NEW APPROACHES TO STUDYING SHALLOW FAULT ZONE PROPERTIES WITH HIGH-RESOLUTION TOPOGRAPHY

by Lia J. Lajoie c Copyright by Lia J. Lajoie, 2019

All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Geophysics).

Golden, Colorado Date

Signed: Lia J. Lajoie

Signed: Dr. Edwin Karl Nissen Thesis Advisor

Golden, Colorado Date

Signed: Dr. John Bradford Professor and Head Department of Geophysics

ii ABSTRACT

Coseismic surface deformation fields provide us with information about the physical and mechanical properties of faults and fault zones. Recent advances in geodetic imaging and analysis allow us to map deformation and infer fault properties at spatial resolutions that were previously unattainable. These high-resolution, remotely-sensed datasets provide an intermediate observational scale that bridges the gap between very local field measure- ments of surficial faulting and far-field satellite geodesy which samples deeper slip, allowing previously-overlooked shallow-subsurface fault structure to be probed. In this thesis, I use new analytical techniques to study the shallow sub-surface properties of three recent and historic earthquakes that together are representative of diverse, remotely-sensed data types now available. For each earthquake, I (along with co-authors) employ a separate, recently- developed technique that is best suited for the specific dataset(s) involved, and in this way, explore how extant datasets can be analyzed (or re-analyzed) to reveal new characteristics of the earthquakes. The earthquakes studied (which comprise the three chapters of this thesis) are: (1)

The 2016 Mw 7.0 Kumamoto, Japan earthquake, for which pre- and post-event gridded digital elevation model (DEM) datasets are available. We compute high-resolution two- dimensional fault offsets along strike using optical pixel tracking on the hillshaded DEMs, and investigate the calculated slip distribution to assess variations in roughness and strain along the rupture and as a function of observation scale. (2) the 2010 Mw 7.2 El Mayor- Cucapah, Mexico earthquake, for which we have both pre- and post-event lidar point cloud data. For this earthquake, full three-dimensional surface displacements are computed using an implementation of the Iterative Closest Point (ICP) algorithm, and fault offsets measured in the resulting x, y, and z displacement surfaces constrain total slip as well as fault dip along strike. (3) The 1992 Mw 7.3 Landers, California earthquake, for which the best existing

iii dataset is a post-earthquake, historical aerial survey. The historical images are used to generate a high-resolution, geo-rectified Structure from Motion (SfM) point cloud. This work serves as a proof-of-concept for a method to study historical earthquakes or remote modern events for which aerial surveys have been undertaken but which lack high resolution topographic data.

iv TABLE OF CONTENTS

ABSTRACT ...... iii

LISTOFFIGURESANDTABLES...... ix

ACKNOWLEDGMENTS ...... xvii

DEDICATION ...... xviii

CHAPTER1 INTRODUCTION ...... 1

1.1 Technical Question 1: What new technologies can be applied to existing, high-resolution topographic datasets for surface-rupturing earthquakes? . . . . . 2

1.2 Technical Question 2: Can we utilize new technologies and techniques to create new high-resolution topographic datasets? ...... 4

1.3 Technical Question 3: What can we learn using datasets that sample a depth range below surface ruptures that past techniques have not beenableto? . . . .5

CHAPTER 2 SURFACE SLIP PROPERTIES OF THE 2016 KUMAMOTO, JAPAN EARTHQUAKE FROM DIFFERENTIAL LIDAR ...... 8

2.1 Introduction...... 9

2.2 OverviewoftheKumamotoEarthquake ...... 10

2.3 SurfaceDeformationField ...... 12

2.3.1 Data...... 13

2.3.2 Methods...... 13

2.3.3 Results...... 15

2.4 SurfaceSlipDistribution ...... 17

2.4.1 Methods...... 17

2.4.2 Results...... 20

v 2.5 SurfaceSlipRoughnessandStrain...... 22

2.5.1 PowerSpectralDensity...... 24

2.5.2 RootMeanSquareDeviation ...... 24

2.5.3 Strain Estimates Derived From Surface Slip Distribution ...... 28

2.6 Discussion...... 28

2.6.1 Relations Between Fault Offsets, Slip Roughness, and Strain ...... 28

2.6.2 ComparisonWithOtherEarthquakes ...... 29

2.7 Conclusions ...... 32

2.8 Acknowledgments...... 33

CHAPTER 3 EXTENT OF LOW-ANGLE NORMAL SLIP IN THE 2010 EL MAYOR-CUCAPAH (MEXICO) EARTHQUAKE FROM DIFFERENTIAL LIDAR ...... 34

3.1 Introduction...... 35

3.2 Overview of the El Mayor-Cucapah Earthquake ...... 37

3.2.1 SeismologicalRuptureModels ...... 38

3.2.2 SatelliteGeodeticRuptureModels ...... 40

3.2.3 FieldObservationsofSurfaceFaulting ...... 42

3.3 DataandMethods ...... 44

3.3.1 Three-Dimensional Surface Displacement Field From Differential Lidar...... 44

3.3.2 Estimating Dault Dip From the 3-D Surface DisplacementField . . . . 45

3.3.3 Estimating Fault Dip From the 3-D Surface Rupture Trace...... 48

3.4 Results...... 50

3.5 Discussion...... 55

vi 3.6 Conclusions ...... 58

3.7 Acknowledgments...... 59

CHAPTER 4 SUB-METER RESOLUTION SURFACE RUPTURE TOPOGRAPHY FROM LEGACY AIR-PHOTOS – A TEST CASE FROM THE 1992 LANDERS EARTHQUAKE ...... 60

4.1 Introduction...... 61

4.2 Data...... 65

4.3 PointCloudGeneration ...... 67

4.4 PointCloudAccuracy ...... 69

4.4.1 Methods...... 69

4.4.2 Results...... 70

4.5 VerticalOffsetMeasurements ...... 73

4.5.1 Methods...... 73

4.5.2 Results...... 75

4.6 Pull-ApartBasinMorphology ...... 79

4.6.1 Methods...... 79

4.6.2 Results...... 80

4.7 Discussion...... 80

4.8 Conclusions ...... 82

4.9 Acknowledgments...... 83

CHAPTER5 CONCLUSIONS ...... 84

REFERENCESCITED ...... 87

APPENDIX SUPPORTING INFORMATION FOR “EXTENT OF LOW-ANGLE NORMAL SLIP IN THE 2010 EL MAYOR-CUCAPAH (MEXICO) EARTHQUAKE FROM DIFFERENTIAL LIDAR” ...... 102

vii A.1 ICPRotations...... 102

A.2 DipMaps ...... 102

viii LIST OF FIGURES AND TABLES

Figure 2.1 (a) Regional tectonic setting. (b) Moment tensor solutions, surface ruptures, and lidar coverage area for the April 2016 Kumamoto earthquake sequence. (c) E-W and (d) N-S displacement fields from correlating SPOT 7 satellite photographs from 14 December 2015 and 20 April 2016. The spatial coverage is much greater than for the lidar data (dashed polygon) but results are also noisier. Because stereo image pairs were used, we are also able to estimate vertical deformation, but this signal is dominated by noise and is not shown...... 11

Figure 2.2 Displacement fields constructed from pre- and post- earthquake hillshaded DSMs. (a) East-west displacement field, with positive values indicating motion towards the East. (b) North-south displacements, with positive towards the North. (c) NE-SW displacement field, with positive towards the NE and thus approximately parallel to the fault. Black dots show locations of field measurements from Shirahama et al.. (d) NW-SE displacement field, with positive towards the NW and approximatelyperpendiculartothefault...... 16

Figure 2.3 Fault offset measurement transect A–B (heavy black line, 3 segments) and fault-perpendicular profiles (thin black lines), which we use to calculate the surface slip profile in Figure 2.5b. 517 surface slip measurements were calculated along 374 fault-perpendicular profiles — for clarity only every fifth profile location is shown here — and then projected onto the transect A–B. The background displacement field is projected into the direction parallel to the nearest fault segment...... 18

Figure 2.4 Examples of swath profiles and derived offset measurements at (a, b) two single-stranded rupture localities and (c) one multi-stranded rupture locality. The x axis shows distance from the simplified fault trace A–B, shown in Figure 2.3, and the Eastings and Northings coordinates of the profile center point (in meters) are given in the lower left of each plot. Black circles are fault-parallel displacement data points. Least squares linear fits with 50% uncertainties are shown by solid red lines, as calculated between paired vertical gray bars. These linear fits are then projected (dotted red lines) to the fault (vertical blue line) where the offset is measured (faint blue rectangles)...... 19

ix Figure 2.5 (a) Locations of lateral offsets measured in the field (from Shirahama et al.; red dots with black border) and from lidar displacement profiles (colored by segment). Dashed black line indicates transect A–B, with dashed grey lines marking inflections in the transect line (panel b and Figure 2.3). (b) Right-lateral surface offsets measurements made from lidar displacement swath profiles with 50% error bounds (blue), and right-lateral offsets measured in the field (red, from Shirahama et al.). The lidar-derived offsets are cumulative across the profile length (Figure 2.3), and capture deformation across the full damage zone rather than only at the primary fault trace . Field offsets tend to be lower, representing single scarp measurements. The lidar-derived offsets can also be used to fill in gaps in the field data, most notably between 10 km and 14.9 km on the transect, which is actually revealed to be the area of high slip. (c) Periodogram, (d) Thomson multitaper and (e) Welch power spectra for the lidar-derived right-lateral offset distribution shown in (a). Red lines indicate best fits to power spectra...... 21

