gravel Coarse Gravel Coarse Gravel VC Gravel VC Gravel Sm Cobble Sm Cobble Lg Cobble Lg Cobble Sm Boulder Sm Boulder Med Boulder Lg Boulder VL Boulder Bedrock Sample total Diameter mm 4096 Reach 1 Reach 2 Reach 3 Reach 4 Reach 5 15 8 12 2 5 4 2 3 6 2 1 3 4 7 10 10 7 6 1 11 8 0 0 1 4 8 10 4 7 1 3 54 57 56 2 37 22 7 4 14 26 11 37 16 11 5 2 9 4 15 5 8 7 10 17 26 19 23 9 8 4 3 3 1 168 158 Table 5 Drainage area and dimensions at each cross-section along BCC and NFBT CrossSections by Reach BCC Reference crosssection 1 1 1 2 1 3 1 4 3 1 3 2 5 1 5 2 5 3 5 4 5 5 Average NFBT 1 1 2 1 2 2 2 3 3 1 5 1 5 2 Average DA in km 2 widths m average depth m 14 5 15 4 15 6 15 6 15 6 16 4 16 4 17 2 17 2 17 2 17 2 17 9 1 3 11 8 7 2 7 2 12 1 12 2 11 4 16 6 19 7 9 7 5 6 4 7 10 7 0 9 2 0 1 0 0 8 0 8 0 6 0 6 0 6 0 6 0 8 0 9 0 8 0 9 39 5 41 2 41 2 41 4 44 6 45 2 45 2 10 4 9 0 10 7 9 5 8 1 19 4 21 7 12 7 0 5 0 8 0 9 0 7 0 7 0 4 0 7 0 7 Crosssection area m2 w:d Drainage Area Crosssectional Area Drainage Area 1 1 23 7 6 8 5 8 9 0 6 7 6 4 10 8 9 0 8 5 5 3 3 3 5 5 8 0 10 1 6 8 5 6 8 3 13 7 38 0 1 0 4 0 5 0 6 1 0 1 2 1 2 1 5 1 8 0 7 0 4 0 3 0 9 0 1 1 5 0 4 0 4 0 6 0 4 0 4 0 6 0 5 0 5 0 3 0 2 0 6 0 3 0 3 0 3 0 3 1 0 0 7 0 5 0 1 0 2 0 2 0 2 0 1 0 2 0 3 APPENDIX A: Survey data information Table A 1 Dimension data for individual LW jam in each reach along BCC Reach 1 2 3 4 5 Area m2 Height m Length m Width m 27 3 14 9 9 0 12 2 70 3 37 0 125 1 18 8 70 9 369 9 161 0 65 1 7 4 15 1 725 1 138 3 104 4 0 5 1 1 1 1 5 1 1 1 8 2 3 3 3 1 5 0 5 2 5 2 1 5 1 8 6 5 5 10 11 23 12 14 25 23 13 10 4 5 57 24 20 3 3 3 3 7 5 4 7 2 5 4 19 8 6 1 5 3 5 15 7 5 Table A 2 Dimension data for individual LW jam in each reach along NFBT Reach 4 had no LW jams Reach Area m2 Height m Length m Width m 1 2 3 125 7 54 6 27 5 16 0 46 1 n a 31 6 6 1 13 8 2 9 203 5 128 4 4 3 92 3 2 1 2 2 1 3 1 n a 3 3 1 75 2 2 5 1 5 1 1 1 5 17 5 15 7 12 13 n a 13 5 4 7 5 3 5 15 21 2 3 16 8 5 4 3 1 5 3 n a 3 3 3 1 10 1 8 1 8 5 4 5 39 Table A 3 Channel bar areas for each reach along BCC and NFBT Study Area Reach Area m2 BCC 1 2 3 4 5 46 2 185 5 196 8 243 4 547 9 855 1 876 4 NFBT 1 2 3 4 5 220 6 104 5 211 9 1742 9 1437 514 9 117 43 120 4 828 9 84 5 40 APPENDIX B: Channel Cross-Sections Figure B 1 Cross-sections along BCC The brown line is estimated bankfull and the blue line is wetted width Depth is relative to eye level of auto level BCC Reach Reference 0 -0 5 0 1 2 3 4 5 6 7 8 -1 -1 5 Depth m -2 -2 5 -3 -3 5 -4 -4 5 -5 -5 5 -6 Width m BCC Cross-Section 1 1 0 -0 5 0 1 2 3 4 5 6 7 8 -1 Depth m -1 5 -2 -2 5 -3 -3 5 -4 -4 5 -5 -5 5 Width m 41 9 10 11 12 13 14 15 BCC Cross-Section 1 2 0 0 1 2 3 4 5 6 7 8 9 10 7 8 9 10 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m BCC Cross-Section 1 3 0 0 1 2 3 4 5 -0 5 -1 Depth m -1 5 -2 -2 5 -3 -3 5 -4 -4 5 Width m 42 6 BCC Cross-Section 1 4 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m BCC Cross-Section 3 1 0 0 1 2 3 4 5 6 7 Depth m -0 5 -1 -1 5 -2 -2 5 Width m 43 8 9 10 11 12 13 BCC Cross-Section 3 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 -0 5 -1 Depth m -1 5 -2 -2 5 -3 -3 5 -4 -4 5 Width m BCC Cross Section 5 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 -0 5 Depth m -1 -1 5 -2 -2 5 -3 Width m 44 BCC Cross-Section 5 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m BCC Cross-Section 5 3 0 -0 5 0 1 2 3 4 5 6 -1 Depth m -1 5 -2 -2 5 -3 -3 5 -4 -4 5 -5 -5 5 Width m 45 7 8 9 10 11 12 BCC Cross-Section 5 4 0 0 1 2 3 4 5 6 7 8 9 10 11 10 11 12 -0 5 Depth m -1 -1 5 -2 -2 5 -3 Width m BCC Cross-Section 5 5 0 -0 5 0 1 2 3 4 5 6 Depth m -1 -1 5 -2 -2 5 -3 -3 5 -4 Width m 46 7 8 9 Figure B 2 Cross-sections along NFBT The brown line is estimated bankfull and the blue line is NFBT Cross-Section 1 1 0 0 2 4 6 8 10 12 14 16 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m NFBT Cross-Section 2 1 0 0 1 2 3 4 5 6 7 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 -4 Width m wetted width Depth is relative to eye level of auto level 47 8 9 10 11 12 13 14 NFBT Cross-Section 2 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 12 13 14 17 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m NFBT Cross-Section 2 3 0 0 1 2 3 4 5 6 7 8 -0 5 Depth m -1 -1 5 -2 -2 5 -3 Width m 48 9 10 11 15 NFBT Cross-Section 3 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -0 5 Depth m -1 -1 5 -2 -2 5 -3 -3 5 Width m NFBT Cross-Section 5 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 -0 5 Depth m -1 -1 5 -2 -2 5 -3 Width m 49 NFBT Cross-Section 5 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 -0 5 Depth m -1 -1 5 -2 -2 5 -3 Width m 50
    • Dilmen, Derya - Ph.D. Dissertation
      The Role of Coral Reefs on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island 2016, Dilmen,Derya,Derya Dilmen Copyright 2016 Derya Itir Dilmen The Role of Corals on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island Derya Itir Dilmen A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2016 Reading Committee: Vasily V Titov Chair Gerard H Roe Joanne Bourgeois Program Authorized to Offer Degree: Earth and Space Sciences University of Washington Abstract The Role of Coral Reefs on Tsunami Dynamics in an Island Setting: A Case Study of Tutuila Island Derya Itir Dilmen Chair of the Supervisory Committee: Affiliate Professor Vasily V Titov Earth and Space Sciences On September 29 2009 at 17:48 UTC an Mw 8 1 earthquake in the Tonga Trench generated a tsunami that caused heavy damage across Samoa American Samoa and Tonga One of the worst localities hit was the volcanic island of Tutuila in American Samoa Tutuila Island located 250 km from earthquake epicenter experienced tsunami inundation and strong currents on the north and east coasts causing 34 fatalities and widespread structural and ecological damage The surrounding coral reefs of the island also suffered heavy damage This damage was formally evaluated based on detailed surveys before and immediately after the tsunami which provides a unique opportunity to evaluate the role of coral reefs on tsunami dynamics In the first part of this research estimates of tsunami dynamics are obtained with the MOST numerical tsunami model Titov and Synolakis 1997 which is currently the operational tsunami forecast tool used by the US National Oceanic and Atmospheric Administration NOAA The earthquake source function was constrained using real-time deep-ocean tsunami data from three DART Deep-ocean Assessment and Reporting for Tsunamis systems in the far field and by tide-gauge observations in the near field We compare the numerically estimated run-up with observations to evaluate the simulation skill of MOST We present an overall synthesis of tidegage data survey results of the run up inundation measurements and the datasets of coral damage around the island in order to evaluate the overall accuracy of MOST run-up prediction for Tutuila and the model s performance of simulating in the locations covered with corals during the tsunami event Our primary findings are 1 there is a tendency for MOST to underestimate run-up on Tutuila and 2 the locations where the model underestimates run-up tend to have experienced heavy or very heavy coral damage whereas well-estimated run-up locations characteristically experienced low or very low damage This brought us to the conclusion regarding how coral reefs affect tsunami dynamics through their influence on bathymetry and dissipation Second we focus on numerical simulations of this event to evaluate: 1 how roughness variations affect tsunami run-up and if different values of Manning s roughness n improve the simulated run-up compared to observations and 2 how depth variations in coral reef bathymetry control run-up and inundation on the coastlines they shield We find as a result of the simulations that no single value of n provides the best match to observations and we find large bay-to-bay variations in the impact of varying n The results suggest that there are aspects of tsunami wave dissipation that are not captured by the drag formulation in the MOST model The primary impact of removing coral bathymetry is to reduce run-up from which we conclude that at least in this setting the bathymetric impact of coral reefs is to increase run-up and inundation We conclude that future studies should focus on two key issues for further research: 1 the representation of the turbulent dissipation in terms of the governing equations and their coefficients and 2 detailed numerical experiments on all aspects of reef settings such as reef widths reef types and coastal geometry on the scale of individual bays TABLE OF CONTENTS List of Figures iii List of Tables iv Chapter 1 Introduction 1 1 1 The phenomenon of tsunamis 1 1 2 The generation of tsunamis 2 1 2 1 The three stages of the tsunami 2 1 3 The history of tsunamis 5 1 4 Tools to prevent decrease the damage and loss of lives due to tsunamis 9 1 5 What are the challenges of tsunami modeling 11 1 6 Island settings coral reefs and an outline of the thesis 16 Chapter 2 Evaluation of the relationship between coral damage and tsunami dynamics 19 2 1 Introduction 19 2 2 Tutuila Island 22 2 3 The Samoa event 24 2 4 Observations of the event 25 2 5 Modeling the event 28 2 5 1 The model set-up 28 2 5 2 Choice of the source function 29 2 5 3 Evaluation of the model results with DART and tide gauges 30 i 2 6 Analysis 31 2 7 Summary and discussion 41 Chapter 3 The Role of coral reef roughness and bathymetry on tsunami dynamics case study: 2009 Samoa tsunami 44 3 1 Introduction 44 3 2 Analysis 45 3 2 1 The impact of changing Manning s roughness n 45 3 2 2 Changes in reef bathymetry 52 3 1 Discussion 56 Chapter 4 Concluding remarks 57 Appendix A 65 Appendix B 66 ii LIST OF FIGURES Figure 2 1 Tutuila Island 24 Figure 2 2 Photographs of the coral survey methods and typical observations 26 Figure 2 3 The boundaries of the nested A B and C grids used 29 Figure 2 4 Observed and simulated water surface elevations at the tide gauge 32 Figure 2 5 Observed and simulated water surface elevations at three DART buoys 33 Figure 2 6 Coral damage versus observational run-up 35 Figure 2 7 Two examples comparing observed run- up with MOST run-up 36 Figure 2 8 Maximum wave amplitudes peak currents peak fluxes a nd max stresses 37 Figure 2 9 Scatter plot of simulated versus observed run-up m 39 Figure 2 10 A summary of the comparison between model run-up and coral damage 40 Figure 3 1 A comparison of model and field run- up for the simulations with varying n 47 Figure 3 2 Simulated maximum wave amplitudes near Seetaga and Amaneve 48 Figure 3 3 Comparison of water surface elevations at selected virtual tide gauges 51 Figure 3 4 C grids of synthetic bathymetry 53 Figure 3 5 Simulated max wave amplitudes for Seetaga and Amaneve for different bathymetry 54 Figure 3 6 Comparison of water surface elevations at selected virtual tide gauges in Seetaga and Amaneve 55 Figure A-1 Scatter plots of coral damage 83 iii LIST OF TABLES Table 2 1 Sources compiled by NGDC to create the three nested grids 28 Table 2 2 Parameters of the two tsunami unit source functions S 1 and S2 31 Table 2 3 Simulated and field run-up differences and coral damage at selected villages 33 Table B1 Simulated run-up for different Manning s roughness values at selected villages 84 Table B2 Simulated run-up for different Manning s roughness values at selected villages 85 iv ACKNOWLEDGEMENTS I would like to take this opportunity to extend my thanks to several people without whom this would not have been possible I am grateful to my advisor Vasily Titov He gave me a wonderful opportunity to study in UW Prof Gerard Roe graciously committed his time and energy that helped to complete my research I am very grateful: For his support and his enthusiasm of teaching mentoring and doing science Thank you to my committee members Joanne Bourgeois Randall LeVeque Frank Gonzales and Ahmet Cevdet Yalciner They were always there whenever I looked for mentorship I would like to acknowledge JISAO for providing the funding that supported this research Thanks to NOAA s tsunami research group NOAA Center for Tsunami Research-NCTR: Yong Wei Liujuan Tang Edison Gica Christopher Moore Marie C Eble and Hongqiang Zhou Thanks to my wonderful friends especially to Daria Valchonak and Gulsah Dagkiran Lastly thank you to my family for their patience It has been privilege to study learn and teach science at University of Washington v DEDICATION to my mom vi Chapter 1 INTRODUCTION 1 1 THE PHENOMENON OF TSUNAMIS Tsunamis are among the deadliest natural hazards on Earth They have caused over 400 000 fatalities in the last century ranking them fourth after earthquakes floods and volcanic eruptions NGDC NOAA 2015 The threats we face from tsunamis are 1 direct deaths and injuries 2 structural and ecological damage and 3 the subsequent spread of diseases and harmful chemical substances A tsunami is a long series of low-crested gravity waves often generated by the energy transferred from a seafloor displacement to the ocean The global historical tsunami database of the National Geophysical Data Center1 World Data Source NGDC WDS provides information on over 2 400 tsunamis from 2100 BC to the present in the Pacific Atlantic and Indian oceans and the Mediterranean and Caribbean seas NGDC WDS 2015 of which 75% of those recorded tsunamis occurred due to earthquakes Most large tsunamis are caused by the seafloor displacement due to large shallow earthquakes along subduction zones Less commonly nonsubduction-zone earthquakes landslides volcanic eruptions nuclear explosions meteorite impacts and meteorological events also generate tsunamis Gusiakov 2007 Etymologically the term tsunami comes from Japanese tsu - breaking upon a harbour name -waves These phenomena were called harbor waves because of strong water currents unexpected wave oscillations and damage to harbors were the first signs of an approaching tsunami for far-field events 1 NOAA s National Geophysical Data Center NGDC was recently renamed the National Centers for Environmental Information NCEI the website remains https: www ngdc noaa gov as of August 2016 In this dissertation I refer to the tsunami database source by its more familiar name NGDC 1 An early appearance of the word tsunami in western literature was an article by Eliza Schidmore in National Geographic about the 1896 Sanriku tsunami which killed more than 22 000 people Cartwright & Nakamura 2008 Schidmore 1896 Although always in the minds of shore-dwelling populations in high-risk areas tsunami hazards received a renewed public focus on tsunami hazards came after the devastating Indian Ocean Tsunami of 26 December 2004 which took close to 230 000 lives and injured countless more USGS 2005 Further sobering evidence of the power of tsunamis to wreak destruction was the Great Japan earthquake and tsunami of 11 March 2011 which - even in this tsunami-aware and prepared society claimed nearly 16 000 lives Subsequently tsunami generated flooding caused a nuclear meltdown and radiation leaks at Fukushima which led to the permanent dislocation of a 230 000 people Oskin 2015 1 2 THE GENERATION OF TSUNAMIS A typical tsunami begins with a rupture on a submarine plate-boundary fault which displaces the ocean floor and transmits a dynamic impulse to the water column Gravity acts to restore mean sea level by converting the potential energy of the water displacement into gravity waves These waves radiate the resulting potential energy away from the source of the tsunami and propagate through the ocean till they reach shorelines The size of the tsunami depends on the main parameters that govern the earthquake: the energy release magnitude the source mechanism and depth of the hypocenter the fault rupture velocity and water depth over the source region Earthquakes with large magnitudes greater than 8 in Moment Magnitude Scale and shallow hypocenters 30 km depth in Earth produce the largest tsunamis 2 1 2 1 The Three Stages of the Tsunami There are three major stages associated with a tsunami: generation propagation and runup inundation: During a typical tsunamigenic submarine earthquake a segment of ocean floor is rapidly uplifted and displaces a volume of water some other part of the seafloor may also subside This creates a hump or trough on the ocean surface which is unstable due to the force of gravity The pressure gradient formed due to gravity causes waves to flow sideways generating a train of waves a tsunami Okada 1985 derived the equation for the initial displacement of the ocean surface by computing the static field of vertical deformation on the ocean floor assuming the water is incompressible and the deformation occurs in seconds The model has been widely used in numerical tsunami models to estimate initial tsunami wave amplitudes Once generated tsunami waves can reach coastal areas after traveling hours to days with negligible frictional dissipation in the open ocean Titov 1997 However the wave structure evolves substantially as waves spread out over the bathymetry When an individual tsunami wave approaches a shoreline it transfers some of its kinetic energy into potential energy The waves increase in height The amplified tsunami wave then overruns and inundates the coastline A broad spectrum of wavelengths formed during tsunami generation leads to dispersion of the wave packet during their travel from the source to the coast consequently there can be a prolonged period of repeated shoreline inundation upon the tsunami s arrival at a coastline A typical tsunami wave length 10 km to 200 km is much larger than typical water depths 2-4km in the deep ocean Therefore the propagation of a tsunami can be described accurately by the equations for waves in inviscid shallow-water until the waves approach the shore These equations are derived from depth-integrated Navier-Stokes equations for conservation of mass 3 and linear momentum in a fluid The assumptions of shallow water equations are: the fluid is incompressible constant density the horizontal length scale is much greater than the vertical length scale and the flow is homogeneous Bricker et al 2015 The shallow-water equations describe a thin layer of fluid where water depth h to wave length L ratio is in the order of 10-2 They are subjected to a constant gravitational force bounded by the bottom topography below and by a free surface above In the case of tsunami for shallow-water approximation the waves are assumed to be non-dispersive and to travel with a linear wave speed c of: 1 1 where g is gravity and h is the water depth For deep-ocean conditions where the ocean depth is several kilometers a tsunami wave velocity of around 200 m s is typical Even communities that receive warning may have only minutes or up to a few hours to prepare for trans-oceanic tsunamis to prepare Within a few minutes after generation the tsunami develops into a sequence of long wavelength 10 km to 200 km typical depending on source parameters waves that grow rapidly in height as the tsunami approaches the shore As the waves approach the depth of water decreases causing the tsunami to slow down at a rate proportional to the square root of the water depth Eqn 1 1 Wave shoaling then forces the wave amplitude A to increase at an inverse rate with local undisturbed water depth h governed by Green s law Green 1837 Eqn 1 2 : 1 1 4 1 2 For energetic events the wave height above sea level at the maximum point of inundation or run-up can reach upwards of 40 m as seen in 2011 Great Tohoku Japan Tsunami run-up observations Mori et al 2011 4 When a tsunami finally reaches the shore it may appear as a rising or falling wave a series of breaking waves or a bore The waves return at intervals of several minutes for up to days before finally dissipating The geomorphology of the littoral setting strongly affects the tsunami Submerged features such as reefs bays entrances to rivers and the slope of the beach all act to modify the dynamics of the tsunami as it approaches the shore and these numerous influences make it harder to comprehend and model tsunami wave dynamics on the coast Therefore understanding the inundation run-up stage of tsunami is the main objective of tsunami hazard mitigation 1 3 THE HISTORY OF TSUNAMIS The present version of the National Geophysical Data Center catalog on tsunamis and tsunamilike events covers the period from 2000 BC till present NGDC WDS 2015 The catalog provides insights into tsunami processes of generation propagation and inundation run-up It also helps determine the source of each tsunami with probabilistic and deterministic approaches identify locations that are particularly prone to tsunamis and forecast probable inundation limits by combining the data of tsunami source of the NGDC data with probabilistic analyses or computational models The forecasting results are also crucial to determine wave amplitude thresholds of operational tsunami warnings and thus whether a tsunami warning will be issued According to the NGDC 2008 catalog more than 600 000 people have died due to 2130 individual tsunamigenic events since 2000 BC Whitmore 2009 Ten trans-oceanic tsunamis during the last 250 years are responsible for 49% of those deaths Gusiakov 2007 Of the total 2130 events 1206 occurred in the Pacific Ocean Every tsunami is unique but here I note a few 5 that have had groundbreaking impact on progress in tsunami research based primarily on more extensive review by Okal 2011 : The 1755 Lisbon tsunami remains the deadliest trans-oceanic tsunami in historical times with a death toll approaching 100 000 in Europe NGDC WDS 2015 The effect of this earthquake and tsunami was not only scientific but also was social and political Since all the churches in Lisbon were destroyed on All Saints Day it has been seen as a manifestation of divine judgment Paice 2008 Numerical model case studies of this event have been used to demonstrate that even a minor change in fault source location could