Figure 2.6 (b) Slip distribution, (c) strain , and (d) strain gradient in relation to (a) surface trace complexity as outlined by locations of field measurements (red dots with black border) and lidar displacement profile measurements (colored dots) of lateral fault offset. Data in panels (b–d) are presented both by individual fault segment (colored according to panel a) and for the generalized fault trace along transect A–B (grey) (Figure 2.3). Dashed, vertical grey lines indicate inflections in the transect A–B. (b) Red dots show field measurements of lateral offset. Plotting the data by individual fault strand shows that much of the discrepancy between field measurements and lidar displacement field measurements in Figure 2.5b from 7 km and 10 km is due to summation of multiple strands across∼ profile. Additionally,∼ these high-density offset measurements show how slip transfers from one fault strand (segments 1-4) onto another (segment 5) – slip remains low (<1 m) on segments 1–3, then increases dramatically on segment 4 at the same distance along transect A–B that segment 5 appears. As slip increases on segment 5, slip on segment 4 lowers, such that the total slip across both faults remains relatively stationary. (c) Strain and (d) strain gradient are presented as 3 point moving averages along the rupture. Red, horizontal dashed lines indicate one standard deviation in strain and strain gradient for the generalized fault trace (grey curves) for a 3 point moving window. Fault offset, strain, and strain gradient all increase significantly northeast of 7 km along the transect, where two majorfaultsegmentsoverlap. . .∼ ...... 23

x Figure 2.7 (a) Root mean square deviation (σRMS) values along transect A–B for detrended slip data, colored by measurement window length. These are related to the fault trace complexity (panel b, same as Figure 2.5a) with dashed grey lines marking inflections in the transect (Figure 2.3). Windows increase in length in 0.5 km increments from 0.5 km to the full length of the fault (the legend shows only whole number window sizes for brevity). Line vertices indicate center points of measurement windows. The finer observation scales show an abrupt increase in σRMS northeast of 7 km in the profile, at the prominent join in fault segments 4 and∼ 5. Roughness peaks approximately at the join for fine spatial scales and 2 km to 3 km north of it at coarser spatial scales. . . 26 ∼ ∼

Figure 2.8 Average root mean square deviation (σRMS) as a function of measurement window length for (a) the 2016 Kumamoto earthquake (colored by fault segment according to Figure 2.5a), (b) the 2010 El Mayor-Cucapah earthquake (colored by fault segment), and (c) the 2013 Balochistan, 1999 Hector Mine, and 1992 Landers earthquakes. Error bars show 1 standard deviation of calculated σRMS for each window dimension and asterisks indicate average σRMS measured over the entire fault length. Grey background curves are σRMS curves from other panels with error bars removed. The Hurst exponent (HRMS) is equal to the slope of these curves, which for Kumamoto is roughly stationary over all measured length scales. Balochistan is less rough (lower σRMS) than all other earthquakes at every observation lengthscale. The relative roughnesses for all earthquakes are strongly scale dependent...... 27

Figure 2.9 Average fault offset (yellow), (a) Strain magnitude (green), and (b) RMS deviation (σRMS, purple) calculated for 1, 3, and 5 km sliding window sizes (solid, dashed, and dotted lines, respectively) along transect A–B (Figure 2.3). The raw slip distribution is plotted in grey in the background of panels (a) and (b). Dashed grey vertical lines indicate inflections in transect A–B. Panel (c) is the same as Figure 2.5a. Correlations between each of the three parameters (fault offset, strain magnitude, and σRMS) are statistically significant (assessed via a p-test) at the 95% confidence level for all three window sizes (Table Table 2.1). . 30

xi Figure 3.1 (a) Tectonic setting of the 4 April 2010 El Mayor-Cucapah earthquake. The red star is the epicenter from the Southern California Seismic Network (SCSN), red lines show the principal surface ruptures from Fletcher et al., and black lines show other active faults. (b) Inset showing wider tectonic setting with the main Pacific-North America plate boundary in bold. (c) Focal mechanisms from seismology with red numbers indicating the dips of the E or NE-dipping nodal planes, marked in red. (d–f) Finite fault models derived from Interferometric Synthetic Aperture Radar and pixel correlation measurements, from Fialko et al., Wei et al., and Huang et al.. Map extents are the same as in (a) and the red star is the SCSN epicenter. Each gray rectangle is an individual model fault segment, shaded darker down dip and labeled withitsdipanddipdirection...... 36

Figure 3.2 Rupture trace within the Sierra Cucapah mountains, colored according to the proportion of the cumulative fault zone slip each segment locally accommodates, using data from Teran et al.. Background hillshaded topography shows the postevent lidar data set...... 39

Figure 3.3 Iterative Closest Point results for a cell size of 100 m, with map extents as in Figure 3.2 and UTM zone 11 coordinates. Panels (a) to (c) show translation components in the x, y, and z axis directions, with positive values indicating motion toward the E, N, and upward, respectively. Major ruptures, locally accommodating >30% of the cumulative fault zone slip, are indicated by black lines . Panel (d) shows rotations about the y axis, with positive values indicating clockwise rotations about the positive axis direction (i.e., tilt toward the east). The annotated faults are the longest, W dipping strand of the Paso Inferior accommodation zone (in the north) and the E dipping Borrego fault (in the south). For ICP x and z axis rotations, see Figure S1 in the supporting information. . 46

Figure 3.4 (a–c) Iterative Closest Point x, y, and z axis displacements within the Puerta accomodation zone. Points A and B are the endpoints of the profile in (d). Faults are marked by black lines, with those accommodating >30% of cumulative strain labeled in (c) . (d) Along-strike profiles of fault dip (small blue/white squares mark individual displacement swath centerpoints, connect by the blue line) and slip (small red/white squares, connected by the red line, with 1σ uncertainties in pink) between points A and B in the Puerta accommodation zone. Because of the strong right-lateral slip component and the oversimplified fault surface trace, we consider only the average results for this fault — a fault dip of 60◦ NE and slip of 2m—as robust. The centerpoints of individual∼ displacement swath∼profiles are plotted in map view in Figure S5 in the supporting information...... 49

xii Figure 3.5 Along-strike profiles of fault dip (small blue/white squares mark individual displacement swath center points, connect by blue lines) and slip (red/white squares, connected by red lines, with 1σ uncertainties in pink) for (a, b) the Paso Superior fault, (c) the longest, W-dipping strand of the Paso Inferior accommodation zone, (d) the Borrego fault, and (e) the Pescadores and Laguna Salada faults. The NW end of each fault is at 0 km distance on the x axis. Corresponding field measurements of dip (blue diamonds) and slip (red circles) are from Fletcher et al.. In (a) and (b), horizontal blue lines show auxiliary dip estimates from plane fitting through four short sections of the Paso Superior fault trace, with blue boxes indicating standard errors. In (e), the short section of dip measurements toward the SW is marked dashed. The center points of individual displacement swath profiles are plotted in map view in Figures S2–S4 and S6 in the supporting information. . . . 51

Figure 3.6 Slip and dip measurements (blue circles) with best fit linear trends (red lines) for (a, b) the Paso Superior fault, (c) the longest, W dipping strand of the Paso Inferior accommodation zone, (d) the Borrego fault, (e) the Puerta accomodation zone, and (f) the northern Pescadores fault. We do not include the southern Pescadores or Laguna Salada faults in this analysis because our dip calculation method fails (i.e. produces largely unconstrained results) for this stretch of fault due to rake values that approach pure strike slip (e.g., 0◦ or 180◦ / -180◦). We therefore only plot results here for the northern section of the Pescadores fault: from 0 to 10.2 km in Figure 3.5e...... 57

Figure 4.1 Tectonic setting of the 1992 Landers earthquake. The 1992 rupture trace (red line) and other late Quaternary faults (black) are from the USGS Quaternary Fault and Fold Database. The 1992 focal mechanism andepicenter(redstar)arealsofromtheUSGS...... 62

Figure 4.2 (a) Overview of the 1992 Landers surface rupture. (b) 10 points/m2 full rupture point cloud. The orange polygon outlines the∼ 17-image higher-resolution point cloud used to make detailed fault measurements of the pull-apart basin in the second test area (Figure 4.5, Figure 4.6, and Figure 4.9). (c) Oblique view of the higher resolution point cloud showing five ground control points. Blue squares indicate camera positions, and black lines their look angles. This point cloud has 329 106 points and covers 8 km2 with an average point density of ∼40 points/m· 2. (d) Zoom in∼ of full-rupture point cloud showing two ∼testsites...... 63

Figure 4.3 Colored SfM-derived point cloud over the first test area. The displayed data are a 9.2 105 point subset of the full rupture-length point cloud (Figure 4.2),∼ cropped· to the same coverage area as a 2008 TLS survey. . . 71

xiii Figure 4.4 Results of cloud-to-mesh (C2M) distance calculations for the first test area. The 7.3 105 point SfM surface from Figure 4.3 is finely registered to, then differenced∼ · against a meshed surface of the 2008 TLS survey. With 18 GPS ground control points, we treat the TLS survey as a “ground truth” representation of the target surface. The average C2M distance is 2 cm with a standard deviation of 14 cm, confirming that our SfM point∼ cloud is geometrically accurate. This∼ C2M distance map outlines (in red) areas of erosion between the 1992 aerial photographic survey and the 2008 TLS acquisition, including both the fault scarp (parallel with the long axis of the differenced cloud) and stream channels(perpendiculartothelongaxis)...... 72

Figure 4.5 Colored SfM point cloud of the second test area. This is a subset of the higher-resolution point cloud generated from seventeen 1:6,000 aerial images. Green lines give locations of six profiles that outline the structure of the pull-apart basin (Figure 4.7)...... 74

Figure 4.6 SfM DEM for the coverage area in Figure 4.5, hillshaded at incidence angle 60◦ and azimuth 055◦. (a) Uninterpreted image displaying fine fault structure across the pull-apart basin. (b) Vertical offsets derived from the point cloud (small circles) and from the field (larger squares), colored by magnitude with positive values indicating east side up. Longer (>100 m) scarps are joined by solid black lines; the dotted black line is the generalized fault trace along which perpendicular profiles are used to determine vertical offsets. Green lines give locations of the six profiles shown in Figure 4.7. (c) Offsets projected onto a N–S profile, with traces of the longer segments joined by solid black linesasin(b). . . 76

Figure 4.7 Example topographic profiles along the cross-sections shown in Figure 4.5, Figure 4.6b, and Figure 4.9 detailing the morphology of the pull-apart basin from north (A–A’) to south (F–F’). Dotted black lines show the center point of each profile, which is the generalized, three segment fault trace in Figure 4.6b. Red dashed lines indicate locations of vertical offset measurements. Note that these profiles have significant vertical exaggeration — the flat-lying alluvial surface (e.g. the surface at negative distances in profile A–A’) dips 2◦ at true scale. These profiles highlight a number of important features∼ of the pull-apart basin: (1) all scarps dip inward toward the basin center, and are thus normal faults; (2) there is significant rotation of the ground surface inside the pull-apart basin, generally towards the nearest normal fault; and (3) there is significant vertical offset associated with the western flank of the basinatnegativeprofiledistances...... 77

xiv Figure 4.8 Histogram of vertical offset measurements (from the locations shown in Figure 4.6b) with 10 cm bin size. Blue bars give bin counts for 173 measurements made through the SfM point cloud; red bars show 21 field measurements . A two-sided Kolmogorov-Smirnov test can not reject the null hypothesis that these two datasets are from the same continuous distribution at the 5% significance level, indicating that point cloud-derived measurements are statistically similar to field measurements...... 78

Figure 4.9 Surface deflection of the 1992 topography from plane fit to the gently-sloping alluvial surface. The older tectonically uplifted alluvial surfaces and the fault are masked out before plane fitting. Red hues show positive deviations from the best fit plane, and blue hues show negative deflections. The dashed black line shows the generalized fault trace along which fault-perpendicular profiles were extracted, and green lines give locations of six profiles that outline the structure of the pull-apart basin (Figure 4.7). This map corroborates measurements (Figure 4.6b) that show west-side-up oblique normal slip south of the pull-apart and east-side-up north of it. Within the pull-apart basin, detailed fault strands are clear, with the maximum negative deflection slightly west of a line bisecting the long axis of the basin...... 81

Figure A.1 Panels (a) to (c) show rotations about the x, y, and z axes, respectively. Positive values indicate clockwise rotations about the positive axis direction. For x axis rotations (panel a), positive values indicate tilt towards the south; positive y axis rotations indicate tilt towards the east (panel b); positive z axis rotations correspond to clockwise rotations in map view (panel c). Parts of the 2010 rupture trace are easily identifiable in the y and z axis rotation results...... 103

Figure A.2 Fault dips calculated along the Paso Superior fault (northern and southern segments) using the calculated x, y, and z offsets in the corresponding ICP displacement fields. Dip values are indicated next to the measurement locations (black circles), and black bars indicate dip direction and magnitude. Magnitudes are displayed as 90◦-dip, such that longer bars indicate shallower dip. The base map displayed gives the magnitude of the vertical ICP displacement field, allowing for rough, visual assessment of how throw varies along the fault. Also shown is the fault trace (red line, from Fletcher et al.) along which the fault profiles are extracted. Dip values are plotted for every other profile...... 104

Figure A.3 Same as Figure A.2, but displaying results for the Paso Inferior fault. . . 105

Figure A.4 Same as Figure A.2, but displaying results for the Borrego fault. Dip valuesareplottedforeveryotherprofile...... 106

xv Figure A.5 Same as Figure A.2, but displaying results for the Puerta accomodation zone. Dip values are plotted for every other profile...... 107

Figure A.6 Same as Figure A.2, but displaying results for the Pescadores and Laguna Salada faults. Dip values are plotted for every third profile. . . . 108

Table 2.1 Correlation results for fault offset, strain magnitude ( ǫ ), and RMS | | deviation (σRMS) for 1, 3, and 5 km sliding window sizes. The correlation coefficient, R, denotes the degree to which two series are related and ranges from -1 to 1. A p-test gives the probability that the null hypothesis (that the two signals are correlated) can be rejected – values < 0.05 indicate a correlation significant at the 95% confidence level. Every correlation in this table is significant at the 95%level. . . . . 31

xvi ACKNOWLEDGMENTS

There are a lot of people to whom I owe a debt of gratitude. Foremost is my thesis adviser, Ed Nissen, for four years of understanding, encouragement, patience, guidance, and access to opportunities. He has been not only an outstanding scientific mentor, but also a fierce snowplow-tuck ski racing adversary. All of the work presented in this thesis is my own. However, I am indebted to several co-authors, named in each individual chapter, for assistance in data gathering and sharing, scientific discussion, and (for the published Chapter 3) minor editing of the manuscript. This thesis has also benefitted from development of concepts and discussion of results with thesis committee members and countless other scientists and friends. Among the many who deserve recognition, I would especially like to thank my fellow DEATH research group members, Kendra Johnson and Ezgi Karas¨ozen. While the majority of funding for this thesis is acknowledged explicitly at the end of each chapter, Newmont Mining is not elsewhere recognized for funding the first year of my PhD work, which did not produce results published herein. I especially appreciate John Lupo, who provided a lot of guidance and resources, and was a pleasure to work with. I am very grateful for small and/or large gestures of support and encouragement that I recieved from faculty members at a number of institutions during difficult stages of my doctoral studies. Emily Brodsky, Hilde Schwartz, Brandon Dugan, Yvette Kuiper, and Manoochehr Shirzaei – thank you. To mom, dad, Cara, grandma Andrea, and grandpa Ken: I am priveleged to be able to chase my dreams with the safety net of your endless love and support. Liz Rose, Kendra Johnson, and Jeffrey Edelen – the family-ship means more than you can know. Thank you, Laura Beer and Courtney McIntyre, for the emotional support, empathy, and inspiration. Many thanks for all the runs and work dates, Danielle Pucherelli.

xvii For:

Grandpa Ken (K. R. Lajoie) – you started this

and

Kate Kelsey – I could never thank you enough

xviii CHAPTER 1 INTRODUCTION

Near-fault surface displacements from high spatial-resolution, remotely-sensed datasets provide a means of characterizing shallow faulting in large earthquakes. Other methods of studying fault structure and properties face significant limitations that can be circumvented using high-resolution topography. Field measurements of faulting only sample the surficial expression of faulting, and are constrained to visible fault offets and deformation. Satellite geodesy samples much broader spatial aperatures of the fault surface deformation, and uses numerical models to study deep ( kilometers below surface) slip and fault structure with ∼ coarse spatial resolution. High-resolution optical and lidar imagery, by contrast, can be used to assess the near-fault surface deformation and more directly evaluate fault properties at higher spatial resolution in the shallow subsurface ( 10s of meters to kilometers). The ∼ ability to constrain fault geometry and behavior at all depths is critical to understanding and mitigating damage during future large earthquakes. With new techniques available to process remotely-sensed datasets, there is an opportunity to analyze existing modern and historical data in new ways, and in some cases, for the first time. This provides both a cost- effective route for future researchers to engage in impactful science as well as an opportunity to expand our understanding of past and present earthquakes. This thesis addresses three key technical questions. (1) What new technologies can be applied to existing, high-resolution topographic datasets for surface-rupturing earthquakes? (2) Can we utilize new technologies and techniques to create new high-resolution topographic datasets? (3) What can we learn using datasets that sample a depth range below surface ruptures that past techniques have not been able to? These questions have implications not only for the mechanics of the ruptures studied herein but also for how to intepret observations in other events where such data are lacking.

1 1.1 Technical Question 1: What new technologies can be applied to existing, high-resolution topographic datasets for surface-rupturing earthquakes?

Differential topography is a relatively new method for assessing geomorphic change, us- ing models of Earths surface to track vertical and/or horizontal surface modification through time. Surface models can comprise, for example, radar images, optical images, or elevation models. Interferometric Synthetic Aperature Radar (InSAR) is ubiquitous in studies of large earthquakes, and is used to measure surface displacements over large areas, though decor- relation along the fault trace of large, surface-rupturing earthquakes limits its usefulness for near-fault studies. Pixel tracking and iterative-closest-point (ICP) registration are cutting- edge correlation techniques developed for optical and elevation datasets (respectively) that allow for detailed offset calculations even in the very near-fault region. Pixel tracking is a method of detecting very fine-scale two-dimensional (2D) offsets between collections of pixels in optical images, while ICP registration calculates rotations and translations for three-dimensional (3D) surfaces. In pixel tracking, a packet of pixels from one image is translated across a second image until the cross correlations between intensities in the x and y dimensions of the translated pixels and static image are maximized. The translation that achieves the maximum cross correlation gives the displacement of the translated pixels relative to the x and y image coordinate axes. Where this is done for many small parcels of pixels (down to about 16-by-16 pixel windows) across a scene, the result is a map of the displacement field from one image to the next. Pixel tracking for earthquake studies is most commonly applied to satellite and/or aerial photograph pairs, after they are first ortho-rectified to account for distortions due to changing viewing angle [e.g. Avouac et al., 2014, Hollingsworth et al., 2012, Milliner et al., 2015, Milliner et al., 2016, Zhou et al., 2016]. The largest drawback of this method is that all offsets are computed within the image plane, which for ortho-rectified images is a horizontal plane parallel to Earths surface, and can produce no vertical deformation estimates. Some studies have attempted to generate two-and-a-half-dimensional (2.5D) displacement surfaces