significantly affect directionality and focusing resulting in a distinctly different distribution of tsunami wave amplitudes Zahibo et al 2011 The 1896 Meiji Tsunami the first identified tsunami earthquake earthquake whose magnitude is smaller than the magnitude of tsunami created Kanamori 1972 remains the deadliest tsunami in Japan s recorded history The tsunami was much larger than expected from the amplitude of its seismic waves with run-up reaching more than 30 m in the near field up to 5 m in Hawaii and damage reported in California Okal et al 2009 After the 1933 Great Sanriku tsunami buildings were relocated to higher grounds as a first countermeasure against a tsunami Murao 2014 The 1923 Kamchatka tsunami is considered as the first tsunami for which a far-field warning was given even though local authorities of Hawaii did not take it seriously It is an early instance of an insufficient interaction between scientists and decision makers Okal 2011 The 1946 Aleutian Islands tsunami is the first tsunami disaster in US history causing fatalities The tsunami warning center at Honolulu Geomagnetic Observatory was established after this event in 1949 Igarashi et al 2011 6 The 1960 Chile tsunami was generated by the largest earthquake in the historical record Mw 9 5 an estimated moment magnitude of 2-5 x 1030 dyn cm An important lesson learned from this disaster was that the maximum wave during a distant tsunami is rarely the first one The long periods of tsunami waves can give a sense of feeling secure to residents and to authorities even though the worst is yet to come Okal 2011 The 1964 Alaska tsunami led the creation of the Alaska West Coast Tsunami Warning Center in 1967 Sokolowski 1990 It was incidentally recorded on a pressure sensor deployed on the ocean floor about 1000 km far from the earthquake epicenter and which had been installed for an unrelated seafloor magneto-telluric experiment Filloux 1982 This observation led to the development of specifically engineered tsunami pressure detectors coupled with realtime communications creating the Deep Ocean Assessment and Reporting of Tsunami DART Network in 2003 by NOAA for the purpose of forecasting coastal tsunami impacts Bernard & Milburn 1985 The 1992 Nicaragua tsunami: was the first to be systematically surveyed by international teams Synolakis and Okal 2005 Such comprehensive and consistent databases of inundation and run-up continue to be used to test tsunami computational model results This tsunami survey documented substantial values of run-up 4-10 m along a 290 km stretch of coastline Satake et al 1993 which was underestimated by then-standard simulation algorithms that stopped the wave height and current estimations at an imaginary reflective boundary wall at a shallow-water depth of typically 10 m Imamura et al 1993 In the models tsunami waves were as much as one order of magnitude smaller than the surveyed values This led to the introduction of new numerical algorithms for computing run-up and inundation that were able to successfully reproduce the surveyed values of waves penetrating over initially dry land Titov and Synolakis 7 1998 The MOST tsunami code used in this thesis is one of the models developed after this event and this new suite of models have been tested by laboratory and field survey data for different events and scenarios since then For the first time in 1995 during the Colima-Jalisco tsunami in Mexico the withdrawal of the sea in was documented with photographs along the southern end of Tenacatita Beach Borerro et al 1995 The 1998 Papua New Guinea tsunami: The event has been the subject numerous discussions and controversies due to its unexpected tsunami magnitude and unresolved mechanism of the earthquake A moderate magnitude of earthquake triggered a submarine landslide which was the source of a locally catastrophic tsunami raising awareness of this mode of tsunami generation Tappin et al 2008 Education on tsunami risk lessened the loss of lives was the lesson taken from this tsunami 1999 the Vanuatu tsunami Okal 2011 A few months previously the 1998 Papua New Guinea tsunami at Vanuatu had occurred and subsequently villagers at Vanuatu were educated to immediately self-evacuate low-lying areas upon feeling strong earthquake tremors especially if followed by a retreating of sea In 1999 an earthquake struck the Vanuatu Island and the earthquake-triggered tsunami completely destroyed the village However only three residents lost their lives Caminade et al 2000 The 2003 Aleutian islands tsunami: This was the first successful operational use of DART buoys in real time Lautenbacher 2005 The Sumatra-Andaman 2004 tsunami: The deadliest tsunami in recorded history with a death toll close to 275 950 was recorded by USGS 2005 Among its many aspects the following changed the attitude of researchers planners and policy makers on both the technical and 8 operational ways of tsunami risk mitigation Okal 2011 1 communication during the disaster was a failure 2 tsunamis have come to be regarded as a global threat 3 caused an acceleration of a global effort to establish tsunami warning centers 4 funding and research investments from national governments increased to enhance tsunami programs 2011 Great Tohoku Japan tsunami: Lessons from this event: 1 Safer more flood resilient buildings - particularly power plants and evacuation structures - are needed 2 Developing a robust tsunami numerical model for prediction of tsunami impacts is urgent 1 4 TSUNAMI MODELING AS A TOOL TO PREVENT DECREASE THE DAMAGE AND LOSS OF LIVES DUE TO TSUNAMIS After the Great Tohoku Japan tsunami event in 2011 the urgency of developing a robust tsunami numerical model for prediction of tsunami impacts has become obvious and globally accepted As noted in 2003 by Titov et al 2003a A robust tsunami numerical model should provide siteand event-specific maximum wave amplitude information well before the first wave arrives at a threatened community and accurate enough to mitigate tsunami hazard in real time Tools such as direct tsunami measurements as well as post tsunami surveys and geological records of tsunami deposits are used to constrain tsunami sources and dynamics in numerical models Direct tsunami measurements in the aftermath of a tsunami taken with tide gauges and DART - type gauges can assist in validating and analyzing earthquake source characteristics and can be incorporated into numerical tsunami simulations Starting from 1908 analog tide gauges were used to estimate tsunami wave heights in Japan Mofjeld 2009 In the 1960s tide gauges reported wave height information to warning centers and were used to determine whether to issue a tsunami warning or just a tsunami watch Nowadays they work as calibration and comparison tools for the numerical tsunami models However it has been established in 9 numerous studies eg Miller 1972 Rabinovich 1997 that the effects of local resonance within the bays or harbors where tide gauges are located have an observable impact on wave characteristics at the tide gauge limiting their value for predicting run-up Titov 2009 Furthermore the wave period recorded by the tide gauge mostly depends its location rather than on the tsunami source characteristics On the other hand bottom-pressure stations DARTs installed in the open ocean obtain more direct tsunami wave data before tsunamis develop complex dynamics on the continental shelf and the coastal region as well as resonance effects inside bays and harbors Measuring fluctuations in bottom pressure by transferring the data via satellite to shore the latest development DART systems provide open-ocean accurate time series of tsunami water levels for tsunami source analysis Titov 2009 The first wave in an observed tsunami time series is particularly important in any analysis related to the tsunami source This is because it is the least affected by the reflections scattering and wave interference that complicate later waves The timing amplitude period and sign trough or crest wave of this first wave indicate the pattern of vertical ground displacement of the earthquake source Numerical models use the first tsunami waves observed at DART Stations to refine the preliminary tsunami sources by inverting the data back to the source using pre-computed model simulations Post tsunami surveys including the information of the extent of the tsunami inundation maximum wave heights on the coast number of damaging waves transport of debris sediment rock and corals provide a ground truth for remotely sensed data and test cases for numerical models of tsunami inundation Later post tsunami surveys such as damages in corals help fill the gaps in the measurements The refined numerical model results by direct tsunami measurements and post tsunami surveys are shared with tsunami warning centers and their related systems to 10 reduce loss of lives by providing warnings to coastal residents Whitmore 2013 Geological records of tsunami deposits also provide test cases for the inundation modules of the tsunami models Bourgeois 2009 1 5 WHAT ARE THE CHALLENGES TO TSUNAMI MODELING In general the run-up of a tsunami on land will be influenced by a very large number of factors including the earthquake source seismic moment and geometry and its physical environment earthquake depth bathymetry of the source area and the properties of the receiving shoreline above and below sea level topography of the beach presence of bays harbors estuaries etc Other factors can play a role too All large earthquakes can trigger landslide failures which in turn can generate tsunamis with run-up values locally much larger than those of the main earthquake as in Plafker 1997 While the basic equations for numerical analysis of tsunamis have been known for decades development of numerical models for real-time forecasting has taken over 20 years beginning with the 1993 tsunami modeling efforts of Japan Models advanced with benchmarks and validation tools such as the large-scale laboratory experiments analytical methods and DART gauge recordings The models have evolved through a meticulous process Synolakis & Kanoglu 2009 of validation and verification In a series of workshops on long-wave run-up models in the 1990s a number of benchmark tests were suggested comparing numerical solutions to analytical predictions and to certain laboratory measurements Liu Woo & Cho 1998 The detailed history and background of the benchmarks and tests are summarized in Synolakis et al 2008 and in Synolakis and Kanoglu 2009 Tsunami models have been developed with a variety of different numerical methods and of spatial and temporal discretization techniques The vast majority of current tsunami models are 11 based either on the Boussinesq or the non-dispersive shallow water long wave equations derived from depth-integrated Navier-Stokes equations In these models the Navier-Stokes equations are averaged from the seafloor to the free surface and viscous stresses are either neglected or presumed to follow bottom friction laws Depth-averaged Navier-Stokes equations are known as the nonlinear shallow water equations linearizing the nonlinear terms then gives the linear shallow water equations Depth-averaged models that study propagation of tsunami waves in one direction are referred to as 1 1 and similarly 2 1 models refer to two-directional propagation On the coast wetting-drying algorithms of the models predict tsunami run-up and inundation limits When the first advances in numerical tsunami models began in the 1970s in Japan they were concentrated on solving either non-linear 1 1 Boussinesq equations reviewed in Shuto and Fujima 2009 or 2 1 shallow water equations Synolakis and Kanoglu 2009 In 1974 Houston and Garcia 1974 solved a linear form of the spherical long-wave equations in 2 1 form up to the edge of the continental shelf using a finite difference method The same year Hibberd and Peregrine 1974 calculated the evolution of bores over a sloping beach with a shoreline algorithm of non-linear shallow water equations Advances in modeling in the 1990s were stimulated through two landmark scientific meetings: the first one was in Russia in 1989 the other was in California in 1990 Synolakis and Kanoglu 2009 In 1997 Goto and Ogawa proposed a finite-difference method with upwind scheme in Eulerian form of the non-linear shallow water equations During the same time interval at a meeting in Russia Titov and Synolakis 1995 presented the finite difference 2 1 algorithm of VTCS now called MOST which computes far-field tsunami propagation and inundation in a variable spatial grid for weakly dispersive tsunamis MOST has been used 12 operationally by NOAA and also is the model used in this thesis for tsunami run-up and inundation calculations in Tutuila At the 1990 meeting in California the pervasive need for laboratory data to enable further progress in computational models particularly for 2 1 run-up computations found voice The following is a review of tsunami models developed by different research groups: In the early 1990s Prof Imamura of the Disaster Center of Japan has developed the TUNAMI Tohoku University s numerical analysis model for inundation model which estimates tsunami propagation in deep water and inundation on land Imamura 1996 Currently TUNAMI has been accepted by 43 organizations in 22 countries as the numerical code to predict damage of tsunami on coasts It is an open source fully tested model evaluated for most of the historical tsunamis such as 1883 Krakatau Tsunami 1935 North Sumatera Tsunami 1992 Flores Tsunami 1994 East Java Tsunami 1996 Toli-Toli Tsunami 1996 Biak Tsunami 2000 Bangai Tsunami 2004 Aceh Tsunami and 2006 South Java Tsunami and 2011 Great East Japan Tsunami and benchmark problems Yalciner et al 2014 Another numerical model extensively used for tsunami modeling is COMCOT Cornell Multi-grid Coupled Tsunami model Liu Woo & Cho 1998 which is composed of a nested grid system The system dynamically couples up to 12 levels with different grid resolutions to fulfill the need for tsunami simulations at different scales In both TUNAMI and COMCOT models shallow-water equations are used and a flux-conserving algorithm preserves the water mass throughout the computations COMCOT adopts an explicit staggered leap-frog finite difference scheme to solve shallow-water equations in both Spherical and Cartesian coordinates In 2001 the Environmental Assessment and Monitoring Department in France developed CEA DASE The model is certified and fully tested with benchmark tools The code has been 13 also applied for the probable tsunami scenarios in French Polynesia Pacific and Indian oceans and Mediterranean Sea eg Hebert et al 2001 A similar model to CEA DASE UBO-TSUFD was developed by Bologna University Italy in 2003 The non-linear shallow water equations were solved using finite-element and two-step time integration methods The grid type is either triangular elements or a Cartesian coordinate system on a fixed boundary The Coriolis force can be included in this model The model is being applied for the several tsunami scenarios and past tsunami events in Mediterranean Sea and in the Indian Ocean 2004 Sumatra 2006 Java and several scenarios Tinti & Tonini 2013 Titov Tsunami Forecasting 2009 In 2002 the Norwegian Geotechnical Institute ICG Norway developed SKREDP The model is certified and tested with analytical benchmarks The coordinate system is Cartesian Any initial sea-surface deformations prescribed source functions for landslides and earthquakes are inputs of the tsunami source for this model The model has been applied to northeast Atlantic to the Arctic and Indian oceans to Norwegian fjords and the Mediterranean and South China seas as well as to hydropower reservoirs in Norway and the Philippines Harbitz et al 2007 GeoClaw is a recently validated tsunami model developed by R LeVeque s Applied Math group at the University of Washington Gonzales et al 2011 It uses a dynamic mesh refinement for an arbitrary number of nested levels The model uses finite volume Riemann solvers as numerical schemes and 2D 1 rectangular mesh with adaptive refinement as mesh grid type During the calculations individual grid cells are tagged for refinement using a criterion such as wave height thus disturbed water parcels are gradually better resolved The flagged cells at each level are clustered into rectangular boundaries for refinement to the next level The 14 model is also robust in calculating wave dynamics in the presence of bores and steep gradients George & LeVeque 2006 The MOST model is used as an operational real-time tsunami forecasting tool at NOAA for the Pacific Ocean Wei et al 2008 and is the model used in this dissertation Examples of the model s forecasting capability are given and explained well in Wei et al 2008 and Tang et al 2012 MOST has ability to track the shoreline by adding new grid points as a function of time A pre-computed generation propagation database and selection of a linear combination of scenarios that most closely matches the observational data can be used as initial conditions for a site-specific inundation algorithm The database contains 246 model scenarios that cover most active subduction zones around the Pacific It stores all simulations for each solutions of numerical analysis including amplitudes and velocities for each offshore location Titov 2009 From all of these examples it is clear that the validation of numerically computed tsunami run-up against observations gathered in real settings is the key Estimation of tsunami behavior on land is essential for tsunami mitigation and also for designing an optimal community evacuation system along the coast in the event of such a catastrophe Furthermore Synolaks et al 2008 further argues that no testing of a tsunami run-up algorithm in idealized laboratory experiments can ensure robust model performance nor can such testing substitute for field data benchmarking Even though there are significant improvements in terms of the accuracy and speed of forecasting tsunamis it is still a challenge to model them and improvements are desirable One way forward is through careful numerical case studies of well observed events field studies in order to better understand tsunami dynamics and numerical model performance One such casestudy example and the focus of my thesis is the 2009 Samoa earthquake and tsunami 15 1 6 ISLAND SETTINGS CORAL REEFS AND AN OUTLINE OF THE THESIS On 29 September 2009 at 17:48 UTC an Mw 8 1 earthquake occurred along the TongaKermadec Trench A complicated fault rupture outer-rise earthquake produced bottom deformations and resulted in tsunami waves that generated localized run-ups exceeding 17 m on the island of Tutuila Fritz et al 2011 These waves claimed 34 lives on Tutuila out of a total 192 deaths for the event and caused extensive damage around the island The impact of the tsunami on Tutuila was well documented in surveys on tide gauges and on far-field deep water pressure gauges The event has been widely discussed in the literature Annunziato 2012 Beaven et al 2010 Clark et al 2011 Fritz et al 2011 Irish et al 2012 Lay et al 2010 Lynett & Lui 2011 Okal et al 2010 Roeber et al 2010 Thompson et al 2011 Zhou et al 2012 The tsunami was detected by coastal tide gauges and offshore sea-level sensors located in the Pacific Ocean The tectonic setting of the Tonga Trench has produced several tsunamis during the past hundred years Okal 2011 A similar tsunami occurred for example on 26 June 1917 after an earthquake with a magnitude of Mw 8 3 located approximately 100 km south of Samoa Gutenberg & Richter 1936 The 2009 tsunami on Tutuila and environs has become a canonical but challenging case study for numerical tsunami models The island setting the presence of both barrier and fringing reefs and the complicated bathymetry and shoreline geometry are all complicating factors of great interest By studying such an event in great detail we can learn general lessons about island tsunamis and in this tropical case about the role of their surrounding coral structures in the resulting run-up and inundation Chapter 2 of this thesis summarizes the existing literature on the role of corals on tsunami dynamics and describes the often contradictory conclusion these studies have reached Chapter 2 16 also describes my numerical modeling of the earthquake source and the subsequent tsunami using the MOST model already introduced above I describe the Tutuila Island event and the earthquake that created it A feature of particular note for this event was pre- and post-tsunami surveys of the damage to the coral structures surrounding Tutuila The run-up and inundation from this event were also documented in detail at several dozen villages around the perimeter of the island Chapter 2 also describes my numerical modeling of the earthquake source and the subsequent tsunami using the MOST model already introduced above The model results show some skill for simulated run-up variations around the island compared to observations but overall the MOST model underestimates run-up by an average of 40% We find no relationship between modeled dynamical fields and coral damage implying either that there are additional complicating factors that preclude an association or that the coral-damage survey although more detailed than any previous study was nonetheless not comprehensive enough to identify the linkages Chapter 3 of this thesis builds on the numerical simulations presented in Chapter 2 Two key factors in modeling tsunami dynamics are studied in more detail: the magnitude of the surface roughness and the near-shore bathymetry surrounding the island Reducing the roughness coefficient used in the model can improve the overall simulation of run-up for this event but the effect is far from uniform for all villages and for a significant fraction of villages the simulation is actually degraded In analyses of virtual tide gauges from the model output I show interesting resonance effects within individual bays For simulations in which the bathymetry is changed we find the basic results reflect Green s Law - overall reefs create shallower bathymetry and model simulations show a corresponding increase in wave amplitude Varying the bathymetry has a strong effect on wave resonance within the bays I studied 17 Our results point to several research directions that will be necessary for improved simulations of tsunami run-up and inundation In the highly heterogeneous littoral and coastal environments spatial variations in basal roughness will have to be considered and perhaps a mathematical reformulation of the dissipation terms used in tsunami modeling The bulk drag formulae used in MOST and many other tsunami models although possessing the advantages of convenience and simplicity are a crude representation of the highly sheared turbulent flow at these scales and their continued use will necessarily limit the predictive capabilities of such models 18 Chapter 2 EVALUATION OF THE RELATIONSHIP BETWEEN CORAL DAMAGE AND TSUNAMI DYNAMICS 2 1 INTRODUCTION Large tsunamis can wreak devastation upon the near-shore environment There is abundant documentation of the impacts on the subaerial portion of that environment but much less on the impacts on the submarine portion In many tropical settings coral reefs form an important component of the submarine environment being the cornerstone of the local ecosystems as well as shaping the near-shore bathymetry There is thus the potential for two-way interactions between reefs and tsunamis The reef bathymetry influences the tsunami dynamics and tsunami events may cause significant damage to fragile coral structures In this thesis we report on a unique opportunity to document tsunami-related damage and to evaluate whether the damage can be straightforwardly related to particular aspects of the tsunami dynamics On 29 September 2009 at 17:48 UTC an Mw 8 1 earthquake occurred along TongaKermadec Trench A complicated fault rupture produced bottom deformations and resulted in tsunami waves that generated localized run-ups exceeding 17m on the island of Tutuila These waves claimed 34 lives out of total 192 deaths for the event and caused extensive damage around the island The tsunami was detected by coastal tide gauges and offshore sea-level sensors located in Pacific Ocean The tectonic setting of the Tonga Trench has produced several tsunamis during past hundred years Okal et al 2010 Following the September 29 2009 tsunami field surveys were conducted Fritz et al 2011 to document the relationship between the physical near-shore environment and the tsunami impact According to survey results the tsunami produced a maximum run up of 17m at Poloa on the western coast of Tutuila 12m at Fagasa on the northern coast and 10m at Tula on the 19 eastern coast The survey team recorded large variations in the impacts of the tsunami along the coastal bays: a wide range of tsunami run-up wave directions and inundation The high degree of spatial variability in these various tsunami fields was somewhat of a surprise to scientists studying the event Fritz et al 2011 Okal et al 2010 Beaven et al 2010 Roeber et al 2010 but was clearly established in the field surveys and confirmed by residents The impact of this tsunami on Tutuila has proven unusually hard to simulate in numerical models Beaven et al 2010 Okal et al 2010 Roeber et al 2010 Fritz et al 2011 The discrepancies between observations and models have been variously attributed to many factors including the low-resolution bathymetry and topography the possibility of resonance over the coral reefs but most importantly the unusual complexity of the tsunami source mechanism that may have included multiple ruptures of several fault systems at the same time Beaven et al 2010 In this study we also perform a simulation of this event and aim to build upon the experience of these earlier studies: we try to eliminate any bathymetric and topographic discrepancies by using a very high-resolution 10 m dataset Lim et al 2009 further we optimize the tsunami source function by calibrating it with direct tsunami observations Both farfield pressure sensors DARTs and near-field coastal sea-level stations tide gauges were used to calibrate the tsunami source for this event We establish good agreement with the near-field tide gauges Section 3 meaning that it is unlikely that additional details in the source function would impact the simulation One challenge of modeling tsunamis in tropical settings such as this are the pervasive barrier and fringing coral reefs which create tremendous complexity in bathymetry and topography Figure 2 1 The impact of reefs in tsunami dynamics has been a topic of discussion in the literature Such analyses point to a complex picture and conclusions can occasionally appear 20 contradictory Baba et al 2008 performed numerical simulations of the 2007 Solomon Islands Tsunami to explore the effect of Great Barrier Reef GBR on tsunami wave height using the low-resolution bathymetry and ignoring sea-bottom friction and wave dispersion The results indicate reefs decrease the tsunami wave height due to the refraction and reflection Kunkel 2006 performs 1D and 2D numerical modeling of tsunami run-up for an idealized island with barrier reefs around the island and shows that coral reefs reduce tsunami run up by order of 50% However the Kunkel 2006 simulations also suggest the possibility that gaps between adjacent reefs can result in flow amplification and actually increase local wave heights Fernando et al 2005 and Fernando et al 2008 lend support to these numerical results: coral reefs protect coastline behind them but local absences of reefs cause local flow amplification due to gaps Their results are based on field observations laboratory measurements Fernando et al 2008 and interviews done by local people in Sri Lanka after the 2004 Indian Ocean tsunami However their laboratory simulations treated corals as a submerged porous barrier made of a uniform array of rods which likely oversimplifies the complex structural distribution of coral reefs Other studies find no effect or even suggest the opposite conclusions Kunkel et al 2006 Based on quantitative field observations of coral assemblages at less than 2m depth in Aceh after the 2004 Sumatra-Andaman tsunami Baird et al 2008 conclude that the limit of inundation at any particular location is determined by a combination of wave height and coastal topography and is independent of the reef quality or development prior to the tsunami Further Chatenoux et al 2006 perform statistical and observational analysis of 56 sites located in Indonesia Thailand India Sri Lanka and Maldives with a coarse resolution bathymetry and qualitative coral damage data They find that the higher the percentage of the corals the larger the 21 inundation distances behind coral reef on the coast Lastly Roeber et al 2010 identify strong correlations between the high variability of run-up and inundation along bays at Tutuila during the 2009 Samoa tsunami with the geomorphology of the island and suggest a role for high concentrations of resonance energy within particular bays All of these locations of high-energy concentration have fringing reefs extending 100 m to 200 m from the shores Based on their tsunami simulations they hypothesize that fringing reefs might amplify near-shore tsunami energy and worsen the impact of short-period dispersive waves In this chapter wave heights inundation at the coast and tsunami wave dynamics are simulated for the island of Tutuila for the 2009 tsunami The simulations are compared with field observations at the coast and wave pressure gauges DARTs located around Tutuila to find a relationship between coral damage and coastal metrics of tsunami dynamics The results contribute to an ongoing discussion about how tsunami dynamics impact corals and how in turn that damage might potentially be used to constrain tsunami simulations The remainder of the chapter is organized as follows Section 2 describes the study area the earthquake and tsunami event and the observational data sets Section 3 describes the numerical modeling of the earthquake source and the subsequent tsunami Section 4 presents an analysis of the relationships among the observational data sets and simulated tsunami fields We conclude with a Summary and Discussion that suggests an outline for future research directions 2 2 TUTUILA ISLAND The study area of my research is Tutuila Island in American Samoa the United States southernmost territory The Samoa island chain in the central South Pacific Ocean includes five islands of which Tutuila is the largest and also its center of the government It is located at roughly 14 south of the equator between longitudes 169 and 173 west Figure 2 1 The 22 following will summarize some aspects of the geometry of Tutuila Island that created unique challenges in modeling of the tsunami The island formed in the late Quaternary period from oceanic crust as the Pacific tectonic plate moved over a hotspot Terry et al 2005 Due to its volcanic formation it has rocky steep topography and bathymetry with narrow valleys that rise from ocean floor McDougall 1985 The island sits on a shallow submarine platform which then drops off to a depth of over 3000 m to meet the abyssal plain Tutuila is approximately 32 km long with a width that ranges from less than 2 km to a maximum of 9 km An insular shelf 100 m depth with an average width of 4 km extends along the entire north coast and the southwest region of the island Figure 2 1 The island is surrounded by fringing and barrier coral reefs which contain a diversity of coral reef habitats and coral species The island has possibly subsided faster than coral reefs could grow upward leaving former barrier reefs as submerged offshore banks along the seaward edges of the insular shelf Birkeland et al 2007 Fringing reefs have a width ranging from 0 to 600 m but 90% of them are less than 217 m Gelfenbaum et al 2011 The barrier reefs are located 2-3 km from the coastline The total area of coral reefs in the territory of Tutuila is approximately 300 km2 23 800 10km N 30 29 Tide Gauge 31 1 28 27 16 23 22 25 24 26 17 18 19 21 15 20 600 400 200 0 2 3 4 -200 5 6 8 9 11 7 10 12 13 -400 -600 14 -800 -1000 Figure 2 1 Tutuila Island The black lines around the island on main map indicate the fringing coral damage survey track lines The beige and light purple colors show the location of the fringing and barrier reefs The location of Tutuila Island is given as red star on the lower right map The yellow dot on the same map shows the epicenter of the 2009 Samoa Earthquake In the inset panel the location of the DART buoys used in optimizing the earthquake fault source used in the MOST simulations are shown In the main panel the location of the PagoPago Tide gauge in Tutuila is shown as red star 2 3 THE SAMOA EVENT The tsunami from the September 29 2009 earthquake was generated at the most active region of deep seismicity of Tonga Trench and reached the Samoan Island chain approximately 20 minutes later The tsunami caused devastating property damage and loss of life on Tutuila Island because of its close proximity to the epicenter and the high population density on its coasts The cause of the earthquake was the rupture of a normal fault with a moment magnitude of Mw 8 1 in the outer trench-slope at the north end of the trench near the sharp bend to the west 24 followed by two inter-plate ruptures on the nearby subduction zone with moment magnitudes of Mw 7 8 Lay et al 2010 Fault displacements measured by seismic signal Global Positioning System GPS Stations and ocean-bottom pressure sensors Beaven et al 2010 for these three separate faulting events support this picture These fault displacements led to vertical movement of the seafloor and created a complex tsunami source mechanism 2 4 OBSERVATIONS OF THE EVENT This particular tsunami afforded a unique opportunity to systematically evaluate the relationship between tsunami dynamics and coral-reef damage Six months prior to the tsunami NOAA Coral Reef Ecosystem Division CRED -certified divers performed comprehensive surveys of the reefs around Tutuila The survey lines totaled 110 km in length Observers measured the number of live dead and stressed corals sea cucumbers micro-algae crown of thorns and urchins along track lines at the depths of 10-20 m In the immediate aftermath of the tsunami the divers retraced most of the original survey lines They documented clear evidence of fresh damage at depths between 10 and 20 m This depth range was selected because of the location of the fore-reef at these depths which is where the coral population is a maximum Damage at depths shallower than 10 m was not recorded during the survey Brainard et al 2008 The divers operated a tow board of instruments as it was tugged behind a boat at a depth of about 15 m Data taken included direct observations from the diver a downward facing camera and electronic instrumentation including GPS Figure 2 2 The downward-pointed camera recorded the sea bottom habitat It also captured images at 15 s intervals NOAA-PIFSC-CRED unpublished data Selected images of broken and overturned table corals and broken branching corals are presented in Figure 2 2 The survey covered a total of 83 km linear distance within a 5 25 m horizontal zone either side of the track line Divers were careful to try to differentiate between damage directly due to the tsunami itself and land-originating debris entrained into the water Figure 2 2 Photographs of the coral survey methods and typical observations Upper left image shows the NOAA-certified diver surveying a track line with a tow board tugged behind a boat Lower left image shows the instrument suite on tow boards among which are observer data sheet gauges and timers a camera and strobes Upper right shows the table and branching corals that have been overturned lower right shows a table coral that has been broken due to the tsunami Images are taken from NOAA-Marine Debris Division The damage survey report synthesized the direct observations aggregating track-line data into groupings based on 31 nearby villages and reported the total number of damage observations Examples of such summaries are: at Onenoa Village coral damage was low with only one damaged tabulate Acropora sighting was recorded between both divers and at 26 Amaluia Village it consisted of isolated sightings of broken branching species of Pocillopora and Acropora corals Even though the survey is not an absolute measure of coral damage and involves a degree of subjectivity it is nonetheless a useful window onto the impact of tsunami dynamics in the immediate aftermath of the event Since the full coral density of the island is not available variation in coral density might influence the results NOAA-PIFSC-CRED unpublished data The datasets of the damage collected by the divers are discontinuous and unevenly distributed and this precludes classifying the data in terms of damage with conventional methods such as standard deviation or equal intervals Instead we used Jenks Natural Breaks classification method a univariate version of k-means clustering Jenks 1967 by sorting it from lowest value to highest and looking for large gaps or natural breaks This is done by seeking to minimize each class s average deviation from the class mean while maximizing each class s deviation from the means of the other classes In other words the method iteratively seeks to reduce the variance within the same classes and maximize the variance between classes The final classification in terms of coral damage is 0 no damage 1-27 low 38-63 medium 83-159 high 310 very high damage While we felt the Jenks method is most appropriate for this data our overall conclusions are not sensitive to this choice An international tsunami survey team observed and recorded tsunami run-up and inundation on the islands of the Samoan archipelago including Tutuila a week after the tsunami Fritz et al 2011 The surveys followed the tsunami survey protocols reviewed by Synolakis & Okal 2005 The team marked the values of run-up at 59 different field locations at Tutuila 27 2 5 MODELING THE EVENT 2 5 1 The Model Set-up We simulate the 2009 Samoa Event using the MOST Model Titov & Gonzales 1997 The primary metrics for comparison with observations are wave run-up and inundation MOST solves the shallow water equations with a leapfrog finite difference scheme Titov & Synolakis 1998 We define three nested bathymetric and topographic grids The earthquake dislocation is input as the tsunami source several predetermined tsunami sources were tried Zhou Wei & Titov 2012 in order to optimize the agreement with tide-gauge observations Regional bathymetry and topography datasets Table 2 1 were compiled and provided by National Geophysical Data Center NGDC and used to create the three nested grids resolutions of 360 m 60 m and 10 m respectively see Figure 2 3 Table 2 1 Sources compiled by NGDC to create the three nested grids Lim et al 2010 Source of Data Production Date NGDC 1962 to 1998 NGDC NGDC 2009 1996-2005 Gaia GeoAnalytical NAVEOCEANO 2008 SCSC USGS 2002 1996-2006 2006 Data Type Single beam echosounder Digitized coastline Multi-beam Swath Sonar Estimated depths from satellite imagery Bathymetrictopographic data Vector Data NED Digital Elevation Model Horizontal and Vertical Datum Spatial Resolution m 100 30 30-90 WGS-1984 and MHW 5 5 10 30 28 Figure 2 3 The boundaries of the nested A B and C grids used in the MOST simulations 2 5 2 Choice of the Source Function We simulated the 2009 Samoa Tsunami with a tsunami source function f calibrated to direct observations For this event several combinations of source functions f have been developed for use in previous works Zhou et al 2012 Uslu Eble & Wright 2013 and Liujuan Tang personal communication 2009 Earthquakes are modeled as a combination of unit sources S1 S2 S3 and so on Eq 1 1 Each unit source is a reverse thrust of a given strike dip and depth and each has a moment magnitude of 7 5 Gica et al 2008 The parameters for these unit sources were chosen according to the inversion results of the method described in Gica et al 2008 The tsunami source function f is converted into an initial wave height using the elastic model of Okada 1985 Okal et al 2010 This assumes the rupture of rectangular fault planes cause vertical displacements of the sea floor and that the initial water level movement is equal 29 and instantaneous with the corresponding vertical sea-bottom displacement The inversion finds the linear combination of unit sources that best matches the DART buoy data Percival et al 2011 We tested four previously optimized source function f Our choice of source function f was based on optimizing the agreement to the PagoPago tide gauge data Of the source functions we considered that of Uslu Eble & Wright 2013 performed the worst underestimating wave heights by a factor of four The other three sources all performed comparably and performed well: for the first four waves they all matched the tide-gauge wave amplitudes to within about 10% and the timing of crests and troughs to within 20 minutes We confirmed our results were robust to the choice of f by simulating time series of wave-height i e virtual tide gauges Appendix A at a model grid-point west of the island for each of the fs The outlier f for PagoPago remained an outlier and there was close agreement among the other three fs Although our results would be similar for any of these three fs we picked the source function with the best agreement to PagoPago for which 6 45 1 6 21 2 2 3 where the specific parameters of S1 and S2 are given in Table 2 2 2 5 3 Evaluation of the Model Results with DART and Tide Gauges We first compare the tsunami wave amplitudes simulated with MOST to the tide-gauge observations in PagoPago in the near field and three DART Buoys 51425 51426 and 54410 in the far field regions For their locations see Figure 2 1 The simulated amplitudes match fairly well with the recorded values particularly for PagoPago Figure 2 4 and particularly the first half-dozen fluctuations The DART buoys record high-frequency crustal Rayleigh waves in the 30 hour or so ahead of the arrival of the lower frequency tsunami waves Figure 2 5 Because the DART buoys lie farther from the source than Tutuila phase discrepancies are expected to appear which is particularly evident for DART Buoy 52425 Figure 2 5a The discrepancies between the computed and recorded values at the DART buoys are likely also due to a secondary rupture occurred during the earthquake which has been characterized in the model as one instantaneous rupture of the source function f However because of the excellent agreement with the PagoPago tide-gauge observations we are confident these discrepancies are negligible for the purpose of run-up and inundation computations around Tutuila Table 2 2 Parameters of the two tsunami unit source functions S 1 and S2 Eq 2 1 used to simulate the 2009 Samoa tsunami Unit Source 1 Longitude E Latitude S Dip 187 2330 16 2754 9 68 Rake Strike Depth m 182 1 5 00 342 4 6 57 90 2 2 6 187 8776 15 6325 57 06 Mw L km W km Slip m 8 1 100 50 1 Scaling parameter 6 45 6 21 ANALYSIS A comprehensive summary of data and analyses are presented in Table 2 3 We first evaluate whether there is any clear relationship between the two main observational datasets for this event the coral damage and tsunami run up for the 31 village sites From Figure 2 6 it is visually obvious that no such relationship exists r 0 12 Even excluding outliers 13 m run up 100 damage numbers at Vaitogi 5 m run up and 310 damage numbers at Fagatele the data still do not yield a clean story r 0 18 Across a range of run ups between 2 and 8 m coral damage is as likely to be low or very low