2 by coupling the 2D pixel tracking results with results of subtracting pre-event from post- event gridded digital elevation models [e.g. Oskin et al., 2012]. However, elevation changes are of limited value in parts of rupture zones characterized by rugged topography and where horizontal motions exceed vertical ones, and this approach should be used with hesitation. Where 3D elevation data before and after an earthquake exist, ICP represents a powerful technique for calculating 3D offsets. A reference point cloud remains fixed in space while an- other point cloud (or small subsets thereof) is iteratively rotated and translated to minimize the distance between the two datasets, resulting in displacement estimates for rotations and translations along the x, y, and z coordinate axes. However, it is important to note that ICP might have the tendency with gridded data (DEMs) to artificially snap displacements to the rasterized data grid. Pixel tracking, by contrast, can compute horizontal offsets of gridded data reliably to a precision of around one tenth of a pixel dimension, but cannot easily be applied to irregular datasets. Therefore, ICP is considered obviously superior to pixel tracking and 2.5D displacement estimates only for ungridded point cloud data. This technique was developed in the early 1990s [Besl & McKay, 1992, Chen & Medioni, 1992], but has thus-far had very limited appliactions to earthquake science. The only examples I am aware of, in fact, are Glennie et al. [2014], Nissen et al. [2014], Scott et al. [2018]. Glennie et al. [2014] is the basis of work presented in Chapter 3, and I am co-author on Scott et al. [2018]. In Chapter 2 of this thesis, I adapt optical image detection techniques to gridded el- evation data, and present the first-ever study to use optical pixel tracking on topographic data. Application to lidar topographic data obviates the need for ortho-rectification, such that we can apply the sub-pixel correlator either directly to raw digital elevation models or to any regularly-gridded derivative such as hillshades or slope maps. The eight day repeat interval between lidar acquisitions for 2016 Kumamoto earthquake is a record for earth- quakes by about three orders of magnitude [Clark et al., 2017, Glennie et al., 2014, Nissen et al., 2014], but I was granted access to only gridded digital surface models (DSMs) and

3 not the raw point cloud data. I elected, therefore, to compute very precise horizontal surface deformation maps. This decision is justified because the Kumamoto earthquake is primarily a right-lateral strike-slip event, and deformation should primarily express in a horizontal plane.

1.2 Technical Question 2: Can we utilize new technologies and techniques to create new high-resolution topographic datasets?

Airborne and terrestrial lidar have become standard methods for rapidly producing high- resolution models of post-earthquake topographic surfaces in the past decade. While it remains perhaps the most accurate method of generating elevation datasets, lidar presents two major drawbacks to earthquake scientists: (1) it is expensive and requires highly special- ized equipment and (2) in areas where no pre-event topographic data exist, it is impossible to retro-actively generate a lidar point-cloud. Airborne lidar surveys may cost between sev- eral hundred to several thousands of dollars per square kilometer depending on target area size, with extra costs incurred for more precise ground-based GPS referencing to improve airplane location. Ground based lidar is less cumbersome and costly, but practical only for small areas. Because of these financial and logistical restrictions, only very limited expanses of Earths surface have been surveyed with lidar, meaning that for most large earthquakes, the chance of a pre-event lidar dataset existing is quite small. Reflecting this improbabil- ity, paired pre- and post-earthquake lidar datasets exist for only very few earthquakes [e.g. Duffy et al., 2013, Oskin et al., 2012]. Two of these earthquakes are studied in this thesis (Chapters 2 and 3). However, a cutting-edge technology allows point clouds to be generated in a new way: using aerial photographic surveys. Structure from motion (SfM) is a method of generating three-dimensional point clouds from optical images taken at various viewing angles over the same target area or object [James & Robson, 2012, Snavely et al., 2008, Westoby et al., 2012]. SfM computes the structure of a scene by triangulating the positions of features recognized in multiple images. Importantly, “structure” refers to both the geometry of the

4 imaged feature (topography, for aerial surveys) as well as camera parameters such as location (relative to the scene), orientation, and focal length – and so SfM can be used even when no survey metadata exist, making it ideally suited for use with legacy datasets where such information is crude or lacking. The feature recognition algorithm employed by SfM [Scale Invariant Feature Transform; Lowe, 2004, Snavely et al., 2008] can also accomodate irregular and/or unknown image acquisition geometries. In Chapter 4, I use SfM to show how that a historical aerial photographic dataset collected just after the 1992 Mw 7.3 Landers, California earthquake can be used to generate point clouds rivalling lidar in both precision and accuracy. This is the first study using historical photographs to generate point clouds for earthquake studies, and is presented as a proof-of-concept to show how such datasets can be generated for other earthquakes.

1.3 Technical Question 3: What can we learn using datasets that sample a depth range below surface ruptures that past techniques have not been able to?

With my thesis adviser and numerous co-authors, I focus on three earthquakes for which various types and qualities of pre- and post-event datasets exist. The data are coupled with relevant cutting-edge processing and differencing tools to generate high-resolution two- and three- dimensional deformation maps or topography, and then analyzed using a semi- automated procedure for measuring fault offsets that I developed within Matlab. These tools and techniques allow us to assess fault geometry, mechanics, and/or long-term behavior.

In Chapter 2, we study the 2016 Mw 7.0 Kumamoto, Japan earthquake, for which pre- and post-event gridded digital elevation model (DEM) datasets are available. We compute high-resolution two-dimensional fault offsets along strike using optical pixel tracking on the hillshaded DEMs, and investigate the calculated slip distribution to assess variations in roughness and strain along the rupture and as a function of observation scale. Unsuprsingly, we find that the surface slip distribution correlates strongly with fault trace complexity. However, we also find that the slip roughness varies spatially, differing across fault strands

5 and achieving maximum values (and highest surface strains) following the merging of two fault segments. Nevertheless, slip roughness is comparable to values calculated for other large earthquakes hosted on similarly immature fault systems [Milliner et al., 2016], but higher than values for large earthquakes on more mature faults. This corroborates other studies finding that faults become progressively smoother with accumulated slip [e.g. Brodsky et al., 2011, Wesnousky, 1988], unless the calculated slip distribution does not directly reflect fault roughness. Chapter 3 presents a new method for calculating shallow subsurface fault dip using three-dimensional surface displacements, and focuses on the 2010 Mw 7.2 El Mayor-Cucapah, Mexico earthquake, for which we have both pre- and post-event lidar point cloud data. For this earthquake, full three-dimensional surface displacements are computed using an imple- mentation of the Iterative Closest Point (ICP) algorithm, and fault offsets measured in the resulting x, y, and z displacement surfaces constrain total slip as well as fault dip along strike. We find evidence for localized coseismic low-angle normal faulting at multiple lo- calities, providing some of the first confirmed examples of seismic slip along a continental low-angle normal fault during the instrumental period. Additionally, we observe depressed slip magnitude along these low angle structures relative to adjacent steeper sections of fault- ing, with a statistically significant correlation between fault dip and offset magnitude for fault segments with oblique-normal sense of offset. Rupture also appears to have jumped from a low-angle structure to steeper neighboring faults at one or two segment boundaries. This suggests that fault dip provided a first order control both on the path of the surface rupture and on the amount of localized surface slip.

In Chapter 4, we explore the 1992 Mw 7.3 Landers, California earthquake and show that legacy aerial photography datasets re-analyzed with modern processing techniques can add to our understanding of even the best-studied historical earthquakes. Airborne lidar topography has become a staple of modern earthquake investigations, and this chapter serves as a proof-of-concept for a method to develop similar-quality, high-resolution topographic

6 datasets for historical earthquakes or remote modern events for which aerial surveys have been undertaken. We exploit a rich set of 365 1:6,000 black-and-white aerial images collected by the USGS just days after the earthquake, and pair it with Structure from motion (SfM) – a method of generating three-dimensional point clouds from optical images taken at various viewing angles over the same target area or object [James & Robson, 2012, Snavely et al., 2008, Westoby et al., 2012] – to generate an accurate and scientifically relevant topographic point cloud with generic, freely available remotely sensed data. Our SfM point cloud has only slight morphological differences from a 2008 GPS-georeferenced terrestrial lidar survey, and we are able to reproduce field measurements of fault offset within statistical significance. Additionally, our measurements prompt a reassessment of the rupture dynamics and fault structure of a small pull-apart basin. In our new interpretation, both bounding branches of the pull-apart basin were coseismically activated. These three manuscripts together highlight the potential for high-resolution topographic analysis of earthquakes, both modern and historical. Advances in analytical methodology allow us to compute detailed surface topography and deformation models, and enable a more complete understanding of fault zone architecture and properties.

7 CHAPTER 2 SURFACE SLIP PROPERTIES OF THE 2016 KUMAMOTO, JAPAN EARTHQUAKE FROM DIFFERENTIAL LIDAR

pending submission to Geophysical Research Letters Lia J. Lajoie1, Edwin Nissen1,2, Emily E. Brodsky3, Chelsea Scott4, Tadashi Maruyama5,J Ram´on Arrowsmith4, Tatsuro Chiba6, and James Hollingsworth7,8

Abstract Coseismic surface deformation fields provide us with information about the physi- cal and mechanical properties of faults and fault zones. Recent advances in geodetic imaging allow us to map deformation and derive fault offset distributions at spatial resolutions that were previously unattainable. In this paper, we utilize high-resolution, 8 day repeat airborne

lidar data to compute lateral offsets along the southwestern half of the 16 April 2016 Mw 7.0 Kumamoto earthquake rupture, which serves as structurally-immature (low cumulative slip) end member amongst the suite of recent large strike-slip events studied using similar meth- ods. Applying the COSI-Corr sub-pixel correlation software to 0.5 m-pixel hillshade models enables us to map horizontal displacements at a resolution of 8 m. From these results, we measured 517 right-lateral offsets from fault perpendicular profiles spaced at 40 m intervals along the rupture trace. We find that the magnitude of slip along the fault correlates strongly with structural complexity along mapped fault trace, and that the calculated measurements of fault slip are in general larger than those recorded in the field, implying a significant shallow slip deficit. The power spectral density and root mean square devation of the slip

1Department of Geophysics, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401, USA 2School of Earth and Ocean Sciences, University of Victoria, Victoria, BC, Canada 3Earth and Planetary Sciences Department, University of California, Santa Cruz, CA 4School of Earth and Space Exploration, Arizona State University, Tempe, AZ 5Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan 6Research and Development Institute, Asia Air Survey Co., Kawasaki, Japan 7Universit´eGrenoble Alpes, ISTerre, Grenoble, France 8CNRS, ISTerre, Grenoble, France

8 distribution are analyzed as proxies for slip roughness. The Kumamoto slip distribution is similarly rough as those of the 1992 Landers and 1999 Hector Mine earthquakes, on some- what more mature fault systems, but is much rougher than the 2013 Baluchistan earthquake slip distribution, on a much more mature fault. Overall, these results support the notion that faults become progressively smoother with accumulated slip.