as it is to be high or very high 31 Figure 2 4 Comparison of observed black and simulated red water surface elevations at the PagoPago tide gauge see Fig 1 in the four hours after the rupture at t 0 17:48:10 UTC on Sep 29th 2009 The MOST model estimated a maximum surface elevation of 2 3m at the tide gauge which agrees well with the recorded value We are obviously constrained by the limitations of the data that is available to analyze but on this basis no clear relationship between observed run-up and coral damage can be inferred It is not known whether this is because of limitations in the coral dataset being only a subsampling of the reef environment whether run-up is not the most relevant metric of tsunami dynamics or whether the occurrence of coral damage is actually driven by many other unknown factors and antecedent conditions 32 Figure 2 5 A comparison of the observed black and simulated red water surface elevations at three DART buoys in the four hours after the rupture at t 0 17:48:10 UTC on Sep 29th 2009 : a Buoy 51425 b Buoy 51426 and c Buoy 54401 High frequency crustal Rayleigh waves are seen ahead of the arrival of the lower-frequency tsunami waves The MOST model estimated maximum surface elevation of 0 05m at selected DART locations Table 2 3 Model simulated and field run-up differences and coral damage at selected 31 villages around Tutuila Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % -170 653 -14 259 3 52 4 31 -0 79 -18 33 -170 651 -14 26 3 6 4 08 -0 48 -11 76 -170 653 -14 26 3 9 4 41 -0 51 -11 56 -170 654 -14 259 3 4 3 75 -0 35 -9 33 -170 652 -14 26 3 69 3 59 0 1 2 79 -170 654 -14 258 3 05 2 59 0 46 17 76 3 2 25 0 75 33 33 -170 654 -14 257 AFONO1 AFONO2 Average by Village % Coral Damage Coral Dam numbers -3 05 medium 41 38 43 medium 41 33 Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % 3 1 2 16 0 94 43 52 4 2 5 89 -1 69 -28 69 -170 654 -14 258 -170 8 -14 332 -170 82 -14 331 AGUGULU 2 5 6 12 -3 62 -59 15 -170 659 -14 253 AMALAU 2 12 2 93 -0 81 -27 65 -170 658 -14 253 2 13 2 4 -0 27 -11 25 -170 83 -170 796 -14 325 -14 33 AMANAVE ASILII 5 25 6 7 74 6 81 -2 49 -0 81 -14 333 AMALUIA -170 792 AFAO AMAUA -170 623 -14 272 -170 584 -170 583 -14 273 -14 273 -170 585 -14 26 -170 571 -14 271 AUASI AUNU U -170 56 -14 286 -170 636 -14 28 -170 632 -14 281 -170 826 -170 827 -14 307 -14 307 -170 725 -14 288 -170 81 -14 299 AMOULI AOA Average by Village % Coral Damage Coral Dam numbers -59 15 lowmedium high 86 -19 45 no data no data -32 17 -11 89 -32 17 -11 89 high medium 151 -3 53 high no damage 116 low 13 5 2 5 39 -0 19 -3 53 3 2 2 91 0 29 9 97 3 36 3 1 3 38 3 -0 02 0 1 -0 59 3 33 2 2 2 23 -0 03 -1 35 3 08 3 79 -0 71 -18 73 -28 69 9 97 1 37 1 42 0 -18 73 no damage medium 38 -0 47 high 121 -3 36 low 14 -1 35 0 2 14 2 15 -0 01 -0 47 3 3 3 92 -0 62 -15 82 3 2 75 0 25 9 09 FAGAILII 5 15 4 61 5 82 6 24 -0 67 -1 63 -11 51 -26 12 -18 82 no data no data FAGASA 4 2 4 13 0 07 1 69 1 69 no data no data 3 6 39 -3 39 -53 05 3 5 6 79 -3 29 -48 45 -48 71 no damage 0 3 2 5 78 -2 58 -44 64 3 3 4 92 -1 62 -32 93 -32 93 very high 310 AVAIO FAGAMALO -170 81 -14 298 -170 81 -14 299 -170 76 -14 365 -170 611 -170 615 -14 27 -14 267 FAGAIT UA 4 75 5 3 5 2 72 1 25 2 28 35 71 83 82 59 77 no data no data -170 826 -14 329 FAILOLO 2 7 6 54 -3 84 -58 72 -58 72 high 159 -170 787 -14 335 2 65 2 75 -0 1 -3 64 -170 783 -14 336 3 2 0 97 2 23 229 9 67 86 high 83-116 -170 789 -14 336 3 75 4 85 -1 1 -22 68 -170 631 -170 63 -14 253 -14 258 MASEFAU 4 4 4 2 96 4 84 1 04 -0 44 35 14 -9 09 13 02 no data no data -170 606 -14 259 MASAUSI 3 15 2 79 0 36 12 9 12 9 no data -170 806 -14 329 4 2 4 09 0 11 2 69 no data no damage -170 582 -14 252 2 6 2 74 -0 14 -5 11 -170 581 -14 251 2 4 2 51 -0 11 -4 38 -170 834 -14 316 7 6 17 59 -9 99 -56 79 -170 834 -14 315 4 93 10 04 -5 11 -50 9 -170 834 -170 834 -14 316 -14 317 8 8 5 12 99 12 31 -4 99 -3 81 -38 41 -30 95 -170 598 -14 257 SAILELE 2 25 2 95 -0 7 -170 812 -14 325 SEET AGA -170 564 -14 256 -170 564 -14 256 FAGAT ELE LEONE NUA ONENOA POLOA T ULA 2 69 0 -4 75 no damage 0 -44 26 low 24 00 -23 73 -23 73 low 1 -2 11 low 5 -40 87 medium 63 00 5 57 5 69 -0 12 -2 11 3 8 9 52 -5 72 -60 08 3 8 7 62 -3 82 -50 13 34 Longitude Latitude Village Model Run-up m Field Run-up m Run-up difference m Difference % -53 25 -170 564 -14 256 3 24 6 93 -3 69 -170 566 -14 253 3 79 3 79 0 0 -170 815 -170 663 -14 329 -14 288 4 1 8 4 51 3 36 -0 51 -1 56 -11 31 -46 43 UT UMEA VAIT OGI Average by Village % Coral Damage -11 31 low -46 43 high Coral Dam numbers 13 96 Figure 2 6 Coral damage versus observational run-up The y-axis shows coral damage numbers reported by the survey team and the x axis is the average of the run up observations after aggregating the data into 31 separate village locations see Table 2 3 and Figure 2 1 There is no clear relationship between these two datasets We begin by presenting a comparison of the MOST simulations with observations for two representative locations For the first Figure 2 7a in the vicinity of the villages of Amaneve 35 Figure 2 7 Two examples comparing observed run-up with MOST run up and maximum wave height Coastal run up is shown as black bars observed and red bars simulated Colors show contours of maximum wave height simulated by MOST a the villages of Amaneve Failolo and Agugulu locations 4 5 & 6 in Figure 2 1 and Table 2 3 b the village of Utumea West Seetaga and Nua locations 7 8 & 9 in Figure 2 1 and Table 2 3 The survey tracks nearest these villages are also shown color-coded according to the damage scale in Figure 2 10 Failolo and Agugulu 4 5 and 6 in Figure 2 1 observed run up averaged 8 m The MOST model does poorly underestimating the run up by an average of 45% This was a region where high coral damage was documented For the second Figure 2 7 b near the villages of Utumea West Nua and Seetaga 7 8 and 9 in Figure 2 1 average run up was 4 m Here the MOST model does well simulating run up to within 2 4% The documented coral damage was very low Even though these two locations are only 3 km apart these very different run ups coral damage and simulation performance illustrate the complexities of the setting Figure 2 8 shows some of the dynamical fields simulated by MOST for this event: maximum wave amplitude panel a maximum current panel b maximum momentum flux 36 panel c and peak stress panel d respectively together with the coral damage along the survey tracks From a visual analysis there are not obvious strong relationships between coral damage and tsunami dynamical fields Take just two examples Leone and Fagatele 13 and 14 in Figure 2 1 : at Fagatele the maximum flux current and maximum amplitudes are low but coral damage is very high In contrast at Leone the maximum flux is high with low maximum amplitudes and currents and high coral damage Figure 2 8 Maximum wave amplitudes peak currents peak momentum fluxes and maximum stresses calculated from the MOST simulation of the 2009 Tutuila tsunami Also shown are the post-tsunami survey tracks with coral damage according to the color scale in Figure 2 10 The absence of a statistically significant relationship between the modeled tsunami fields and the observed damage is confirmed by averaging MOST output along each survey track and creating scatter plots of observed damage vs track-averaged model output for several relevant model fields see Appendix A 37 The clearest basis that we identify for comparing the observations and the model is the observed coral damage and run-up and the simulated run up at each of the 31 sites where observations were made Table 2 3 compiles the complete results from all the available observations We have aggregated the observed and computed run-up values into reports at 31 villages by taking the mean of the total data points at every village The complete data set for the whole island is presented graphically in Figure 2 9 and in Figure 2 10 A scatterplot of simulated vs observed run up correlates at r 0 78 demonstrating significant overall skill for the MOST model Figure 2 9 Despite this success it is also clear MOST underestimates in many places Of the 31 total villages there are 15 for which MOST underestimates run up by more than 10 percent Figure 10 shows the bulk of these are on the west side of the island although not exclusively so At only 5 villages was the run-up overestimated by more than 10% Therefore at the remaining 11 villages the model simulated the observed run up to within 10% Thus while the nearby tide-gauge observations are well simulated by MOST Figure 2 9 there is an overall tendency for MOST to underestimate run-up for this event Turning to the coral damage reports for these villages the data is suggestive of a general relationship with the accuracy of the run-up simulations Table 2 3 Of the 15 villages where the model under-estimated the run up the breakdown in terms of coral damage is 8 very high high 4 medium 3 low very low 1 no damage 1 no data For 11 villages where the model estimates run up well the coral-damage is 2 very high high 1 medium 3 low very low 4 no damage 1 no data 38 Figure 2 9 Scatter plot of simulated versus observed run-up m The blue line shows the 1to-1 line The simulated vs observed run up is correlated at r 0 78 Pearson product-moment calculation coefficient but MOST underestimates run up at many places For the 5 villages where run-up is overestimated limited coral-damage data precludes strong interpretation 1 high 1 medium 3 no data We expected to see a relationship between coral damage and tsunami dynamics since damage is directly relevant with tsunami energy and this with the dynamics of waves 39 Figure 2 10 A summary of the comparison between model run-up skill and coral damage where Rectangles indicate the difference between modeled and observed run ups The filled dots indicate the coral damage reports using the qualitative classification described in the text Lines are the color-coded survey track-lines followed to estimate the damage on corals See also Table 2 3 40 2 7 SUMMARY AND DISCUSSION Focusing on the impact of the 2009 Samoa tsunami on Tutuila Island we conducted numerical model simulations of tsunami run-up and inundation at the coastal zones We performed an integrated analysis to evaluate the relationship between the tsunami hydrodynamics and the coral damage by using numerical modeling and post-tsunami surveys The results for 31 villages on Tutuila island suggest that while the numerical model simulates run-up with a high correlation to the observations there is also a tendency to underestimate run-up in regions of high or very high coral damage and that run-up tends to be better estimated in locations where coral damage is low The dataset synthesized in Table 2 3 is a preliminary assessment of the damage to the fringing reef coral Although the 2009 Tutuila tsunami was a one-of-a-kind opportunity to investigate coral damage and tsunami dynamics the data has some limitations In particular the damage assessments inevitably involve a degree of subjectivity and the damage reports have not been normalized to the background coral density Moreover the data covers only the east and west side of Tutuila due to the bad weather conditions that existed on the south and north side of the island during the surveys In the present setting of Tutuila island the variable simulated run-up differences in our highresolution tsunami model might be due to sharp changes in bottom roughness values caused by coral reefs One expects that in reality there are strong spatial variations in roughness values Nunes et al 2008 However a constant roughness value was defined in the MOST simulations To our knowledge this is a limitation shared by most current tsunami models A model sensitivity analysis simulating the effect of varying the depths where coral reefs exist may better elucidate their role in controlling run-up on the coastlines they shield 41 While we have found some intriguing relationships between tsunami dynamics and coral damage at least in the spatial variations in the skill of the numerical simulations it is clear these are only tentative gleanings amid a great deal of variability We did not find any clear relationships between coral damage and other simulated dynamical tsunami fields Such relationships might be drawn out in more targeted and more detailed simulations but the real situation is obviously very complicated at small scales and many factors operate The failure to establish a stronger connection between the simulated dynamical tsunami fields and coral damage may be because the coral-damage dataset was not comprehensive enough or because the MOST model does not represent the correct spatial scales in roughness or bathymetry or the MOST model does not represent the processes that actually cause damage for instance damage may be inflicted on corals by retreating waves carrying debris and sand or because coral damage is inherently stochastic and unpredictable and depends unknowably on antecedent conditions Since so little is known about the damage to coral reefs by tsunamis more studies are needed to examine the influence of water depth three-dimensional effects wave-wave interactions and coral strengths In some ways it is discouraging to find no correlation between the run-up and coral datasets On the other hand it is important to establish that result and it also points to new questions The documentation of the submarine ecological impacts of a tsunami is an important goal in its own right but the tentative inference from our study the first of its kind is that the relationship of coral damage to a variety of tsunami metrics i e observed run-up and inundation modeled maximum currents fluxes and stress is not a simple one at least in our setting Tutuila represented a target of opportunity since the all-important pre-tsunami survey existed Therefore understanding in more detail the impact of two important controls: magnitude of the 42 roughness and the near-shore bathymetry is the research subject of the following chapter in understanding impact of reefs on tsunami run-up and inundation results 43 Chapter 3 THE ROLE OF CORAL REEF ROUGHNESS AND BATHYMETRY ON TSUNAMI DYNAMICS CASE STUDY: 2009 SAMOA TSUNAMI 3 1 INTRODUCTION It has proven difficult for numerical simulations of 29 September 2009 Samoa tsunami event to successfully reproduce the large variations in tsunami run-up and inundation among the many coastal villages where observations were made One challenge for numerical tsunami models in tropical settings such as this is to properly simulate the impact of the pervasive barrier and fringing coral reefs Figure 2 1 In many respects the 2009 Samoa tsunami serves as a benchmark event for tsunami numerical modeling experts to test their models in a complex submarine environment and to better understand tsunami risks for island communities like Tutuila around the world In Chapter 2 of this dissertation we showed that numerical simulations had some predictive skill but overall the model tended to underestimate run-up by about 40% we also showed that there was a high degree of variability in simulated run-up even among adjacent bays The work further suggested that understanding in more detail the impact of two important controls roughness and bathymetry would be a useful next step in understanding the impact of reefs on tsunami dynamics In this chapter we investigate the effects of reef roughness and reef bathymetry on Tutuila Island We focus on two main goals: firstly we want to understand how roughness variations affect run-up and inundation secondly we perform a model sensitivity analysis varying the bathymetry where fringing coral reefs exist to elucidate their role in controlling run-up on the coastlines they shield 44 The remainder of the chapter is organized as follows: Section 2 presents the analyses of this chapter Section 3 is the summary and discussion 3 2 ANALYSIS 3 2 1 The Impact of Changing Manning s Roughness n In the MOST numerical model the effects of bottom friction are implemented by incorporating a basal shear stress with components into the shallow water equation and parameterized by a drag formula: 2 2 3 1 where U V are the components of the velocities D is the fluid depth is density Titov et al 2003 CB is a dimensionless friction coefficient which can in turn be related to Manning s roughness parameter n as: 2 1 3 3 2 The concept of Manning s roughness was originally developed for open channel flow Manning s n values have been measured empirically for a wide variety of different materials in laboratory experiments Chow 1959 and by large-scale field studies of river flow for fully turbulent conditions Bricker et al 2015 From Eq 3 1 is depth-dependent with increasing depth implying decreased friction For example for n 0 025 s m-1 3 CB 0 006 for D 1 m but CB 0 0025 for D 15 m Bottom friction typically has the greatest impact at depths of 0 10 m and is negligible for tsunami propagation in the deep ocean Levin & Mikhail 2016 The simple form of n and its relatively straightforward implementation within shallow-water equations has led to its 45 widespread adoption in tsunami modeling Imamura et al 2008 for the representation of frictional dissipation of tsunami energy in coastal zones for both the submerged and subaerial portions of the domain In many studies a value of n 0 025 s m-1 3 has been adopted as appropriate for a smooth sea bottom or land A range of other values has also been suggested from n 0 01 to 0 1 s m-1 3 depending on the setting and basal conditions Kunkel et al 2006 Tang et al 2009 Jaffe et al 2010 Gelfenbaum G et al 2011 and Bricker et al 2015 In Chapter 2 of this thesis we selected n 0 03 s m-1 3 Both far-field pressure sensors DARTs and near-field coastal sea-level stations tide gauges were used to calibrate the tsunami source for this event Simulated wave amplitudes matched well with tide-gauge observations However the comparison of simulated and observed run-up for 31 villages in Tutuila revealed that MOST underestimates the run-up at 15 village sites for this event In this part of the research we first evaluate whether a different value of n can decrease the discrepancy between simulated and observed run-up at selected 31 villages For some villages several separate run-up observations were made For such villages we took the average of all run-up observations In the MOST model we took the highest value of computed run-up within a 3x3 grid box 30 m x 30 m around the locations of each of the observations and averaged them We also tried taking the highest value of computed run-up around the locations of all observations and compared this value with the highest value of the run-up observations at that village Finally we tried taking the value of computed run-up at the exact locations where we have run-up observations without averaging them and concluded that our results are not sensitive to which of these various methods we use for selection of simulated run-up We performed MOST simulations varying n from 0 01 to 0 1 s m-1 3 where the lowest n value represents an essentially smooth reef For n 0 01 s m-1 3 although the simulations could be 46 completed the MOST model exhibited clear signs of numerical instability in the simulations gridpoint noise and unphysical wave heights and therefore we do not present those results In Figure 3 1 we present the remaining simulations for varying n as a scatterplot of observed vs simulated run up at 31 villages around Tutuila Locations of the villages are shown in Figure 2 1 A comprehensive summary of data and analyses is presented at Table A1 Figure 3 1 A comparison of model and field run-up for the simulations with varying n at 31 villages in Tutuila Island The blue line shows the 1:1 line Points falling on or close to the blue line show where there is good agreement between simulations and observations Overall for most of the villages the variation of run up with n is straightforward with higher values of n having less run-up For some villages however the relationship is not monotonic and the highest simulated run-up does not always occur for the lowest value of n Thus at individual locations the complex patterns of refraction and reflection and nonlinear interactions can complicate the relationship between dissipation and run-up This is also clear 47 from the different spread among the simulated run-ups for different values of n at individual villages At some villages there is very little spread in simulated run-up values as n varies e g Fagatele village observed run-up 4 92 m the spread is 4% of the mean simulated value whereas at others the spread is large e g Poloa village observed run-up 13 5 m the spread is 76% of the mean simulated value 1km 1km Figure 3 2 Simulated maximum wave amplitudes are shown for the bays near the villages of Seetaga top panels and Amaneve lower panels for n 0 08 0 04 0 02 and 0 015 s m-1 3 The pre-tsunami shoreline is shown as a thin black line Colors inland of that line therefore show the degree of inundation Village locations are shown as red stars Black arrows indicate tsunami direction from its source 48 The results are mixed with regard to whether different values of n improve the simulated run up compared to observations The model estimation of run-up is improved by changing n for some villages and doesn t change significantly at others Of the total 31 villages at 10 villages the difference between observed and estimated run-up is smallest when n 0 02 s m-1 3 At 9 villages the closest match occurs for n 0 03 s m1 3 At 5 villages the closest match occurs for n 0 015 s m-1 3 For the remaining 6 villages two villages each achieve the closest match to observations when n 0 04 s m-1 3 n 0 06 s m-1 3 and n 0 08 s m-1 3 In our simulations n is uniform throughout the model domain which obviously does not capture the real situation of a heterogeneous littoral and coastal environment Equations 3 1 and 3 2 represent dissipation in these environments An obvious next step in tsunami modeling is to evaluate whether variations in basal conditions might be represented by spatial variability in n Introducing spatial variations in n would add tunable degrees of freedom in the model and in practical applications it would be important not to over-constrain a model Nonetheless evaluating whether spatial variations in n might be optimized to provide agreement with detailed measurements in case studies such as ours would represent a best-case for the ability of equations to simulate run-up in these events Next we evaluate the spatial patterns of the maximum tsunami amplitudes for two representative villages Seetaga and Amaneve as a function of n In Chapter 2 we showed that for standard parameters n 0 03 s m-1 3 MOST successfully simulated the run-up observations at Seetaga agreeing to within 2 4% On the other hand just 3 km southeast from Seetaga MOST did a relatively poor job for the village of Amaneve MOST underestimated observed run-up by 45% This very different simulation performance illustrates the complexities of the setting and thus 49 makes Seetaga and Amaneve suitable to use for the comparison of case studies for change in n and reef bathymetry The simulated maximum wave amplitude fields are shown in Figure 3 2a-d for Seetaga and in Figure 3 2e-f for Amaneve For Seetaga n 0 03 s m-1 3 provides the best agreement in run-up 5 69 m observed 5 57 m MOST whereas for Amaneve n 0 02 s m-1 3 gives closest agreement 7 74 m observed 6 32 m MOST For higher values of n the wave amplitude fields vary smoothly on scales of a few hundred meters with the highest values of run-up are found in the center of both bays suggesting a refraction or focusing of wave energy there As n is reduced from 0 04 to 0 02 s m-1 3 some significant localized increases in wave amplitude and inundation appear particularly in Amaneve bay where wave amplitude approaches double that of the n 0 08 s m-1 3 simulations For n 0 015 s m-1 3 wave amplitudes have increase throughout each bay and the increases are clearly co-located with the clusters of near-surface reef structures that are dotted around the perimeter of each bay and which can be seen in detail in Figure 3 3a and Figure 3 3c Figure 3 2 also shows evidence that lower values of n have some impact offshore with a more complex wave pattern and more small-scale structure perhaps indicating more scattering of wave energy and a cascade to smaller scales We next turn to a comparison of water surface elevations estimated for shallow-water virtual tide gauges near the coasts of Seetaga and Amaneve for varying n Figure 3 3b-d At these villages the wave amplitude maximizes during the first surge For the Seetaga tide gauge the maximum water elevations are 3 1 3 2 and 3 3 m for n 0 08 0 04 and 0 02 m s-1 3 respectively Figure 3 3b At Amaneve the maximum water elevations are 3 1 3 4 and 3 9 m for n 0 08 0 04 and 0 02 m s-1 3 respectively Figure 3 3d The various values of n do not affect the timing of the waves and have most impact on the amplitude of the first wave 50 Both Seetaga and Amaneve tide gauges show some evidence of resonance or constructive interference between approaching and receding waves Figure 3 3 We generally expect successive wave heights to decrease in amplitude after several waves but at both sites wave elevations increase between the fourth and sixth waves then decrease again after the seventh wave At the tide gauge close to Seetaga after the third wave approaching and reflecting waves from the reefs interfere and form constructive superposed waves Another intriguing thing to see at the Amaneve virtual tide gauge is that the tsunami waves drop off in amplitude more quickly than at Seetaga and have a less sinusoidal form By 1 5 hr after the first waves the tsunami has become a distorted noisy wave-train This behavior indicates more nonlinearity and more overall dissipation compared to Seetaga perhaps because of the more complicated reef structures within the bay that cause the waves to be dispersed in the reef areas Figure 3 3a compared with Figure 3 3c Figure 3 3 Comparison of water surface elevations at selected virtual tide gauges in the near-shore regions of villages of Seetaga Fig a-b and Amaneve Fig c-d Maps show the location of the 51 villages as red stars and the locations of the virtual tide gauges are shown as blue square In b and d water surface elevations are given for varying n during the 4 h after the fault rupture at t 0 3 2 2 Changes in Reef Bathymetry In this section we evaluate how variations in coral reef bathymetry affect the tsunami run-up and inundation limits inside the bays at the 31 villages around Tutuila We generate synthetic bathymetries for the B and C grids by first removing all bathymetry with less than 90 m depth i e bathymetry in the range 0 to 90 m is set equal to 90 m Let be the real bathymetry and let be the extreme flattened bathymetry We performed several experiments varying the bathymetry smoothly between these limits using the parameter r in the following equation: 1 3 3 Thus r 1 corresponds to the real bathymetry and r 0 to the flattened bathymetry We varied r from 0 to 1 in increments of 0 2 The resulting bathymetries are shown in Figure 3 4 In all simulations a value of Manning s roughness of n 0 03 m s-1 3 has been implemented We first focus on maximum wave amplitudes in the MOST simulations with these varying bathymetries implemented The wave-amplitude fields near Seetaga and Amaneve are shown in Figure 3 5 and the results for simulated run-up for villages around Tutuila are given in Table A2 In general we find that wave amplitudes and run-up are smaller when the reef bathymetry is removed contrary to the common belief that reefs protect reef-surrounded coasts from tsunamis Baba et al 2008 Kunkel et al 2006 When there is no reef r 0 the tsunami run-up achieves its lowest value at 22 out of the 31 villages For the remaining 9 villages 4 villages achieve the smallest run- 52 up when r 0 2 2 villages achieve the smallest run-up when r 0 4 and 3 villages achieve the smallest run-up when r 0 6 Table A2 Figure 3 4 C grids of synthetic bathymetry generated from Eqn 3 shown for the west side of Tutuila Island r 1 original bathymetry r 0 no reefs from 0 m to 90 m depths The same basic behavior is observed in the maximum wave amplitude fields near Seetaga and Amaneve Figure 3 5 Wave amplitudes are larger for the real reef bathymetry than for the flattened bathymetry The MOST model estimates the maximum water surface elevations at Seetaga village as 3 2 2 2 and 2 1 m for r 1 0 0 8 and r 0 0 respectively At Amaneve the maximum water surface elevations at the tide gauge are 3 4 2 8 2 1 m for r 1 0 0 8 and 0 0 respectively These simulations are most simply explained as a manifestation of Green s Law wave amplitudes increase when reefs are present because of the shoreward-shoaling bathymetry and the extra dissipation occurring over the shallower depths is not enough to offset this basic tendency When the reefs are removed the impinging tsunami waves encounter more of a wall and are 53 predominantly reflected rather than dissipated The inundation limits can be seen in Figure 3 5 from the color shading that lies inland of the pre-tsunami shoreline It is interesting to note that the inundation limits are not a strong function of the offshore bathymetry despite the very large variations we ve implemented It suggests that inundation is determined more by the coastal geometry than the tsunami wave dynamics in these bays 1km 1km Figure 3 5 Simulated maximum wave amplitudes are shown for the bays near the villages of Seetaga top panels and Amaneve bottom panel for different bathymetry r 0 0 0 4 0 8 and 1 0 The pre-tsunami shoreline is shown as a thin black line Colors inland of that line therefore show the degree of inundation Village locations are shown as red stars Black arrows indicate tsunami direction We also present simulated wave heights calculated at the same virtual tide gauges near Seetaga and Amaneve villages Figure 3 6 In contrast to the results for varying n changing the 54 bathymetry has a big impact on the wave dynamics recorded at the tide gauges As the bathymetry is progressively removed 0 the first waves arrive 5 to 10 minutes earlier and the period of successive waves gets shorter consistent with faster velocities in deeper water Figure 3 6 Comparison of water surface elevations at selected virtual tide gauges in the near-shore regions of villages of Seetaga and Amaneve Refer to Figure 3 3 for location of gauges Water surface elevations are given for varying r in the 4 h after the fault rupture at t 0 17:48:10 UTC on Sep 29th 2009 A notable feature of the simulations is that varying the bathymetry has a big impact on the wave resonance that was observed to be particularly prominent in Seetaga bay Figure 3 5a As the bathymetry is progressively removed 0 the increase in amplitude of waves 4 to 7 seen in Seetaga Bay diminishes and eventually disappears Obviously then the bathymetry is playing an 55 important role in the constructive interference of reflected and incident waves As the bathymetry is progressively removed the first waves arrive earlier and the period of successive waves gets longer consistent with faster velocities in deeper water The dataset synthesized in Table A1 and A2 are summaries of the model results In a related study Roeber et al 2010 showed the shortening of wave period by comparing their model results with the reef distribution around the island In locations of observed higher runup i e Poloa Fagasa Tula and Pago Pago the reefs extend from 0 m to at least 100 m from the shore The reefs capture the tsunami waves and their energy and form wave resonances around the Tutuila Island Wave resonances formed inside the bay cause increase in wave run-up on the coast The reefs trap the tsunami energy and worsen the impact of short period waves Roeber et al 2010 3 1 DISCUSSION The impact of the 2009 Samoa tsunami dynamics on the coral reefs of Tutuila island has been the main focus of this study We conducted numerical model simulations of tsunami run-up and inundation at the coastal zones for varying Manning roughness n and reef bathymetry For 31 villages on Tutuila island there is an overall tendency that when n decreases in the model the estimated run-up values increase However the results are mixed with regard to whether different values of n improve the simulated run up compared to observations: the model estimation of run-up is improved by changing n in the model at some villages and doesn t change significantly at others 56 Manning roughness n was spatially uniform in the simulations Although this is standard practice in most current tsunami models arguably such an approximation is only valid at large scales and cannot capture the real situation of a heterogeneous reef environment An important frontier in tsunami modeling research is whether in pursuit of more accurate predictions models should incorporate spatially varying n or whether the mathematical representation of the dissipation Eqns 1 and 2 must be reformulated When we remove reefs the modelled run-up values on the coast decrease consistent with Green s law A notable feature of the simulations is that varying the bathymetry has a big impact on the wave resonance that was observed The bathymetry is playing a significant role in the constructive interference of reflected and incident waves Inundation was not strongly impacted by varying the bathymetry which suggests it is determined more by the coastal geometry than the tsunami wave dynamics Rather than focusing on individual structures we focused on reef bathymetry broadly around the island and to some degree our results must depend on the proximity of the reefs to the shore Broader reefs further from shore for instance might dissipate wave energy enough to reduce onshore run up Given the degree of complexity we found in simulations it would for instance be hazardous to conclude that reefs provide universal protection for their inshore coastlines Chapter 4 CONCLUDING REMARKS This study is the first attempt to quantify the relation between corals tsunami run-up and tsunami dynamics The role of reefs in tsunami dynamics remains enigmatic Our results add to a body of literature exploring the important question: What is the role of reefs on tsunami dynamics for an island setting The second chapter concludes that non-linear shallow water models have a 57 tendency to underestimate run-up in regions of high or very high coral damage and that run-up tends to be better estimated in locations where coral damage is low No clear relationship has been observed between coral damage and tsunami dynamics with the existing coral damage data of 2009 Samoa Tsunami In Chapter 3 at the first set of our experiments for 31 villages on Tutuila island there is an overall tendency that when n decreases in the model the estimated run-up values increase However the model estimation of run-up is improved by changing n in the model at some villages and doesn t change significantly at others Variation of Manning s n does not change the accuracy of run-up In the second set of experiments we removed reef bathymetry and found that run-up decreases with removing the reef bathymetry Rather than focusing on individual structures we focused on reef bathymetry broadly around the island and to some degree our results must depend on the proximity of the reefs to the shore Broader reefs further from shore for instance might dissipate wave energy enough to reduce onshore run up Given the degree of complexity we found in simulations it would for instance be hazardous to conclude that reefs provide universal protection for their inshore coastlines We also found that the geometry of the bays is a more important factor than the bathymetry on determining the limits on inundation To conclude while the impact of coral reefs on the dynamics of tsunamis impinging on tropical islands is obviously complicated and depends on many factors our results reinforce a focus on two key issues that call for further 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N Titov V V Kanoglu U & Gonzales F I 2008 Validation and Verification of Tsunami Numerical Models Pure and Applied Geophysics 165 11 2197-2228 Synolakis C & Kanoglu U 2009 Tsunami Modeling: Development of Benchmarked Models In P Lynette Ed Nonlinear Wave Dynamics 1 pp 127-145 Novosibirsik: World Scientific Singapore Tang L Titov V V & Chamberline C D 2009 Development Testing and Applications of Site-specific Tsunami Inundation Models for Real-time Forecasting Journal of Geophysical Research 114 C12 114-124 Tang L Titov V V Bernard E Wei Y Chamberline C Newman J C Spillane M 2012 Direct Energy Estimation of the 2011 Japan Tsunami Using Deep-Ocean Pressure Measurements Journal of Geophysics Research Letters 117 C8 1-28 Tappin D R Watts P & Grilli S T 2008 The Papua New Guinea Tsunami of 17 July 1998: Anatomy of a Catastrophic Event Natural Hazards Earth Syst Sci 8 2 243-266 Terry J P Kostaschuk R A & Garimella S 2005 Sediment Deposition Rate in the Falefa River Basin Upolu Island Samoa Journal of Environmental Radioactivity 86 1 45-63 Thompson R Fine I Rabinovich A Muhaly S Davis E Heesemann M & Krassovski M 2011 Observation of the 2009 Samoa Tsunami by the NEPTUNE-Canada Cabled Observatory: Test Data for an Operational Regional Tsunami Forecast Model Geophysical Research Letters 38 11 L11701-L11708 63 Tinti S & Tonini R 2013 Thr UBO-TSUFD Tsunami Inundation Model: Validation and Application to a Tsunami Case Study Focused on the City of Catania Italy Natural Hazard and Earth System Sciences 13 7 1795-1816 Titov V V 1997 Numerical Modeling of Long Wave Run-up University of Southern California 58 05 2613-2628 Titov V V 2009 Tsunami Forecasting In A N Bernard A R Robinson A N Bernard & A R Robinson Eds The Sea Volume 15: Tsunamis Vol 15 pp 371-400 Cambridge MA USA: Harvard University Press Titov V V & Gonzales F I 1997 Implementation and Testing of the Method of Splitting Tsunami MOST Model NOAA Technical Memorandum ERL PMEL 11 30 Titov V V & Synolakis C E 1998 Numerical Modeling of Tidal Wave Run-up Journal of Waterway Port Coastal and Ocean Engineering 124 157-171 Titov V V Gonzales F I Bernard E N Eble M C Motfjeld H O Newman J C & Venturato A J 2003 Real-time Tsunami Forecasting: Challenges and Solutions Natural Hazards 35 35-41 Titov V V Gonzales F I Motfjeld H O & Venturato A J 2003 NOAA TIME Seattle Tsunami Mapping Project: Procedures Data sources and Products Seattle: NOAA USGS 2005 1 1 USGS Retrieved from http: earthquake usgs gov: http: earthquake usgs gov earthquakes eqinthenews 2004 us2004slav us2004slav php Uslu B Eble M & Wright L 2013 A Tsunami Forecast Model for PagoPago Harbor American Samoa NOAA Technical Memorandum 19 1 Wei Y Bernard E Tang E Weiss L Titov V Weiss R Kanoglu U 2008 RealTime Experimental Forecast of the Peruvian Tsunami of August 2007 for U S Coastlines Geophysical Research Letters 35 4 1-7 Whitmore P 2009 Tsunami Warning Systems In E Bernard A R Robinson & E B Robinson Ed The Sea Vol 15 pp 14-28 Cambridge USA: Harvard University Press Yalciner A C Zaytsev A Aytore B Insel I Heidarzadeh M Kian R & Imamura F 2014 A Possible Submarine Landslide and Associated Tsunami at the Northwest Nile Delta Mediterranean Sea Oceanography 27 2 68-75 Zahibo N Pelinovsky E Yalciner A C Kurkin A Koselkov A & Zaitsev A 2003 The 1867 Virgin Island Tsunami Natural Hazards and Earth System Sciences 3 367-376 Zahibo N Pelinovsky E Yalciner A Zaytsev A Talipova T Nikolkina I & Chernov A 2011 Trans-Atlantic propagation of 1755 tsunami and its effects on the French West Indies Open Oceanography Journal 8 5 30-41 Zhou H Wei Y & Titov V V 2012 Dispersive Modeling of the 2009 Samoa Tsunami Geophysical Research Letters 39 16 603-610 64 APPENDIX A We construct scatterplots by averaging the MOST output for maximum amplitude current flux and stress along each survey track associated with a village Figure 2 1 and plotting against the corresponding observed coral-damage numbers The correlations for each scatter plot are given in the caption of Figure A1 None are statistically significant Figure A-1 Scatter plots of coral damage on the x-axis vs a maximum amplitude b maximum current c maximum flux and d maximum stress along coral damage track-lines The dynamical fields are averaged over each track-lines associated with each village Figure 2 1 to evaluate any relationship between coral damage and dynamica l fields 65 APPENDIX B These tables present MOST model output for maximum amplitude along selected villages Figure 2 1 for locations of the villages There is a tendency that run-up increases with decreasing Manning and the model better estimates run-up Table B1 There is also a tendency that run-up decreases with removing reefs Table B2 66 Table B1 Model simulated run-up for different Manning s roughness n values at 31 villages around Tutuila Villages LAUILI AMALAU AFONO1 AFONO2 AVAIO MASEFAU AMAUA FAGAITUA MASAUSI SAILELE AOA AMOULI ONENOA AUASI TULA AUNUU POLOA AMANAVE FAGAILII FAILOLO AGUGULU UTUMEA SEETAGA FAGAMALO NUA AFAO ASILII AMALUIA LEONE FAGATELE Field Run-up Run-up Run-up Run-up Run-up Run-up Run-up m n 0 08 n 0 06 n 0 04 n 0 03 n 0 02 n 0 015 3 36 1 35 1 58 1 78 1 80 2 12 2 35 2 5 1 46 1 49 1 52 2 12 1 55 1 72 2 18 1 92 1 98 2 06 3 00 2 20 2 45 3 8 2 04 2 11 2 21 3 50 2 41 2 68 3 7 2 81 2 95 3 12 3 15 3 59 3 98 4 3 32 3 30 3 27 4 20 3 37 3 74 2 91 3 05 3 23 3 43 3 20 3 81 4 23 3 5 3 60 4 26 5 02 4 75 5 31 5 90 2 79 2 46 2 48 2 50 3 15 2 56 2 84 2 95 1 99 2 01 2 01 2 25 2 00 2 23 2 23 1 36 1 60 1 82 2 20 2 05 2 28 3 15 2 76 3 18 3 53 3 20 4 18 4 64 3 6 2 20 2 21 2 23 2 50 2 24 2 48 3 79 2 57 3 06 3 47 3 08 3 73 4 14 7 3 11 3 44 3 66 3 80 3 89 4 32 2 15 1 54 1 71 1 85 2 14 2 03 2 25 13 23 6 10 6 49 7 03 7 30 7 62 10 74 7 74 4 69 4 85 4 93 5 25 6 32 5 79 6 4 77 4 78 4 84 4 90 5 33 7 90 6 54 2 87 2 79 2 69 2 70 3 29 3 14 6 12 1 93 2 11 2 35 2 50 2 23 2 43 4 51 3 05 3 15 3 76 4 00 4 52 5 68 5 69 4 98 5 09 5 50 5 57 6 29 5 19 6 39 2 88 3 22 3 37 3 30 3 30 15 00 4 09 3 61 3 86 4 15 4 20 3 85 3 86 5 89 3 46 3 83 4 10 4 20 3 98 4 74 6 81 5 05 5 30 5 66 6 00 6 94 5 74 5 39 5 14 5 26 5 26 5 20 5 60 6 21 2 8 1 26 1 89 2 58 3 00 2 66 2 01 4 92 3 12 3 21 3 28 3 30 3 33 3 33 67 Table B2 Model simulated run-up for different r values representing varying bathymetry at 31 villages around Tutuila Villages Field Run-up m Run-up r 1 LAUILI AMALAU AFONO2 AFONO1 AVAIO MASEFAU AMAUA FAGAITUA MASAUSI SAILELE AOA AMOULI ONENOA AUASI TULA AUNUU POLOA AMANAVE FAGAILII FAILOLO AGUGULU UTUMEA SEETAGA FAGAMALO NUA AFAO ASILII AMALUIA LEONE FAGATELE 3 36 2 5 2 18 3 8 3 7 4 2 91 3 5 2 79 2 95 2 23 3 15 3 6 3 79 7 2 15 13 23 7 74 6 6 54 6 12 4 51 5 69 6 39 4 09 5 89 6 81 5 39 2 8 4 92 1 8 2 12 3 3 5 3 15 4 2 3 2 4 75 3 15 2 25 2 2 3 2 2 5 3 08 3 8 2 14 7 3 5 25 4 9 2 7 2 5 4 5 57 3 3 4 2 4 2 6 5 2 3 3 3 Run-up Run-up Run-up Run-up Run-up r 0 8 r 0 6 r 0 4 r 0 2 r 0 0 1 13 2 05 2 34 2 70 2 46 2 80 1 93 3 14 2 15 1 55 1 90 3 67 1 69 2 24 2 38 2 07 5 32 3 29 4 75 2 11 1 93 3 12 3 71 1 99 2 78 2 87 4 14 4 50 3 44 2 23 1 05 1 89 2 30 2 79 2 25 2 49 1 86 2 78 2 10 1 63 1 76 2 87 1 41 2 16 2 22 1 90 5 12 3 06 4 36 2 07 1 99 2 86 3 30 1 92 2 46 2 80 4 34 4 15 2 69 1 85 0 98 1 76 2 33 2 75 2 25 2 58 1 79 2 86 1 99 1 47 1 72 2 93 1 42 2 02 2 07 1 78 4 79 2 85 4 08 2 10 1 96 2 86 3 43 1 84 2 53 2 65 3 91 4 06 2 75 1 88 0 94 1 65 2 24 2 77 2 27 2 61 1 75 2 88 1 95 1 49 1 69 2 87 1 40 2 02 2 07 1 78 4 46 2 73 3 82 2 02 1 98 2 88 3 46 1 81 2 54 2 60 3 96 4 01 2 69 1 85 0 89 1 54 2 17 2 72 2 30 2 70 1 67 2 95 1 98 1 43 1 63 2 80 1 33 1 88 1 98 1 67 4 14 2 59 3 56 1 95 1 94 2 92 3 59 1 72 2 17 2 64 3 83 3 86 2 62 1 75 68 VITA Author of this research is born and raised in Turkey She came to US to study her PhD At University of Washington with the privilege of getting fellowship from Joint Institute for the Study of Atmosphere and Ocean University of Washington She gained interest into tsunami science starting from her senior level in Middle East Technical University Ankara Turkey She published two peer-reviewed papers and coauthored three papers during her education She takes motivation of working on tsunami science by thinking that she can save a person s life from tsunamis She can speak English Turkish and German fluently She likes to ski swim and travel Education: PhD: Department of Earth and Space Sciences 2009-2016 University of Washington Seattle WA USA B Sc & M S : Civil Engineering Hydromechanics & Ocean 2002-2009 Middle East Technical University-METU Ankara Turkey Publications: 1 Dilmen D I 2009 GIS Based Tsunami Inundation Maps Case Studies From Mediterranean Masters Thesis Middle East Technical University Civil Engineering Ankara Turkey 2 Dilmen D I Kemec S Yalciner A C Duzgun S Zaytsev A 2014 Development of Tsunami Inundation Map in Detecting Tsunami Risk in Gulf of Fethiye Turkey Pure Appl Geophys 2014 Springer Basel 3 Dilmen D I Titov V V Roe G H 2015 Evaluation of the Relationship Between Coral Damage and Tsunami Dynamics Case Study: 2009 Samoa Tsunami Pure Appl Geophys 2015 Springer Basel 4 Kemec S Duzgun S Zlatanova S Dilmen D I Yalciner A C 2010 Selecting 3D Urban Visualisation Models for Disaster Management: Fethiye Tsunami Inundation Case Proceedings of TIEMS 2009 Annual Conference Istanbul 5 Pelinovsky E Zahibo N Yalciner A Zaitsev A Talipova T Chernov A Insel I Dilmen D Ozer C Nikokina I 2009 1755 Tsunami Propagation in Atlantics and its Effects on the French West Indies Geophysical Research Abstracts Vol 11 EGU2009502 2009 EGU General Assembly 6 Yalciner A Y Gulkan P Dilmen D I Aytore B Ayca A Insel I Zaytsev A 2014 Evaluation of Tsunami Scenarious for Western Peoponnese Greece Bollettino do Geofisica Teorica ed Applicata Related Work Experience: 1 Research GSRA and Teaching Assistant TA at University of Washington Seattle 2 Project Engineer at European Union Funded Research Projects SEEHELLARC and TRANSFER METU Turkey 70