2.1 Introduction

Earthquake surface ruptures are normally the only place where one can observe seismo- genic faulting directly. Measurements of surface slip and its variability along strike therefore provide crucial insights into the physical and mechanical characteristics of faults and fault zones. Within the past decade, advances in geodetic imaging data and techniques have enabled sampling of surface slip in large earthquakes at much higher spatial densities than were previously possible. Whereas finite fault models inferred from far-field geodetic data and/or seismic waveforms depend upon assumed Green’s functions and artificial smoothing constraints in order to link surface displacements to slip at depth — often leading to a vari- ety of published slip distributions for a given earthquake, with no clear ‘correct’ solution — there is no such reliance for surface slip profiles. These can provide a more immediate eval- uation of vital properties such as slip roughness, which is likely important in the generation of damaging seismic waves [e.g. Milliner et al., 2016], and the apparent ‘shallow slip deficit’ commonly observed in earthquakes, which is a crucial factor in interpreting paleoseismic or geomorphic records of long-term slip [e.g. Dolan & Haravitch, 2014, Gold et al., 2015, Zinke et al., 2014].

The 2016 Mw 7.0 (Mjma 7.3) Kumamoto (Japan) earthquake was captured using a rich as- sortment of geodetic data ranging from satellite surface displacement measurements, through airborne lidar topographic surveys, to field measurements of fault offsets. This earthquake occurred on a structurally-immature fault system with relatively little cumulative geological offset, and therefore serves as an end-member in the spectrum of recent large earthquakes studied using these methods, most of which occurred on faults with at least twice as much

9 cumulative offset. In this paper, we first determine the near-field displacement field of the Kumamoto earthquake using sub-pixel correlation of pre- and post-event lidar topography (Section 2.3), for which this is amongst the first events ever imaged [Clark et al., 2017, Glen- nie et al., 2014, Nissen et al., 2014, Scott et al., 2018]. From these measurements, we then derive the surface slip distribution (Section 2.4) and examine its characteristics in light of other recent large earthquakes surveyed by similar correlation methods (Section 2.6). This inter-event comparison serves to test whether coseismic surface slip characteristics are gov- erned by the structural maturity and complexity of the host faults, as has been proposed previously [Dolan & Haravitch, 2014, Milliner et al., 2016].

2.2 Overview of the Kumamoto Earthquake

The 16 April 2016 Mjma 7.3 Kumamoto earthquake was the largest of a sequence of shallow, predominantly dextral strike-slip earthquakes along the Hinagu-Futagawa fault zone (HFFZ), central Kyushu, in April 2016 (Figure 2.1). This fault zone is located at the western end of the right-lateral Median Tectonic Line (MTL) (Figure 2.1a) and marks the southern margin of the Beppu-Shimabara graben [Ikeda et al., 2009, Kamata, 1992, Kusumoto, 2016].

A large Mjma 6.5 foreshock on 14 April produced minor, scattered surface ruptures across the intersection of the NNE-trending Hinagu fault segment and the NE-trending Futugawa fault segment [Sugito et al., 2016] (Figure 2.1b). On 15 April, a second large foreshock of

Mjma 6.4 occurred south-west of the first, likely on the Hinagu fault. Other aftershocks of the largest foreshock appear to have migrated toward the triggering site of the mainshock at the northern end of the Hinagu fault zone [Kato et al., 2016, Yoshida et al., 2016]. The mainshock ruptured unilaterally northeastwards from the Hinagu fault onto the Futagawa fault and arrested on the western slopes of Aso volcano, producing a 34 km- ∼ long surface rupture with measured dextral offsets of up to 220 cm across the principal fault trace [e.g. Asano & Iwata, 2016, Hao et al., 2016, Lin et al., 2016, Miyakawa et al., 2016, Shirahama et al., 2016, Yagi et al., 2016]. Along the central part of the rupture, mapped surface faulting and kinematic inversions indicate strong slip partitioning between

10 a Honshu 130˚55' 131˚00' Line tonic Tec b ian Shikoku ed M Aso Volcano Main Figure

Okinawa Terraces of Quaternary Kyushu h Trough ug volcanic rocks ro Aso Caldera i T a k n a N

Idenokuchi Fault Kumamoto Plain 14th April 2016 (Pleistocene alluvium) first foreshock, 12:26 JST Mjma 6.5, depthjma 11 km “North strand” Futagawa Fault minor foreshock ruptures observed on 15th April (Sugito et al., 2016) 15th April 2016 second foreshock, 00:03 JST Mjma 6.4, depthjma 7 km

32˚45' time 32˚45' 32˚50' Hilly terrain of Cretaceous first airborne lidar survey sedimentary and Quaternary volcanic bedrock 16th April 2016 mainshock, 01:25 JST Mjma 7.3, depthjma 12 km mainshock surface ruptures Hinagu Fault (Shirahama et al., 2016) 24th April 2016 5 km second airborne lidar survey

130˚45' 130˚50' 130˚55' 131˚00'

130˚40' 130˚50' 131˚00' 130˚40' 130˚50' 131˚00'

33˚00' +3 c +3 d +2 +2 +1 +1 0 0 -1 -1 -2 -2 -3 -3 meters meters

32˚40' 32˚50' 10 km 32˚40' 32˚50' 10 km 32˚40'32˚40' 32˚50' 32˚50'

130˚40' 130˚50' 131˚00' 130˚40' 130˚50' 131˚00'

Figure 2.1: (a) Regional tectonic setting. (b) Moment tensor solutions, surface ruptures, and lidar coverage area for the April 2016 Kumamoto earthquake sequence. (c) E-W and (d) N-S displacement fields from correlating SPOT 7 satellite photographs from 14 December 2015 and 20 April 2016. The spatial coverage is much greater than for the lidar data (dashed polygon) but results are also noisier. Because stereo image pairs were used, we are also able to estimate vertical deformation, but this signal is dominated by noise and is not shown.

11 distinct strike slip and normal faults [Himematsu & Furuya, 2016, Shirahama et al., 2016]. The largest surface offsets coincide spatially with peak slip at depth of 6 m inferred from ∼ geodetic and seismological data [e.g. Asano & Iwata, 2016, Hao et al., 2016, Yagi et al., 2016]. Paleoseismic trenching at the locations of greatest surficial strike-slip offset on the Hinagu and Futagawa faults suggests late Holocene recurrence intervals for surface-rupturing events of 1000 years, with corresponding slip rates of 0.5–0.7 mm/yr (Hinagu fault) and 1.7– ∼ 2.7 mm/yr (Futagawa fault) [Lin et al., 2017]. Projecting these slip rates to the approximate inception of the HFFZ, at 0.7–0.5 Ma, yields an estimated cumulative offset of 250–500 m ∼ ∼ and 850–1,900 m for the Hinagu and Futagawa faults, respectively [Lin et al., 2017, Toda ∼ et al., 2016] – in agreement with a geological dextral offset of 750 m of prominent interbeds ∼ in Cretaceous Ryoke metaphorphic rocks on the south-western Hinagu fault (Gneiss and schist, unit 151; Geological Survey of Japan, AIST [2009]).

2.3 Surface Deformation Field

To analyze the surface slip distribution in detail, we first tested two standardized, satellite- borne geodetic imaging techniques: sub-pixel correlation of satellite optical images (com- monly known as ‘pixel tracking’), and Interferometric Synthetic Aperture Radar (InSAR). In the first case, Satellite Pour l’Observation de la Terre 7 (SPOT 7) images were correlated using the Caltech COSI-Corr (Co-registration of Optically Sensed Images and Correlation) software package, a widely-used raster pixel tracking algorithm [Leprince et al., 2007]. The resulting E-W and N-S displacement fields capture the complete rupture extent, but are too noisy to resolve fine details of the slip distribution (Figure 2.1 c and d). In the second case, interferograms constructed using Sentinel-1A SAR images are successful at detecting line- of-sight displacements several kilometers or more from the surface rupture, but break down at closer distances due to steep phase gradients, a common limitation of this method. This leads us to examine the use of lidar imagery in contraining surface slip along the rupture trace.

12 2.3.1 Data

We utilized two 0.5 m-resolution raster digital surface models (DSMs) derived from air- borne lidar surveys flown by Asia Air Survey, Co. on 15 April 2016 (in response to the pair of strong foreshocks) and eight days later on 23 April (in response to the mainshock). We were not initially granted access to the raw point clouds, nor the ‘bare earth’ terrain models stripped of vegetation returns, and so the data used approximates the canopy top in forested areas. Nevertheless, the eight day repeat interval is a record for an earthquake spanned by lidar acquisitions by about three orders of magnitude [Clark et al., 2017, Glennie et al., 2014, Nissen et al., 2014] — indeed, it rivals satellite methods for short duration — and so vegeta- tive growth and seasonal changes are likely to be minimal. The difference between the two lidar surveys mostly reflects coseismic mainshock deformation, with an additional one day of foreshock postseismic deformation and one week of mainshock postseismic deformation. The overlapping area between the two surveys covers the south-western half of the main- shock surface rupture, from near the southern terminus of the rupture on the Hinagu fault, across the Hinagu-Futagawa fault junction, to about half way along the main Futugawa rupture, but stopping well shy of the rupture termination at Aso Caldera (Figure 2.1).