    • Dovinh Ong, Amanda - M.S. Research Paper
      OBSERVATIONS OF JOINTS PRESENT IN THE LAWTON CLAY MEMBER OF THE VASHON STADE, EXPOSED AT A COASTAL BLUFF IN DISCOVERY PARK, SEATTLE, WASHINGTON 2016, Dovinh Ong,Amanda,Amanda Dovinh Ong OBSERVATIONS OF JOINTS PRESENT IN THE LAWTON CLAY MEMBER OF THE VASHON STADE EXPOSED AT A COASTAL BLUFF IN DISCOVERY PARK SEATTLE WASHINGTON Amanda Dovinh Ong A report prepared in partial fulfillment of the requirements for the degree of MASTERS OF EARTH AND SPACE SCIENCES: APPLIED GEOSCIENCES UNIVERSITY OF WASHINGTON JUNE 2016 Project Mentor: Kathy Troost Reading Committee: Dr Juliet Crider Dr Joanne Bourgeois MESSAGe Technical Report Number: 038 i Copyright 2016 Amanda Dovinh Ong ii ABSTRACT The southwest-facing coastal bluff present at Discovery Park Seattle Washington displays distinctive joints throughout the exposed Lawton Clay Member Exhibiting a characteristic local stratigraphy of permeable advance outwash over the impermeable proglacial lacustrine clay this bluff is located in an area of Seattle at high risk from landslides This project addressed the relationship between the joints observed at this coastal bluff and the coherency of the bluff as a whole through remote sensing and field measurements Aerial drone photography taken of the bluff was processed through a photogrammetry software to produce a 3-dimensional Structure from Motion model allowing for a digital manipulation and broad examination of the bluff not possible by foot Stereonet plots produced from these measurements provided insight into patterns of varying joint strike along a horizontal transect of the observed bluff face Taken together these two visualizations provided a better picture of the possible chicken-and-egg interaction of the joints and bluff topography they demonstrated the likelihood that the joint formation at the bluff was most likely to be primarily influenced by the local topography of the bluff over other sources of possible tensional stress in the immediate area iii TABLE OF CONTENTS LIST OF FIGURES v ACKNOWLEDGEMENTS vi 1 0 INTRODUCTION 1 2 0 BACKGROUND 1 2 1 Study Site 2 2 2 Local Geologic Setting 2 2 3 Local Geologic Hazards 3 2 4 Prior Work on Joints in the Lawton Clay 4 3 0 METHODS 5 3 1 Fieldwork 5 3 11 Joint Measurements 5 3 12 UAV Survey 6 3 13 Trimble Geo7x GPS Measurements 7 3 2 Post-processing 7 4 0 RESULTS 8 4 1 GPS and SfM 8 4 2 Field Observations 8 4 3 Joint Orientations 11 5 0 DISCUSSION 12 5 1 Joint Origin Hypotheses 12 5 2 Further Work 14 5 21 Measuring Rate and Volume of Bluff Retreat 15 6 0 CONCLUSIONS 15 7 0 REFERENCES 40 8 0 APPENDICES 43 iv LIST OF FIGURES Figure 1: The Seattle area relative to the Puget Sound Lake Washington and Bainbridge Island Figure 2: Map of Discovery Park Figure 3: Generalized stratigraphic profile of Puget Sound glacial units Figure 4: Photo from 3 6 2015 marking out unit locations on the bluff Figure 5: Landslides mapped using LiDAR on a shaded relief map generated from LiDAR-derived bare earth DEM Figure 6: Landslides along Magnolia bluff mapped by hand and by LiDAR Figure 7: Idealized stratigraphic representation of perched aquifer Figure 8: Stratigraphic profile of type section at Discovery Park Figure 9: Eroding wedge example Figure 10: Site of sudden sheet failure witnessed by me and Dr Juliet Crider Figure 11: 4-part figure of example joints Figure 12: Map showing horizontal placement of tape measure Figure 13: Lateral extent of drone survey Figure 14: Beach view of SfM model Figure 15: Domains marked out on SfM model of bluff Figure 16: Example plumose fracture structures in clay Figure 17: Example ripple bedding structures in clay Figure 18: Example stairstepping series of joints Figure 19: Domains and bluff angles marked out on SfM model Figure 20: Stereonet plots of all planes measured and of the poles to the plane Figure 21: Stereonets with only parallel joints plotted and perpendicular joints plotted Figure 22: Scatterplot of joint location vs joint orientation annotated with the average bluff and parallel joint strikes for each domain Figure 23: Domains bluff angles and stereonet plots marked out on SfM model v ACKNOWLEDGEMENTS A great thanks to Dr Juliet Crider and Ms Kathy Troost the Program Director and Program Coordinator of the Masters in Earth and Space Sciences Applied Geosciences MESSAGe Program respectively for their academic guidance and suggestions as my mentors I m grateful to Kathy Troost especially for the opportunity to work on this project as my program internship and Dr Crider for her help in narrowing the focus and direction of my research to something manageable In addition to Dr Crider I thank Dr Jody Bourgeois for being a part of my reading committee and Mr James Bush for my peer review and assistance with initial edits Mr Tait Russell proved to be an invaluable help in seeing this project through to the end and I can t thank him enough for allowing me access to his personal drone and technical expertise with Structure from Motion I also thank my parents Toan and Mary Ong and my extended family for their continued support through my academic studies vi 1 0 INTRODUCTION The intent of this project is to determine the relationship of the joints present in the Lawton Clay as exposed at a coastal bluff in Discovery Park Seattle Washington to the general shape of the bluff itself through a combination of field measurement and remote sensing There are two main scenarios to be addressed: 1 Is it accurate to consider these joints representative of the frequency and prevalence of such fractures elsewhere in the unit 2 What is the origin of these joints and are these observed joints a direct result of the topography of the bluff and erosive conditions contributing to a distinct pattern of failure If the former this study seeks to consider the general significance of these joints as potential zones of increased groundwater movement through an otherwise-impermeable unit from the overlying aquifer If the latter what precise processes contribute to consistent forms of bluff failure and is it appropriate to take these failure planes as indicative of further failures within the Lawton Clay as a whole Examining the orientation of the joints relative to the orientation of the bluff may provide insight into greater jointrelated patterns of bluff failure at exposures of the Lawton Clay elsewhere in the Puget Sound 2 0 BACKGROUND The observations and analyses in this report are primarily focused upon the widespread if locally clustered jointing across the study site with the intent of interpreting the possible origin of these joints Of particular interest is the fact that these joints are present in exposures of glacial lacustrine clay and transitionary lenses of clay silt sand Hencher 2012 and Selby 1993 both define joints as discontinuities in rock distinguished from faults by the lack of displacement along a plane parallel to the joint surface Hencher 2012 emphasizes that joint formation including orientation roughness persistence and structure depends upon conditions of local stress and other factors such as material strength and water pressure He outlines three forms of joint development: primary from the original formation stresses of the geologic unit secondary from the tectonic and gravitational deformation and tertiary from the geomorphological stresses and local weathering Primary formation stresses can be ruled out for the joints in the Lawton Clay since the joints at the study site cross-cut fine-grained planarbedded glacial deposits Thus two possible joint origins remain: tectonic or geomorphic weathering stresses The study site is also an area of rapid erosional change general visual observations spaced over the course of a year support the hypothesis that the study site is prone to a combination of sliding blocky and sheet failures Although the origin of the joints along which these failures occur will be discussed later in the body of the paper further visual observations of water draining out of the transitionary contact between the overlying sand unit and underlying clay unit may indicate conditions where the secondary hydraulic conductivity of the clay unit may control the rate of groundwater movement through that portion of the bluff in addition to compromising the stability of the bluff along wetted fracture planes Stephenson et al 1988 note that the difference between the hydraulic conductivity of unweathered and fractured lacustrine silt and clay glacial deposits can be upwards of 5 orders of magnitude the hydraulic conductivity of unweathered lacustrine silt and clay ranges between 10 -4 10-8 m day while the fractured hydraulic conductivity ranges between 10-3 and 10-6 m day Selby 1993 describes water-infiltrated mudrocks and other fine-grained deposits to be subject to the weakening of diagenetic bonds taken in conjunction with the softening of the material that occurs when water content increases in the apertures of joints the presence of water may exacerbate the failure rate of the joints at the study site or possibly obscure the source of the original joint formation stresses 1 2 1 Study Site The site of interest is a southwest-facing northwest-to-southeast trending coastal bluff located at the southern beach of Discovery Park in Seattle Washington Figures 1 and 2 Discovery Park is a converted military base Initially developed as Fort Lawton the base occupied most of the northwestern area of Magnolia Bluff although it was infrequently used for military training it never grew into the major military installation it was originally planned to be and was subsequently purchased by the City of Seattle for the express purpose of creating parkland in the area City of Seattle 2007 Currently the park houses the West Point water treatment facility adjacent to the northern beach and the Daybreak Star Indian Cultural Center in addition to fields a residential historical area forested trails and rocky beaches that are popular with the public year-round The park is bordered by the neighborhood of Magnolia an area known for its steep bluffs and also for its susceptibility for landslides The Holiday Storm of 1996 1997 triggered a large landslide at Perkins Lane in the Magnolia neighborhood near Discovery Park taking out four homes and a significant portion of the road Shipman 2001 Large highly destructive landslides have occurred at Perkins Lane before notably in 1968 Tubbs and Dunne 1977 Along with Perkins Lane the areas of West Point and Discovery Park have been noted to be zones of persistent geologic instability particularly responsive to potential seismic stresses via significant landslide hazard discussed further below In light of the 1996 1997 landslides in particular the Seattle Public Utilities department commissioned the comprehensive Seattle Landslide Study Shannon & Wilson 2000 which generated a database of 1 326 landslides dating back as far as 1890 2 2 Local Geologic Setting The study site is in the city of Seattle which is located within the Puget Lowland of Washington State The Puget Lowland is an arcuate basin between the Cascade and Olympic mountain ranges opening to the north towards Canada and the Strait of Juan de Fuca Galster and Laprade 1991 The Puget Lowland is subject to complex tectonic stresses from the active interrelationships between the oblique subduction of the Juan de Fuca plate beneath the North American continental plate the north-lateral movement of the Pacific plate along the San Andreas Fault and the extension of the Basin and Range Province east of the area Booth et al 2004 Throughout the Cenozoic the resulting northeast rotation of the coastal west of Washington State relative to the stable continent and the resisting craton of southwestern Canada has resulted in a series of east-west and southeast-northwest folds and faults from the north-south crustal shortening Lamb et al 2012 Wells et al 1998 Quaternary glacial deposits up to 2000 feet thick dominate the surface stratigraphy of the area in a discontinuous series of deposits from alternating glacial and interglacial periods Borden and Troost 2001 Exposed at the Discovery Park bluff are two units of primary interest: the Lawton Clay and Esperance Sand The impermeable Lawton Clay underlies the Esperance Sand which is the most widespread permeable deposit in the Puget Lowland with free-flowing groundwater normally present throughout the unit Shannon & Wilson 2000 The exposure of interest at Discovery Park belongs to the Vashon Stade of the Frasier Glaciation the glacier occupied the Puget Lowland 15-13ka Thorson 1979 The initial deposition of the Lawton Clay is attributed to the blockage of the Puget Lowland drainage into the Strait of Juan de Fuca by the Puget Lobe of the Cordilleran ice sheet approximately 15ka the resulting proglacial lake drained southwards into Grays Harbor and accumulated widespread deposits of silt and clay Mullineaux et al 1965 The continued southwards movement of the Puget Lobe deposited the overlying proglacial fluvial sand of the Esperance Sand Mullineaux et al 1965 produced approximate ages for each unit generated from a radiocarbon analysis of peat and woody debris from the immediate Seattle area: both units were deposited within the range of 15 13 5ka although as Troost and Booth 2008 cite from Porter and Swanson 1998 the limiting ages of both units was 15 14 5ka 2 Savage et al 2000 presents a general stratigraphic section that places the depositional representatives of the Vashon Stade in order from the bottommost proglacial lacustrine clay to the overlying advance outwash to the uppermost lodgement till Figure 3 These are the Lawton Clay Vashon Advance Outwash Esperance Sand and Vashon Till members Figure 4 shows the relative stratigraphy of the beds at the Discovery Park bluff as roughly marked out on a photograph the lower boundary of the Lawton Clay is conformable with the nonglacial Olympia beds beneath Galster and Laprade 1991 The boundary between Lawton Clay and Esperance Sand is not definitive Tubbs and Dunne 1977 cite Mullineaux et al 1965 for the observation of a transition zone between the two units typically consisting of an interbedded sand and clay deposit Tubbs and Dunne 1977 support Mullineaux et al s 1965 observations that whereas the transition zone would technically lie within the boundaries of the Esperance Sand in regards to the type section and stratigraphic description the same zone is better fit to be mapped and examined when considered as the uppermost section of the Lawton Clay Thus the contact between the Lawton Clay and the Esperance Sand as marked in Figure 4 was determined to fall at the upper boundary of these transition units According to Mullineaux et al 1965 the approximate thicknesses of the Lawton Clay the clay silt sand transition zone and the Esperance Sand are 70ft 80ft and 100ft respectively at the Fort Lawton type section Galster and Laprade 1991 note that although the Lawton Clay at the type section location has a precise thickness of 82ft 25m it could range between 0 and 100ft 30m at other exposures in the Puget Lowland Supplemented by the full unit description of the Lawton Clay from Mullineaux et al 1965 my observations of the Lawton Clay indicate that it is dark-grey laminated and ripple-marked clay interbedded with lighter-grey silt with a very stiff-to-hard density with a unit thickness upwards of 30 meters Fallen blocks of well-dried Lawton Clay fracture easily along bedding planes of particular interest is the noted presence of vertical fractures listed under qualities that would affect the permeability of the unit Troost and Booth 2008 The conjugate joints that Mullineaux et al 1965 observed as being spaced within a few inches of each other were only present with high density at the driest northwestern corner of the exposure otherwise they were spaced sparsely along the bluff The Esperance Sand is a well-sorted fine-to-medium sand and gravel deposit locally interbedded with silt clay and peat lenses Troost and Booth 2008 As exposed at Discovery Park Mullineaux et al 1965 describe the unit as loose well-sorted medium-grained cross-bedded sand containing three silt beds and rounded fragments of clay and peat The transition zone fine-to-medium horizontally-bedded sand interbedded with grey clayey silt between the Esperance Sand and the Lawton Clay is typically attributed to the Esperance Sand in stratigraphic descriptions 2 3 Local Geologic Hazards The study site is at risk from a number of geologic hazards Seismic activity in the Puget Lowland is primarily attributed to the stresses generated from the subduction of the Juan de Fuca plate and the northsouth shortening from the Basin and Range extension to the south the rigid mafic basement 25-30km below the area undergoes brittle deformation Troost and Booth 2008 ten Brink et al 2002 The Seattle fault zone is an example of an active tectonic structure in the Puget Lowland extending roughly east-west directly through downtown Seattle in a swath 4 7km wide and 60 65km long Troost and Booth 2008 ten Brink et al 2002 Landslides are common in the area often featuring an interaction between anthropogenic modifications high-permeability deposits overlying low-permeability deposits steep slopes abundant colluvium coastal wave undercutting and seismic initiation triggers Troost and Booth 2008 3 Magnolia where Discovery Park is located is not the only area prone to dramatic slope failure several neighborhoods around Seattle have significant landslide risk Allstadt and Vidale 2012 Savage et al 2000 attribute the landslide frequency in Seattle to the characteristic glacial stratigraphy of the Puget Lowland which results from several phases of Quaternary glaciation They write that these units are often overconsolidated have a wide range of hydraulic conductivities are laterally heterogeneous and form steep landslide-prone coastal bluffs Most slope failures around Seattle occur in or near the contact between the Esperance Sand and the underlying Lawton Clay Schulz 2004 2005 and 2007 These failures have been mapped extensively Schulz 2004 2005 and 2007 focuses primarily on mapping historical landslides and current landslide susceptibility in Seattle using bare-earth DEMs generated from Light Detection and Ranging LiDAR imagery but not with other forms of remote sensing He has produced multiple susceptibility maps for the Seattle area such as ones presented in Figures 5 and 6 The study site at Discovery Park s South Beach bluff has a profile characteristic of many other high bluffs in the Puget Sound the contact between the permeable Esperance Sand and impermeable Lawton Clay is marked by a mid-slope bench that widens from upslope failure caused by water saturation at the contact Shipman 2004 Harp et al 2006 Figure 7 Tubbs and Dunne 1977 examined the study site in detail in a geologic hazards field guide generated for the Geological Society of America Annual Meeting They attribute the frequent landsliding and erosion at the bluff to be the result of wave erosion strong southerly winds and groundwater movement at the Esperance Sand Lawton Clay contact Upper slump failure at the bluff is primarily due to this groundwater presence the downward percolation of groundwater through the Esperance Sand is diverted at the impermeable contact of the uppermost laterally-extensive beds of the Lawton Clay and thus moves laterally until it intersects with an exposed slope Tubbs and Dunne 1977 According to them this is one of the direct contributors to the rapid destabilization and retreat of the upper bluff which eventually causes the formation of a bench at the elevation of the impermeable contact Tubbs and Dunne 1977 further suggest that the slumping at intercalations of sand in the uppermost section of the Lawton Clay instead of at the