2.3.2 Methods

From the paired lidar DSMs, we mapped the surface deformation field in COSI-Corr [Leprince et al., 2007], which resolves horizontal displacements from two-dimensional (2-D) gridded images by correlating pixel subsets. We opted to use 2-D pixel tracking as opposed to three-dimensional registrations based on the Iterative Closest Point algorithm [Nissen et al., 2012], having found that the latter produces noisier horizontal displacements, likely reflecting a tendency to snap displacements to the rasterized data grid. Pixel tracking, by contrast, can compute horizontal offsets of gridded data reliably to a precision of around one tenth of a pixel dimension, but cannot easily be applied to irregular datasets. For this earthquake, with access initially only to gridded data, and with horizontal displacements

13 likely to far exceed vertical ones along most of the captured rupture trace, we therefore chose to use COSI-Corr. Pixel tracking is most commonly applied to satellite and/or aerial photograph pairs, after they are first ortho-rectified to account for distortions due to changing viewing angle [e.g. Avouac et al., 2014, Hollingsworth et al., 2012, Zhou et al., 2016]. Application to lidar topographic data obviates the need for ortho-rectification, such that we can apply the sub-pixel correlator either directly to the raw 0.5 m DSM or to any regularly-gridded derivative such as hillshades or slope maps. We used COSI-Corr’s frequency correlator, which is more accurate for low noise images and produced dramatically more detailed results for our datasets than the statistical correlator [Leprince et al., 2007]. Frequency correlation computes a rough estimation of displacement on large patches of pixels, which is then used to pre-condition a final, sub-pixel correlation using a smaller patch size. We selected an initial window of 256 by 256 pixels (128 128 m), to accommodate noise in the gridded × data (mostly due to vegetation cover), and a final patch size of 32 by 32 pixels (16 16 m) × to minimize the degree of smoothing in the final correlation results. We used a step size of 16 pixels in both the x (E–W) and y (N–S) directions for a final displacement field resolution of 8 meters. We found that using the raw DSMs fails to produce robust pixel displacements that capture the fault discontinuity, perhaps due to subdued topographic relief within the fault zone with respect to the overall scene. By contrast, hillshaded images produced a robust dis- placement field that clearly resolves offset along the surface rupture trace. This improvement represents the accentuation of topographic texture, irrespective of absolute surface elevation, in the hillshade image compared to the original elevation model. We tested combinations of six illumination azimuth values (030◦, 045◦, 060◦, 135◦, 225◦, and 315◦), and four illumi- nation elevation angles (30◦, 45◦, 60◦, and 75◦), but could not visibly discern differences in the resulting displacement fields. The method is therefore largely insensitive to the altitude and elevation of the artificial lighting source, but our final results were determined using

14 hillshades with lighting azimuth and elevation angles of 45◦ and 60◦, respectively. Granted access to the classified lidar point clouds, Scott et al. [2018] recently used a win- dowed adaptation of the Iterative Closest Point algorithm to map 3-D surface displacements across the same study area. A qualitiative, visual comparison of our own 2-D displacement field with the horizontal components of Scott et al.’s [2018] 3-D displacement field reveals no discernable differences, lending confidence in both methods.

2.3.3 Results

The resulting horizontal displacement field is shown in Figure 2.2. By projecting the E–W component (Figure 2.2a) and N–S component (Figure 2.2b) into the fault parallel direction (045◦), we calculated offsets in the approximate bulk transport direction for the predominantly strike-slip earthquake (Figure 2.2c). In subsequent analyses, we use a more complex, three-segment approximation to the fault trace. To first order, the fault-parallel displacements are consistent with the observed right-lateral slip mechanism for the 2016 Kumamoto earthquake, with negative (southwestward) motions SE of the fault, and positive- to-neutral motions NW of it. These data also clearly delineate the main fault strands where fault scarps were measured in the field [Shirahama et al., 2016] (Figure 2.2c). Projecting displacements instead into the 315◦ direction — roughly perpendicular to the fault surface trace — highlights a clear fault birfurcation in the northeastern part of the lidar double coverage area (Figure 2.2d). Prominent northeast-southwest trending (i.e. roughly fault-parallel) stripes are clearly visible at the edges of the lidar acquisition swaths, as has been observed in other differ- ential lidar datasets [Glennie et al., 2014]. Fortunately, except for a few localities where these artifacts closely align with the rupture trace, they do not pose a severe challenge for determining the slip distribution. Additionally, smaller polygonal artifacts identify areas of poorly-constrained displacement with low correlation coefficients. These artifacts are con- centrated within the flat Kumamoto Plain, an area of low relief in which there is often little variation among neighboring pixels in either topography or slope. However, some of these ar-

15 a b

E N 2 2 1 1 0 0 −1 −1 −2 −2 displacement (m) W displacement (m) S −30000 −25000 −20000 −30000 −25000 −20000 −20000 −15000 −10000 −20000 −15000 −10000 c d

NE NW

−25000 −20000 2 −25000 −20000 2 1 1 0 0 −1 −1 −2 −2 displacement (m) SW displacement (m) SE −30000 −30000 −20000 −15000 −10000 −20000 −15000 −10000

Figure 2.2: Displacement fields constructed from pre- and post- earthquake hillshaded DSMs. (a) East-west displacement field, with positive values indicating motion towards the East. (b) North-south displacements, with positive towards the North. (c) NE-SW displacement field, with positive towards the NE and thus approximately parallel to the fault. Black dots show locations of field measurements from Shirahama et al. [2016]. (d) NW-SE displacement field, with positive towards the NW and approximately perpendicular to the fault.

16 tifacts may indicate areas of concentrated building collapse [Moya et al., 2017], which would also lead to poor correlation, though we have not been able to verify this against ground surveys of building damage. Regardless of their cause, this second type of artifact is rarely observed close to the fault trace where it might complicate surface offset measurements. Consequently, there is no justification for increasing correlation window size, which would decrease the number of artifacts but at the expense of reducing the spatial resolution of the displacement field.

2.4 Surface Slip Distribution 2.4.1 Methods

Next, we measured 517 right-lateral offsets along the fault from 374 evenly-spaced swath profiles through the fault-parallel horizontal displacement field (Figure 2.3). For this analysis we use a generalized, three-segment approximation to the rupture trace to better reflect the morphology of the surface rupture, rather than an overly simplistic 045◦ trend. Each swath profile is oriented perpendicular to the nearest segment of the generalized rupture trace, and displacements are likewise projected into the direction parallel to this segment. The swath profiles are 40 m wide, 3 km long, and are spaced at 40 m increments along the fault. Offsets are measured by fitting straight lines through the surface displacement data pro- files on each side of the visible fault scarp or fault zone using a least squares approach, extrapolating the two curves to the fault, and differencing. Because we are computing these offsets from fault parallel horizontal displacements, they represent horizontal (right-lateral) slip. We semi-automate this process within Matlab, with the user specifying only the fault location and the lateral intervals over which curves are fit to the displacement profiles. This allows for human discretion in avoiding artifacts in the displacement data, where identifi- able, rather than attempting to remove artifacts by smoothing the data. Figure 2.4 shows examples of linear fits with associated 50% error bounds through swath profiles containing single faults (Figure 2.4a,b) or multiple faults (Figure 2.4c).

17 B −20000 −24000

displacement (m) in direction parallel to closest fault segment 2

1 −28000 0 −1 A −2

−20000 −16000 −12000 −8000

Figure 2.3: Fault offset measurement transect A–B (heavy black line, 3 segments) and fault- perpendicular profiles (thin black lines), which we use to calculate the surface slip profile in Figure 2.5b. 517 surface slip measurements were calculated along 374 fault-perpendicular profiles — for clarity only every fifth profile location is shown here — and then projected onto the transect A–B. The background displacement field is projected into the direction parallel to the nearest fault segment.

18 2

1

0 fault-parallel

displacement (m) a -1 -11273/ -20072 -2000 200 400 600 800 1000 distance along fault-perpendicular profile (m) 3 2 1 0 fault-parallel

displacement (m) -1 b -11497/ -20300 -2 -400 -200 0 200 400 distance along fault-perpendicular profile (m)

2

1

0

fault-parallel -1 displacement (m) c -13793/ -22643

-1000 -800 -600 -400 -200 0 200 distance along fault-perpendicular profile (m)

Figure 2.4: Examples of swath profiles and derived offset measurements at (a, b) two single- stranded rupture localities and (c) one multi-stranded rupture locality. The x axis shows distance from the simplified fault trace A–B, shown in Figure 2.3, and the Eastings and Northings coordinates of the profile center point (in meters) are given in the lower left of each plot. Black circles are fault-parallel displacement data points. Least squares linear fits with 50% uncertainties are shown by solid red lines, as calculated between paired vertical gray bars. These linear fits are then projected (dotted red lines) to the fault (vertical blue line) where the offset is measured (faint blue rectangles).

19 2.4.2 Results

In Figure 2.5b, cumulative offset measurements for each of the 374 profiles are plotted as a function of distance along the 15 km-long simplified rupture trace (A–B in Figure 2.3). ∼ The slip distribution for this southwestern half of the rupture (recalling the limits of the lidar double-coverage area shown in Figure 2.1b) shows markedly varying behavior along transect A–B. Along the southwestern section of the profile, offsets are scattered in the 0–1 m range without showing any clear general trend. Moving to the northeast, in the area of overlap between the main and north strands of the Futagawa fault, total fault slip increases abruptly at 7 km to between 1.5–3 m, and remains high for the length of transect A–B where fault ∼ ∼ segments 4 and 5 overlap (Figure 2.5a,b). Northeast of the merging of these strands, slip decreases somewhat at 11 km, and then increases once more starting at 14 km. The ∼ ∼ region northeast of the join, from 7–15 km, is also marked by a noticeable increase in ∼ along-strike slip variability. These patterns in cumulative slip are clarified by plotting offsets for each fault strand individually (Figure 2.6a,b). Rupture initiates at depth along segment 1, propagating north- wards onto segments 2–4. There is very little change in offset amplitude as rupture steps from segment 1 to segment 2 – from the pattern of lidar-derived offset measurement loca- tions, this appears to be a releasing step-over along a right-lateral oblique fault. It appears that the transfer of slip onto the next two segments (both apparent restraining step-overs) is accompanied by an increase in lateral offset, although we note these increases also co-locate with the start of segment 5. Starting around kilometer 7, slip on segment 4 increases steadily to a maximum around 9 km, after which it decreases rapidly and terminates at 11 km along ∼ transect. Along this same stretch, slip on segment 5 remains low until slip on segment 4 peaks, after which slip on segment 5 increases rapidly to its maximum around kilometer 11, such that the total slip across both faults in the overlap region remains relatively stationary. North of the overlap area (starting at 11 km), slip on segment 5 remains relatively high, ∼ while net slip is depressed by antithetic fault slip on segment 6. Thus, the transfer of slip

20 a -20000 -18000 -16000 -14000 -12000

Segment 4 Segment 5

Segment 1 Segment 6

Segment 2 Segment 3 A -28000 -26000 -24000 -22000 B

3.5 b 3

2.5

2

1.5

1

0.5

measured fault offset (m) 0

-0.5 0 2 4 6 8 10 12 14 distance along transect A-B (km) 104 104 104 ) ) ) 3 c Peridiogram method 3 d Thomson multi- 3 e Welch method taper method

102 102 102

100 100 100 D = 2.077 D = 1.883 D = 1.862 H = -0.077 H = 0.117 H = 0.138 R = 0.244 R = 0.773 R = 0.775 power spectral density (m power spectral density (m 10-2 10-2 power spectral density (m 10-2 102 103 104 102 103 104 102 103 104 wavelength (m) wavelength (m) wavelength (m)

Figure 2.5: (a) Locations of lateral offsets measured in the field (from Shirahama et al. [2016]; red dots with black border) and from lidar displacement profiles (colored by segment). Dashed black line indicates transect A–B, with dashed grey lines marking inflections in the transect line (panel b and Figure 2.3). (b) Right-lateral surface offsets measurements made from lidar displacement swath profiles with 50% error bounds (blue), and right-lateral offsets measured in the field (red, from Shirahama et al. [2016]). The lidar-derived offsets are cumulative across the profile length (Figure 2.3), and capture deformation across the full damage zone rather than only at the primary fault trace [Dolan & Haravitch, 2014]. Field offsets tend to be lower, representing single scarp measurements. The lidar-derived offsets can also be used to fill in gaps in the field data, most notably between 10 km and 14.9 km on the transect, which is actually revealed to be the area of high slip. (c) Periodogram, (d) Thomson multitaper and (e) Welch power spectra for the lidar-derived right-lateral offset distribution shown in (a). Red lines indicate best fits to power spectra.

21 from one segment to another is accomplished by maintaining constant right-lateral offset across the whole system. The lidar-derived slip measurements fill in several significant gaps in the field data (red datapoints in Figure 2.5b), most notably at the intersection between the Hinagu and Fu- tagawa faults ( 2 km to 3.5 km of the transect A–B) and along a section of high slip ∼ ∼ ( 10 km to 15 km). The two sets of measurements mostly agree within error within the ∼ ∼ low slip ( 0–1 m) southwestern region between 0 km and 7 km, but further northeast, ∼ ∼ ∼ lidar-derived cumulative slip tends to be higher than colocated field measurements. This dis- crepancy can be expected because (1) the lidar profiles capture the cumulative displacement across all offset features measured, and thus provide an estimate of the total deformation across the fault zone, and (2) offset measurements made in profile can capture non-localized shear zones as well as other off-fault deformation (both elastic and plastic) that might not be measurable or noticeable in the field. An examination of individual fault offsets in Fig- ure Figure 2.6b shows that offset measurements along the entire fault length are in general agreement, though with a slight bias towards smaller field measurements. This discrepancy may also represent a true shallow slip deficit along the fault trace that can be detected in profile because surface deformation at distance from the fault trace is recording deformation that occurred deeper along the fault plane. This question is examined in detail by Scott et al. [2018], and we do not discuss it further here.

2.5 Surface Slip Roughness and Strain

Finally, we assess the roughness of the slip distribution and estimate the surface strains that slip variations accommodate. Previous studies of fault slip distributions [Mai & Beroza, 2002, Milliner et al., 2016] and fault surfaces [Candela et al., 2009, Candela et al., 2011, Renard et al., 2006, Schmittbuhl et al., 2006] indicate fractal behavior, with variability dependent on observational length scale. We use two analytical methods to assess this behaviour: the frequency spectrum and root mean square deviation. For a fractal sequence, both measures will vary linearly with measurement length scale in logspace.

22 a -20000 -18000 -16000 -14000 -12000

Segment 4 Segment 5 Segment 1 Segment 6

Segment 2 Segment 3 A -28000 -26000 -24000 -22000 B

b 3

2

1

0 lateral fault offset (m)

-1

0.01 c

0 strain

-0.01

× 10-4 )

-1 d 2

0

-2

strain gradient (m 0 2 4 6 8 10 12 14 distance along transect A-B (km)

Figure 2.6: (b) Slip distribution, (c) strain , and (d) strain gradient in relation to (a) surface trace complexity as outlined by locations of field measurements (red dots with black border) and lidar displacement profile measurements (colored dots) of lateral fault offset. Data in panels (b–d) are presented both by individual fault segment (colored according to panel a) and for the generalized fault trace along transect A–B (grey) (Figure 2.3). Dashed, vertical grey lines indicate inflections in the transect A–B. (b) Red dots show field measurements of lateral offset. Plotting the data by individual fault strand shows that much of the discrepancy between field measurements and lidar displacement field measurements in Figure 2.5b from 7 km and 10 km is due to summation of multiple strands across profile. Additionally, these ∼high-density∼ offset measurements show how slip transfers from one fault strand (segments 1-4) onto another (segment 5) – slip remains low (<1 m) on segments 1–3, then increases dramatically on segment 4 at the same distance along transect A–B that segment 5 appears. As slip increases on segment 5, slip on segment 4 lowers, such that the total slip across both faults remains relatively stationary. (c) Strain and (d) strain gradient are presented as 3 point moving averages along the rupture. Red, horizontal dashed lines indicate one standard deviation in strain and strain gradient for the generalized fault trace (grey curves) for a 3 point moving window. Fault offset, strain, and strain gradient all increase significantly northeast of 7 km along the transect, where two major fault segments overlap. ∼

23 2.5.1 Power Spectral Density

Power spectra describe the relative importance of sinusoidal components of a signal, with a steeper slope in logspace indicating more scale dependence, and a greater vertical shift (prefactor) indicating larger amplitude oscillations. Scale dependence is captured by the

Hurst exponent (HPSD) and fractal dimension (D) – related to the slope (β) of the power spectrum by D = (5 β)/2 and to each other by HPSD = 2 D [Turcotte, 1997]. Fourier − − power spectral density (PSD) methods are in common usage for fault surface roughness analysis [e.g. Candela et al., 2009, Milliner et al., 2016, Sagy et al., 2007]). We calculate the PSD of slip using three different methods: peridiogram [Schuster, 1898], Thomson multitaper [Thomson, 1982], and Welch [Welch, 1967]. The resulting power spectra (Figure 2.5c–e) are all roughly linear to first order, but contain significant variability. Linear least squares fits through each of the PSDs from the smallest resolved wavelength (0.8 km) to a wavelength that approximates the total sampled rupture length ( 15 km) results in ∼ slopes of 0.85, 1.23, and 1.28 for the peridiogram, Thomson multitaper, and Welch methods, respectively. Associated R values are 0.24, 0.77, and 0.78.

Hurst exponents (HPSD) are -0.08 for the peridiogram method, 0.12 for the Thomson multitaper method, and 0.14 for the Welch method. Using the relationship D = (5 β)/2 − [Turcotte, 1997], fractal dimensions are 2.08 for the peridiogram method and 1.88 and 1.86 for the Thomson multitaper and Welch methods, respectively. For comparison, these values are dramatically higher than fractal dimensions of 1.72 and 1.62 computed for the Landers and Hector Mine earthquakes using a Thomson multitaper approach [Milliner et al., 2016]. We discuss these differences further in Section 2.6.

2.5.2 Root Mean Square Deviation

We also analyze slip roughness using the root mean square deviation, σRMS. A measure of the geometric spread of data values around a central mean (or best-fitting line or plane),

σRMS captures a dataset’s scatter or roughness. Its scale dependence, HRMS, is simply the

24 slope of σRMS plotted as a function of spatial measurement scale. For spatial data, σRMS is the square root of the power spectral density integrated over some interval [Bistacchi et al.,

2011]. Advantages of using σRMS over PSD methods are threefold: firstly, it is a direct measure of the roughness of a sequence; secondly, it is insensitive to point spacing, allowing analysis and comparison of unevenly spaced data sequences; and thirdly, it is more robust for smaller datasets.