larger impermeable contact is due to the effects of pore pressure within the beds 2 4 Prior Work on Joints in the Lawton Clay Both Mullineaux et al 1965 and Tubbs and Dunne 1977 worked at Discovery Park primarily to characterize the well-exposed stratigraphic section seen at the South Beach bluff Mullineaux et al 1965 sought to describe and divide the Lawton Formation of previous usage from the prior nomenclature previously the Esperance Sand and the Lawton Clay were considered to be one unit with a clay phase and a sand phase Figure 8 Tubbs and Dunne 1977 sought to describe the general landslide hazards in the immediate Seattle Area approaching their description of the coastal bluff primarily as a sum-offactors that contributed to past slope failures at the site with the primary contributor to slope failure being the high pore-pressure conditions generated by groundwater at the contact between the Esperance Sand and the Lawton Clay Although Mullineaux et al 1965 mention the presence of conjugate joints in their unit description of the Lawton Clay Tubbs and Dunne 1997 do not note joints in their field guide and neither Mullineaux et al nor Tubbs and Dunne discuss the significance of the joints upon the general shape of the bluff or vice versa Harp et al 2006 along with many others cite Tubbs 1974 1975 and 1977 when generating illustrative figures such as the one in Figure 7 and for the now-commonly accepted theory that landsliding in these units is strongly influenced by the buildup of water at the permeable impermeable contact between the Esperance Sand and Lawton Clay Galster and Laprade 1991 suggest in their unit description of the Lawton Clay that the conjugate joint sets mentioned by Mullineaux et al 1965 were the result of loading-related destressing after deglaciation but do not expand upon the identity or work of the investigators who proposed this hypothesis 4 3 0 METHODS In order to examine the hypotheses of joint origin at the bluff I intended to generate and georeference a 3dimensional digital model of the bluff to which I could compare stereonet plots produced from the joints measured at the site To do this I made manual observations of the joints and study site collected aerial photography and took GPS points However various physical and technical limitations prevented me from completing all the analyses initially planned 3 1 Fieldwork Fieldwork was conducted in late spring during days of fair dry weather Foot access to the field site was via a steep trail off of the main loop trail a short 10-minute walk from the south parking lot This path is visible in Figure 2 Navigating the trail down to the bench level took another 10 minutes through dense underbrush In addition to work at the bench-level one day of fieldwork was conducted at beach-level for the purpose of collecting aerial photography The winter of 2015-16 was wet and warm resulting in a burst of early springtime vegetation growth which limited my ability to access certain parts of the research site There was a dense presence of horsetail fern which indicates a significant amount of water in the surface soil There was ponding at some areas of the bench and seepage emerging at various points in the bluff at the clay sand interface Figure 9 shows a large fractured corner wedge at the bluff that changed dramatically over the course of months most likely due to the combination influence of increased water movement throughout the slope and failure along preexisting planes Tubbs 1974 and 1975 theorized that landslides along the Puget Sound were the direct result of groundwater buildup During winter when there is an increased volume of water moving through a permeable unit the intergranular pore pressure increases and thus reduces the coefficient of friction in the slope This in conjunction with the unique stresses generated by the aquifer overburden of the Esperance Sand over the Lawton Clay result in mass failures characteristic of this area Fieldwork was restricted to periods of drier weather to avoid increased instability due to wet weather however during a field excursion on a clear day I observed a sudden sheet failure at the area shown in Figure 10 indicating that larger failures at this could happen at any time even during longer stretches of dry conditions The approximate boundaries of the area examined for joints and photographed for the SfM model were chosen on basis of foot accessibility and bare exposure surfaces This was to limit the scope of the area to features that I could visually verify in the field even if those areas were vertically inaccessible 3 11 Joint Measurements The bluff exhibits joints throughout the exposed clay unit and into the sand clay transition zone as seen in Figure 11 These were split into three primary groups pertaining to accessibility: 1 joints present at the upper portion of the bluff in the lower part of the Esperance Sand and sand-clay transition 2 joints present at the middle portion of the bluff that can be visually observed and 3 joints present at the lowest portion of the bluff at bench level that can be easily measured by hand without use of additional 5 equipment Due to safety concerns the use of rappelling equipment to measure the joints in the middle and uppermost areas of the bluff was prohibited by the Seattle Parks and Recreation Department Measurements of the remaining joints were further limited by the risk of falling blocks of material and steep crumbly talus slopes of fine silt clay and sand Some joints although present at the base of the upper bluff were not accessible because of a talus slope too unstable to climb safely Every joint that could be accessed from the top of the talus was measured Hand measurements of the joints present were taken using a Silva Ranger CL compass set to the local magnetic declination of 16 5 east General observations were taken of aperture infilling weathering seepage and modes of failure Strikes and dips were measured according to the right hand rule : a flat extended right hand is oriented parallel to the plane measured with the fingers pointing in the direction of downward dip The direction of the thumb then indicates the strike orientation Observations of the bluff were taken along the length of an inch-feet and decimal-feet tape measure This 300-foot tape measure was strung out along the base of the upper bluff at the top of the talus slope where possible but due to the irregularly increasing elevation of the top extent of the talus slope from the northwestern extent to the southeastern extent of the study range the horizontal accuracy of the tape measure was approximate at best Figure 12 The length of the bluff necessitated the relocation of the tape towards the southeast and upslope on the talus surface so the tape had to be moved several times and the distance recalculated these measurements were converted to meters for the purpose of Table 1 in the appendix and for the observations in the Results section Hand measurements were taken where possible this was usually at the top of the talus slope at the direct base of the bluff surface underneath overhanging fractured material This meant that horizontal distance measurements of the joints were taken more parallel to the generalized slope of the talus contact with the bluff face rather than to the planar beach surface or to the irregular base level of the bench and thus the distribution of the features recorded in Table 1 may not accurately represent the true horizontal distribution Measurements of strike and dip were taken without the use of a bubble level although these numbers were observed as close to a level standard as possible by hand Most exposed observable surfaces were planar or required some scraping to remove surface material but some were irregular even after cleaning Where space allowed the flat cover of my field book was used as an even surface from which to measure dip Where the joint surface was too small or shallow to use my book a best visual approximation was made of the area most accurately representative of the joint dip and measurements were taken from there 3 12 UAV Survey Photographs for the digital model were taken by UAV Unmanned Aerial Vehicle or drone The UAV survey was on March 30th and began at 3pm in sunny windy conditions Tait Russell a recent graduate from the University of Washington provided the equipment and technical support piloting his recreational civilian drone to take aerial photography with the intent to help me develop a Structure from Motion SfM model SfM is new relatively inexpensive approach in the field of photogrammetry which utilizes photography to remotely survey and map objects of interest SfM allows for the automated construction of a 3-dimensional digital model of the photographed surface which can then be exported as a Digital Elevation Model DEM once georeferenced through the use of GPS points or other Ground Control Points GCPs e g Russell 2016 Photogrammetry via the use of a UAV was first conducted in 1979 and the first high-resolution Digital Terrain Model generated from UAV photography was done as recently as 2005 Niethammer et al 2012 Low tide at 4:30pm allowed us set up the drone far enough away on the beach from the bluff to visually assess the entirety of the area to be photographed Figure 13 shows the lateral extent of the area that was 6 modeled from the landslide bowl at the northwestern end of the bluff and the vegetated gully at the southeastern end Tait piloted a DJI Phantom 2 Vision equipped with a 14-megapixel camera The drone s three rechargeable batteries allowed for approximately 45 minutes of flight time which we subdivided into three 15-minute flights focusing on the different areas of the bluff The first flight covered the general scope of the bluff from each side of the boundary marked in Figure 13 The drone was controlled by a combination remote and phone application that allowed Tait to view the images from the drone as they were taken allowing him to more clearly focus on the areas I described as most crucial to model The second and third flights were close-ups of each respective half of the bluff focusing primarily on the sheer bluff surfaces and not on the vegetated bench The photos were taken continuously in a JPEG format at a rate of one picture every three seconds 3 13 Trimble Geo7x GPS Measurements A total of 12 GPS points were taken at various points along the bench and at the upper treeline These points were necessary to provide a geographic reference frame for the completed SfM model and were split up into two files: 9 bench-level points spread out on the lower surface and 3 treeline points placed at the base of distinctive trees at the very edge of the upper bluff These points were collected using a Trimble Geo7x GPS receiver and transmitter in conjunction with a Zephyr Model 2 external antenna I recorded data at each location until the average accuracy of all the points was reported by the instrument to be within 15cm or better Photos of the control points are included in the appendix 3 2 Post-processing Post-processing of the field data involved a stereonet analysis of the measured joint orientations and the development of a Structure from Motion model from the drone photographs taken The stereonet program used was Stereonet 9 5 3 Allmendinger 2016 The Trimble GPS points were intended to georeference the SfM model but unforeseen complications during the data collection phase prevented differential corrections from being done Without corrected GPS I could not georeference the SfM model this would not have been possible even with corrected GPS due to the amount of vegetation and bench-level blurring that obscured the exact areas where I collected points More information regarding the GPS errors are located in the appendix Before the photographs taken by the drone could be used to generate the SfM model they required some pre-processing I followed the processing procedure described in Russell 2016 with further advice from Tait himself The drone collected inaccurate GPS information stored as geotags attached to each photograph These must be removed otherwise the SfM processing software Agisoft PhotoScan Pro v 1 2 3 may misalign the photographs and produce a deformed model Russell 2016 recommends EXIFtool to remove the geotags These adjusted photos were then loaded into a new project in Agisoft Photoscan Pro this program was run on a Dell Precision Tower 7000 Series desktop computer equipped with two Intel Xeon hyper-threading 6-core processors for a total of 12 cores with the capability of 24 With 64 gigabytes of RAM and two graphics cards GeForce GTX 70 Ti and Quadro 4000 this computer was the most powerful that I could access for modeling There were two main modeling steps completed in Agisoft Photoscan Pro The first was to generate a point cloud made of the feature patterns found in the aligned photographs called a sparse point cloud This was done by first adjusting the photo alignment to the high accuracy setting changing the photograph selection to generic and increasing the maximum threshold of detected patterns in each 7 photograph to 400 000 from the default 40 000 and the maximum threshold of corresponding patterns in other photographs to 10 000 from the default 1 000 per Russell s 2016 steps Once the sparse point cloud was completed the second step was to generate a dense point cloud The difference with the dense point cloud is that whereas Agisoft Photoscan Pro detected and correlated patterns in the photography to generate the sparse point cloud the dense point cloud is made by utilizing the estimated camera positions and the approximate depth to surface resulting in a smoothed solid model Russell 2016 suggests setting the cloud density to medium and the depth filtering to mild to reduce over-interpolation and to preserve the angularity of exposed surficial features Due to a lack of GPS data imported to the model as markers building a DEM was not possible However an orthophoto could be built I used the default pixel size suggested of 0 00427961 meters and allowed the program to estimate the bounding area Likewise when exporting the orthophoto I kept the suggested default export pixel size of 0 00427961 meters and kept the program settings to automatically estimate the bounding area I kept the default TIFF compression as LZW the JPEG quality at 90 and exported as both a TIFF and JPEG file Despite the suggested default pixel size the resolution of the output orthophoto was unlikely to be accurate to 10-8m The orthophoto itself did not display a view of the bluff that could be easily interpreted and was not included in this report 4 0 RESULTS 4 1 GPS and SfM In regards to the SfM model although imperfect due to the lack of georeferencing limited computer processing power and site limitations the resulting output was sufficiently precise in the areas of interest to be examined and the model provides a valuable tool for freely manipulating the viewpoints of the bluff to gain a more thorough grasp on the topography Due to the technical issues discussed in-depth in the appendix the results from both the GPS and SfM process were ultimately inconclusive or produced far less workable data than originally planned The GPS points were not able to be differentially processed without corrected points to export and georeference the Structure from Motion model a DEM could not be created and further analyzed in ESRI ArcGIS However considering the ability of Agisoft Photoscan Pro to manipulate the completed model into various views at various levels of zoom the SfM model still acted as a useful tool to visually confirm physical features of the bluff that could otherwise only be seen in partial during fieldwork at either bench or beach-level Figure 14 is the completed model seen from a beach view additional images of the model from different angles are in the appendix 4 2 Field Observations Detailed fieldnotes are located in the appendix along with a table of the joints measured The outermost portion of the bench away from the talus-covered lower bluff face and extending to the beachside edge of the bench exhibited a hummocky topography which was mostly hidden by a dense patch of young alders blackberry and horsetail The winding trail used to descend from the trailhead at the top of the bluff down to bench level passed by audibly trickling water and over older rotting woody 8 debris sunken into soft wet mud that adjacent to visible standing water a small pond was mostly obscured by surrounding vegetation but was large enough to make a deep splashing sound when objects were thrown into the center The bluff surface examined was generally near-vertical sloping the most near the bench at the edge of the talus cone The joints present at measurable elevations in the bluff were clustered at both far ends and intermittently in the middle From beach-level there was visible steady water trickling observed pouring down in rills and minor channels over the greyish clay-mantled underlying Olympia beds and down onto the beach Due to the changing conditions of moisture vegetation and elevation across the bluff it was simplest to characterize the bluff in terms of general domains separated from one another by distinguishing differences in such attributes like bluff section orientation joint frequency seepage and primary talus slope material Five domains were distinguished and are identified in Figure 15 as domains A B C D and E Domain A begins at the westernmost end of the bluff and runs 20m with an estimated bluff strike of 140 degrees There is no obstructive vegetation to reduce the amount of sun or wind exposure at this domain resulting in a very dry section of the Lawton Clay that resembles more coherent rock Talus material is clay dry greyish tan in color and powdery in texture Surface color of the clay is also tan but fresh surfaces within the bluff are dark grey indicative of higher moisture content A hand sample taken from the bluff was determined to be of S6 very hard grade weak rock and indented with difficulty by a thumbnail It splits readily along bedding planes and fractures to powder under blows from a geological hammer it is also relatively easy to scrape with a sharp edge Larger joints present in this domain were spaced about 10cm 1m apart with a distinct stair-stepping structure parallel to the bluff at the far corner Figure 9b The majority of the exposure was highly fractured and irregular exhibiting small block or wedge failures The smaller fractures had spacings of 1 20cm and were oriented both perpendicular and parallel to the bluff Some exposed joint surfaces showed red-black discolorations further indicative of past water movement through minor apertures Apertures themselves were minor between 0 1 and 0 5mm between both sides of the joints and bearing no distinct chemical or detrital infilling Small fractured blocks were easily dislodged by hand or some prying numerous plumose structures and associated hackles were observed Figure 16 Nearer to the boundary with Domain B some root and insect infilling was observed and some small plants were growing out of joint partings Near-surface fractures in the most weathered areas and adjacent to the talus zone at bench level were more irregular frequent and closely spaced than upper bluff fractures which appeared to fail in larger sheets 2 3 meters square rather than in smaller blocks Nearly all fallen blocks had smooth faces and sharp edges along the planes of breakage Upper bluff failure within this domain and all the domains was observed to occur at the intersection between 3 planes: an uppermost horizontal failure along bedding an irregular perpendicular failure along a conjugate joint and a backside sheet failure parallel to the bluff Domain B runs from position 20m 60m with an estimated bluff strike of 110 degrees The 20m position marks a large broken corner wedge visibly separated from the upper bluff The characteristics of Domain A and B are mostly similar dry tan surface exposures with powdery clay talus and smaller irregular fracturing close to bench-level and an upper bluff area marked by larger thicker longer sheet fractures with an irregular perpendicular fracture plane a smooth horizontal upper plane that failed along the bedding and a smooth fracture plane against the bluff surface The upper bluff appeared primarily intact with very minor perpendicular fractures that were often covered in soil wash and organic debris from above Most of the upper fractures appeared to be shallow and roughly parallel to the bluff face with tight apertures only discernable by the stairstepping pattern produced by sun shadow Fallen blocks that had broken along bedding planes exposed distinctive ripples Figure 17 Unlike the consistently dry Domain A Domain B marks the transition in the bluff to an in-situ increase in water content and vegetation bench-level talus material at about 30m becomes darker grey and firm with a greater density of larger vegetation The gradual elevation of the top of the talus increases along the length of the tape measure 9 providing access to more of the upper sandy sections of the stratigraphy Domain B also has larger bluff failures than those present in Domain A displaying fresh dark blocks on the bench and fallen young trees from the top of the bluff The leaves on these toppled trees were fresh at the time of field observations and the roots were partially exposed some were clumped together with original soil material and some were buried beneath a mixture of overhead sand and clay Besides this fresh failure and the dry zone adjacent to Domain A the area of Domain B closest to Domain C was covered with a significant amount of overhead dark soil wash and overgrown with lichen and moss Removing the soil and vegetative cover revealed dark grey underlying clay indicating water present either within the clay itself or water movement through the soil mantle sourced from overhead seepage out of transitionary sand clay lenses Domain C runs from 60m 80m with an estimated bluff strike of 120 degrees Domain C had significantly more moisture than Domain B the water flowing over the surface was enough to support a mat of plant roots with plenty of moss lichen horsetail and other plants sprouting directly out of the bluff There were few prominent or pervasive joints observed possibly due to the lack of recent failures that would expose fresh planes visually obstructive vegetation and or the reattachment of fallen clay particles onto the lower surfaces of the bluff resulting in a dark indistinct nubby texture Exposed surfaces were dark and moist with what partings present often densely infilled with roots and moss if not infilled by reattached clay Primary talus material was vegetation-covered dark clay mixed in with broken logs fallen chunks of clay were blocky but exhibited rounding of the corners and edges unlike the chunks present in most of Domains A and B At about 75m overhead seepage was observed coming directly out of a fracture plane running parallel to the bluff face About 10m above the elevation of the seepage the bluff material was drier and exhibited fewer visible joints although vegetation cover remained At about 80m was an exposed dark grey portion of bluff that was missing surface vegetation I observed a large sheet failure detach from the bluff at this location This failure zone is featured in Figure 10 The exposed material was very moist upon immediate examination after the failure but this failure as a whole could indicate that although the remainder of Domain C appeared to be mostly coherent the coherency was an illusion brought about by soil cover and vegetation growth rapidly covering exposed joints and fracture planes from previous failures Domain D runs from 80m 130m with an estimated bluff strike of 125 degrees Domain D similar to Domain B marks a transitionary zone between moist mostly-clay talus and bench material into dry mostly-sand talus and bench material This domain is distinguished by multiple points of water seepage dripping out from the soil mantle present at 100m and 120m and by a decrease in obstructive moss and lichen across the lower portion of the bluff Access to the bluff was limited in this domain due to the steepness of the talus it was too unstable to climb safely and take closer measurements 85m approximately marks the location of slightly slumped stairstepping fractures Figure 18 The presence of these fractures support the hypothesis that the pattern of irregular deep perpendicular joints crosscutting multiple layers of preexisting parallel joints extends through Domains A and D joint patterns similar to Figure 18 in Domain D are found in Figure 11b from Domain A A large corner fracture at 87m had a large sandy talus pile directly beneath the overhanging soil material the upper portions of the bluff were thus freed of vegetation and exposed fresh surfaces that included both the Lawton Clay and some of the overlying sandy transition lenses However like with the remainder of the bluff within this area it was difficult to pick out joints in the lower exposures of clay due to bumpy clay reattachment surfaces The immediate area of the corner failure was dry but at about 100m enough seepage was present to support the dense sprouting of horsetail out of the surface Here the only lower visible failures appeared to be small sloughing movements of the clumped clayey talus material away from the main bluff face Some of these partings were wide and deep enough that I was unable to see to the bottom although depth was indeterminate the talus was separated from the main bluff at widths of 1cm 15cm The gradual elevation increase along the very top of the bluff had become great enough at this location relative to Domain A that the presence of sandy transition lenses in the uppermost section of the clay unit became evident distinguished from the rest of the bluff by the numerous insect burrows spotted throughout At 10 about 110m a combination of increasing vertical thicknesses of the uppermost overlying sand unit increasing frequency of sand lenses at the transition zone between the clay and the sand and decreasing vertical thicknesses of lower exposures of the underlying clay unit covered up by increasing thicknesses of talus contributed to medium quartz sand becoming the primary talus material on the bench Domain E runs from 130m 180m with an estimated bluff strike of 140 degrees Domain E extends into a forested area off of the main bluff this required navigation over steep sandy talus high above the bench the eye-level bluff material was no longer exclusively clay Domain E is distinguished from the other domains by being entirely within the sand silt clay transition zone between the Lawton Clay and the Esperance Sand Larger measureable joints in the lower portion of the bluff were infrequent from 20 130m but there were a number of accessible joint sets present in the transitionary zone These joints extended through cross-bedded medium quartz sand and laminar-bedded silt and clay and were mostly parallel to the bluff there were some smaller evenly-spaced irregular fractures exhibiting red-black oxidation surfaces similar to those in Domain A Some flat concretions observed at 170m support Mullineaux et al s 1965 observations of the Lawton Clay although these concretions are located nowhere else in the bluff accessible by foot The same problem with joint visibility was present in Domain E as it was in Domains C and D nubbly surface textures and moss often hid or partially obscured measurable surfaces Unlike with other domains the bluff surface vegetation appeared to root deeper than just the overlying soil layer some of the joints that were parallel to the bluff exhibited roots growing through the cracks and forming enough space to between the parallel sheet and the bluff to form small caves Figure 19 is identical to Figure 15 except where each domain is annotated with the approximate bluff strike for that domain 4 3 Joint Orientations Forty-five joints were measured in all with the majority of them clustered at the far northwestern end of the bluff in Domain A Figure 20a shows a completed stereonet with all 45 joints plotted and Figure 20b a plot of all the poles to the plane shows nearly a full-180 spread of strike orientations As observed in the field the joints had two major orientations relative to the orientation of the bluff surface joints that were roughly parallel to the local strike of the bluff face Figure 21a and joints that were roughly perpendicular to the strike of the bluff face Figure 21b Joints designated parallel mostly strike 100 160 degrees The perpendicular fractures show a broad distribution with no clear common strike orientation Figure 21b which corresponds to field observations of their relative irregularity Due to the fact that the perpendicular parallel determination of joint orientations were taken relative to the local strike of the bluff at which the joint was measured some of the parallel joints in Figure 21a do not fall within the average strike of the bluff within each domain where the majority of the other joints lie The field determination of parallel vs perpendicular was entirely dependent on the local variation in the bluff I noted certain joints as parallel if my visual assessment of the joint plane relative to the localized block from which I was measuring it was approximately parallel but this sometimes meant that those joints might not have been parallel to the bluff in a broader view The determination of perpendicular joints was likewise but I categorized perpendicular joints as any joint that was not definitively parallel to the bluff All of the dips measured were high-angle varying between 70 90 degrees with a calculated average of 80 Figure 22 is an annotated scatterplot that shows the spatial variation of joint strike orientations to plot strike all values were converted to the 0 180 hemisphere by subtracting 180 degrees from strike values that were greater than 180 Domains A E are subdivided in the plot by vertical blue lines and horizontal 11 shading in orange and blue 10 wide centered around the average strike values of the bluff and of the parallel joint orientations respectively The strike orientation patterns seen in the joints roughly correspond with the generalized strike orientations along the horizontal expanse of the bluff as seen in Figure 23 but more obviously so in Figure 22 when comparing the orange and blue strike averages Although the range of strike values for the joints tended to be greater than the estimated approximate strike of the bluff in which they were located the general trend indicates that more southward-striking joints were clustered at the ends of the transect where the bluff strike was more southwards while the joints in the center more east-striking area of the bluff also happened to be striking more eastwards However as shown in Figure 23 which divides up all the joints into five separate stereonets by domain most of the joints observed were already clustered at either end Domain C only has one joint recorded for a horizontal span of about 20m This is especially clear in the Figure 22 scatterplot which more distinctly shows the clustering of joints in domain A The distribution patterns or lack thereof observed in these joints although intriguing may be the result of disproportionate statistical representation during joint measurement due to the surface conditions and accessibility limitations at various locations along the bluff for the horizontal distance between 20m and 130m joint measurements were few and far between Not many joints were observed because the higher water content in this area encouraged the widespread growth of moss lichen and other plants over the surface of the bluff the exposed textures of the bluff itself were complicated by the uneven reattachment of clay particles to the lower accessible bluff area near to the bench which may have caused the infilling or sealing of joints that would otherwise be visible In addition the bench material transition from primarily clayey talus to slipperier sandy talus made some stretches of the bluff manually inaccessible I was not able to climb up the steep talus slope and stand close enough to an observed joint measure it However it is possible that the fewer observed joints in this horizontal range could suggest a lower frequency of joints in the sandier sections relative to the rest of the bluff 5 0 DISCUSSION 5 1 Joint Origin Hypotheses Hencher 2012 outlines three stress-related origins of joint formation only two of which would apply at this site: tectonic or geomorphic weathering Primary origins of joint formation resulting from the original formation stresses of the material do not apply at this bluff because the joints crosscut bedded glacial deposits Here I divide the geomorphic weathering stresses further into two mechanisms and so examine three major hypotheses regarding the origin of the joints: 1 tectonic 2 drying or unloading and 3 related to the topography of the bluff Of the two joint sets observed at the bluff the parallel joints show more consistency and so it may be most worthwhile to focus on the orientations of the parallel set Narr and Suppe 1991 describe tectonic joints in bedded sedimentary rock to be generally oriented perpendicular to the bedding and occurring in sets of parallel fractures but they make the claim that an outcrop usually only has one well-developed joint set This joint set would typically be oriented perpendicular to local fold axes Narr and Suppe 1991 or parallel to the compression direction The tectonic stresses in the immediate area are from north-south shortening and compression in the Washington fore arc which are thus responsible for east-west trending uplifts faults and folds with north-south compressive axes Wells et al 1998 Galster and Laprade 1991 and Booth et al 2008 12 Joints tend to form in tension as extensional fractures parallel to the maximum compressive strength Hencher 2012 Thus it would be expected that the parallel joint set at the bluff would be approximately north-south perpendicular to the east-west orientation of the nearby Seattle fault system and other features However for the joint orientations to be indicative of larger regional stresses I would expect that they would remain consistent for the entire exposure Figure 21a shows that the parallel joints are oriented between 102 160 degrees and dip to the southwest Figures 22 and 23 showing the horizontal distribution of all the joints along the domains of the bluff indicates that joint orientations did not remain consistent over the area of the observed bluff exposure Because the joint orientations are not consistent with each other over the exposure and do not align with the expected north-south shortening direction it is unlikely that the joints at the bluff are tectonic in origin Goehring 2013 describes joint sets that form under cyclical wetting drying conditions in sedimentary deposits as typically surficial hexagonal or rectilinear contraction cracks These are usually not found in glacial lacustrine clay deposits but in dried mud which itself is a mixture of clay silt and organic matter Goehring 2013 Water was definitively observed flowing through most of the bluff either over the surface or out of joint partings close to the relatively impermeable boundary between the Lawton Clay and the Esperance Sand the discolored joint surfaces found where no waterflow was observed indicated that water movement through the joint spaces at those areas had occurred before and may be a reoccurring phenomenon dependent upon seasonality or other groundwater parameters Although Domain A was distinctly dry the cracks present were neither rectilinear nor hexagonal and penetrated into the bluff at inconsistent depths Of interest is the presence of multiple initiation points and the associated hackles in Domain A showing fracture propagation outwards from a preexisting flaw these plumose structures are generally considered to be indicative of tension stresses Hencher 2012 Helgeson and Aydin 1991 Figure 16 However Domain A had the greatest amount of irregular fracturing compared to the remainder of the bluff the plumose structures observed did not consistently appear only in joints that corresponded to the parallel-to-bluff joint sets but throughout the domain and oriented both parallel and perpendicular The fracture planes whether those were perpendicular parallel or irregular and inbetween did not closely resemble the fracture patterns of cracks formed from cycles of wetting and drying and are thus unlikely to have formed under repeated desiccation periods However the irregularity of the closely-spaced fractures at a wide range of orientations as seen in Figure 22 could indicate that drying might have partially influenced the joint formation in Domain A Crider 2016 personal correspondence The final hypothesis is that the origin of the parallel joint set is directly related to the orientation of the bluff Hencher 2012 makes note that tension fractures could occur as a result of the stresses generated by intergranular pore water pressure in sediment piles sheeting joints in particular he defines as being directly related to the near-surface stresses generated by local topography Hencher 2012 considers these joints to be relatively rarer in sedimentary rocks and conglomerates as compared to massive igneous rocks but emphasizes the positive feedback between alternating failure events and erosion weathering processes contribute to the continued development of new parallel-to-surface sheeting joints as fresh surfaces are exposed by the failure of the old slab Selby 1993 goes into more mathematical detail the use of a finite-element stress analysis allows for the calculation of the predicted amount of tensile deformation at an area based upon a geometric cross-sectional model of the deformable body an examination of the nodal displacements of the geometric elements upon loading permits the analysis to determine the induced strains and stresses on the system This analysis allows him to create simplifications of natural models and to predict modes of failure based upon strain he references his prior work Augustinus and Selby 1990 to discuss the likelihood of vertical joints forming in sheer orthoquartzite and sandstone faces as a result of tensile stresses generated by the weight of overlying material and by the differing rates of deformation between two different materials in direct contact however he also implies that the propagation of these near-vertical tensile joints are responsible for a 13 significant amount of steep slope failure and recession thus controlling the development of the actual cliffs that are subject to this kind of stress Selby 1993 Figures 22 and 23 roughly demonstrate that the parallel joint orientations change along with that of the bluff within a range The high-angle dips of all joints measured are reflective of the high-angle dip of the bluff itself Given that Figures 22 and 23 show the measured joint orientations correlating roughly with the orientations of the bluff it s likely that the tension stresses generated by the sheer bluff surface are at fault for the parallel-to-surface sheet and block failures the near-vertical orientation of these tension joints in the horizontally-bedded Lawton Clay and the irregular nature of the perpendicular fracture planes in the uppermost clay silt sand part of the bluff correspond with observations by Selby 1993 of tension joints in horizontally-bedded sedimentary rock frequently being near-vertical and in mudrock and other weak rock as frequently curved and discontinuous At the most exposed corner end of Domain A where the properties of the clay more closely resembled that of rock due to the extreme dryness failure occurred not only in sheets but also in blocks and wedges Elsewhere on the bluff where more moisture was present as seepage out of the interbedded clay silt sand between the Esperance Sand and the Lawton Clay failure was primarily in large sheets parallel to the bluff In light of this it is less accurate to describe the parallel joints as one joint set but rather as an approximate series of five different parallel-to-bluff joint sets corresponding to the five bluff domains where they are located From this it would be inaccurate to consider these joints representative of the frequency and prevalence of such fractures in the Lawton Clay elsewhere in the Puget Lowland Because strike orientations of the joints are not consistent across the bluff but shift accordingly as the strike of the upper bluff surface shifts it can be inferred that the joints are a result of the unique conditions at the bluff itself It is therefore unlikely that the joints at Discovery Park are representative of the Lawton Clay regionally This finding suggests that bluff exposures such as this one may not provide data by which to evaluate the presence of regionally-extensive joint systems for evaluation of joint-compromised impermeability or fracture control of fluid migration in or through the Lawton Clay It is difficult to ascertain if the parallel joints are responsible for the bluff topography or if the topography is responsible for the joints In all likelihood joint formation and bluff development are interrelated tensile stresses acting in conjunction with pore pressures promote joint propagation and eventual sheet and block failure but the exposure of fresh surfaces along that parallel surface opens up new surfaces to weathering and other environmental stresses which could promote a faster rate of joint formation behind the fresh surface The presence of vegetative cover mosses lichens surficial root matting tree canopies may impede this cycle of positive feedback as possibly suggested by the lack of joints observed from Domains B to D where vegetation and reattached clay provided a thin barrier between fresh surfaces and weathering processes Figure 10 demonstrates that this barrier is not foolproof despite the possible slowing of the bluff retreat due to vegetation parallel joint development persists in the lower clayey portion of the bluff When considering that the large deeper-set recent sandy failures in Domains B and D occurred at the uppermost visible stratigraphy such parallel joints may extend to cover a large surface area set further back into the bluff than would be suggested by the numerous other instances of smaller near-surface sheet failure occurring lower on the bluff 5 2 Further Work Further work at this bluff would include more precise observations of each individual joint and minor joint set measured For this project I examined each joint individually but I did not consider grouping them into minor sets such as those seen in Figures 9a and 9b Domain classifications were determined retroactively from field notes and horizontal measurements so concurrent field observations with field measurements could more clearly delineate the boundaries of these domains If possible closer 14 examinations of Domains B D might be able to reveal more joints than initially observed Collecting more joint data would allow for more precise analyses of joint orientation changes occurring alongside bluff orientation changes and allow me to solidify the foundation of the topographic-stress hypothesis or to possibly refute it depending on the insight these additional joints could provide 5 21 Measuring Rate and Volume of Bluff Retreat This coastal bluff as seen in Figure 9 is prone to rapid significant change over a short period of time and thus becomes ideal as the focus of a time-lapse study on coastal erosion or of bluff evolution If possible a high resolution SfM model could be georeferenced with several GPS points at key unchanging