We calculate σRMS for detrended slip data, taking it as the quadratic mean of the differ- ence between observed slip values and their linear trend:

n v 1 2 σRMS = u s (2.1) un X i t i=1 where n is the number of detrended slip measurements, si. We compute σRMS on sliding windows that increase in size by half kilometer increments from 0.5 km to the full measured fault length of 15 km. A plot of σRMS for each window along the rupture trace shows a ∼ trend of low roughness in the southwest, with an abrupt increase in roughness at 7 km along ∼ the rupture, corresponding to where a secondary fault strand joins (Figure 2.7). Roughness drops immediately after 7 km, but remains significantly higher than the low-roughness ∼ southwest section. A loglog plot of average σRMS versus window size is remarkably linear over all measurement scales, with a Hurst exponent (HRMS) of 0.26 and a corresponding fractal dimension (DRMS) of 1.74 (Figure 2.8a, blue line). Additionally, we plot average

σRMS versus window size for the four longest individual segments in our study area and find, unsurprisingly, that segments 1 and 2 (Figure 2.5a,b) are the least rough across all measurement scales. σRMS for segments 4 and 5 are similar to that of the full-transect cumulative offset curve. Visually, it is apparent that all segments for this earthquake have similar slopes (HRMS).

25 0.7 a 0.5 km 0.6 1 km 2 km 3 km 4 km 0.5 5 km 6 km 7 km 8 km 0.4 9 km 10 km 11 km 12 km 0.3 13 km 14 km full measured fault length 0.2 RMS deviation of windows (m)

0.1

0 0 2 4 6 8 10 12 14 distance along transect A-B (km) b -20000 -18000 -16000 -14000 -12000

Segment 4 Segment 5 Segment 1 Segment 6 Segment 3 Segment 2

A -28000 -26000 -24000 -22000 B

Figure 2.7: (a) Root mean square deviation (σRMS) values along transect A–B for detrended slip data, colored by measurement window length. These are related to the fault trace complexity (panel b, same as Figure 2.5a) with dashed grey lines marking inflections in the transect (Figure 2.3). Windows increase in length in 0.5 km increments from 0.5 km to the full length of the fault (the legend shows only whole number window sizes for brevity). Line vertices indicate center points of measurement windows. The finer observation scales show an abrupt increase in σRMS northeast of 7 km in the profile, at the prominent join in fault segments 4 and 5. Roughness peaks approximately∼ at the join for fine spatial scales and 2 km to 3 km north of it at coarser spatial scales. ∼ ∼

26 a 2016 Kumamoto earthquake

100

All segments Segment 1 Segment 2 Segment 4 10-1 Segment 5

100 101 102 b 2010 El Mayor-Cucapah earthquake

100

Pescadores/L. Salada Borrego Paso Inferior Paso Superior 10-1 Puerta accomodation zone

100 101 102

average value of RMS variance (m) c Other earthquakes

100

Balochistan Hector Mine 10-1 Landers

100 101 102 length of window for calculation (km)

Figure 2.8: Average root mean square deviation (σRMS) as a function of measurement win- dow length for (a) the 2016 Kumamoto earthquake (colored by fault segment according to Figure 2.5a), (b) the 2010 El Mayor-Cucapah earthquake (colored by fault segment), and (c) the 2013 Balochistan, 1999 Hector Mine, and 1992 Landers earthquakes. Error bars show 1 standard deviation of calculated σRMS for each window dimension and asterisks indicate av- erage σRMS measured over the entire fault length. Grey background curves are σRMS curves from other panels with error bars removed. The Hurst exponent (HRMS) is equal to the slope of these curves, which for Kumamoto is roughly stationary over all measured length scales. Balochistan is less rough (lower σRMS) than all other earthquakes at every observation lengthscale. The relative roughnesses for all earthquakes are strongly scale dependent.

27 2.5.3 Strain Estimates Derived From Surface Slip Distribution

Finally, we assess the localized strain and strain gradient along the fault. A difference in measured offset (ds) along a length of fault (dx) equates to effective shortening or lengthening across that distance, such that strain (ǫ) = ds/dx. Strain gradient is the spatial derivative of strain, d2s/dx2. Calculated strain values range from 3.6 10−2 to 3.0 10−2, with an ∼− · ∼ · average value of 1.4 10−4 and an average magnitude ǫ of 6.4 10−3. Strain gradients vary · | | · between 1.7 10−3 to 1.3 10−3, with an average value of 3.6 10−7 and an average ∼ − · ∼ · · magnitude of 2.6 10−4. · Strain and strain gradient vary about their mean values by multiple orders of magnitude, and so in Figure 2.6 we plot them as running averages across 3 profiles (lengthscale of 120 m). Both strain (Figure 2.6bc) and strain gradient (Figure 2.6d) mimic the pattern of measured fault offset (Figure 2.6b), with low amplitudes along the southwest half of the measured transect, and a moderate increase at 7 km that persists to the end of the transect. Similar ∼ to σRMS, the highest strain and stain gradient values are at 7 km, with moderate values ∼ thereafter, corresponding with the section of fault where the main and north strands of the Futagawa fault merge. Oth et al. [2017] calculate an average stress drop (∆σ) of 4.5 MPa for the 2016 Kumamoto mainshock. By assuming a standard value for Young’s modulus (E = 3 1010), we convert · ∆σ to an average strain drop of 1.5 10−4, markedly similar to our average strain of 1.4 10−4. · · 2.6 Discussion 2.6.1 Relations Between Fault Offsets, Slip Roughness, and Strain

The slip distribution, slip roughness (σRMS), strain, and strain gradient for this earth- quake all show a striking correlation to fault trace complexity (Figure 2.7 and Figure 2.6). This reflects a common observation in large earthquakes that surface slip variations are strongly regulated by geometrical complexities in the rupture trace [Klinger, 2010, Klinger et al., 2006, Milliner et al., 2016, Wei et al., 2011]. All four measurements increase moder-

28 ately within the region of overlap between the main and north strands of the Futagawa fault, starting at 7 km along the measured transect (recall that the earthquake ruptured from ∼ southwest to northeast). σRMS, strain, and strain gradient peak at 7 km; slip peaks more ∼ broadly between 7 km and 11 km, corresponding with the region of overlap between the ∼ ∼ main and north strands of the Futagawa fault (segments 4 and 5 in Figure 2.6).

We quantify the relations between fault offset, strain magnitude ( ǫ ), and σRMS by | | computing correlation coefficients (R) between each parameter averaged over 1, 3, and 5 km sliding windows along the fault (Figure 2.9; Table Table 2.1). The three window sizes allow for varying degrees of smoothing, capturing either fine or coarse variations in each parameter. A p-test confirms statistical significance at the 95% confidence level for all parameters (fault offset and strain magnitude, fault offset and σRMS, and strain magnitude and σRMS) at all window lengths. We find, therefore, that fault offset, strain magnitude, and σRMS are all correlated for this earthquake. The correlation between σRMS and strain magnitude is unsurprising, as for evenly spaced data the average magnitude of fluctuations is directly proportional to strain. However, the correlation between strain magnitude and fault offset is less obvious, and suggests that strain scales with slip.

2.6.2 Comparison With Other Earthquakes

Earlier, our examination of the root mean square deviation (σRMS) and power spectral density (PSD) of the Kumamoto surface slip distribution revealed that the frequency con- tent of slip variations are generally self-affine fractal in nature with a dimension (DRMS) of

1.74 computed from σRMS and 2 from PSD (DPSD), with associated Hurst exponents of ∼ HRMS 0.26 and HPSD 0. These values are strikingly constant over all length scales, as ∼ ∼ indicated by the linear trend between σRMS and measurement scale on Figure 2.8a. We now compare these metrics with those of four other large, dominantly strike-slip earthquakes which have each been mapped with repeat high resolution imagery and charac- terized with similar profiling methods [Lajoie et al., 2018, Milliner et al., 2016, Vallage et al.,

2015]. The 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes [Milliner et al.,

29 4 a 0.016

3 0.012

2 0.008

1 0.004 strain magnitude 0 measured fault offset (m) measured fault offset 0 0 2 4 6 8 10 average fault offset 4 average strain 0.6 b average σRMS 3 0.5

0.4 2

0.3 1

0.2 RMS deviation (m)

measured fault offset (m) 0 0.1 0 2 4 6 8 10 12 14 distance along transect A-B (km) c -20000 -18000 -16000 -14000 -12000

Segment 4 Segment 5 Segment 1 Segment 6 Segment 2 Segment 3 A -28000 -26000 -24000 -22000 B

Figure 2.9: Average fault offset (yellow), (a) Strain magnitude (green), and (b) RMS de- viation (σRMS, purple) calculated for 1, 3, and 5 km sliding window sizes (solid, dashed, and dotted lines, respectively) along transect A–B (Figure 2.3). The raw slip distribution is plotted in grey in the background of panels (a) and (b). Dashed grey vertical lines indicate inflections in transect A–B. Panel (c) is the same as Figure 2.5a. Correlations between each of the three parameters (fault offset, strain magnitude, and σRMS) are statistically significant (assessed via a p-test) at the 95% confidence level for all three window sizes (Table Table 2.1).

30 Table 2.1: Correlation results for fault offset, strain magnitude ( ǫ ), and RMS deviation | | (σRMS) for 1, 3, and 5 km sliding window sizes. The correlation coefficient, R, denotes the degree to which two series are related and ranges from -1 to 1. A p-test gives the probability that the null hypothesis (that the two signals are correlated) can be rejected – values < 0.05 indicate a correlation significant at the 95% confidence level. Every correlation in this table is significant at the 95% level.

Parameters Correlated Window Size R p Offset and ǫ 1km 0.63 2.8 10−4 Offset and |ǫ| 3km 0.79 2.7·10−6 Offset and |ǫ| 5km 0.86 4.5·10−7 | | · −4 Offset and σRMS 1km 0.59 6.7 10 · −4 Offset and σRMS 3km 0.62 8.9 10 · −4 Offset and σRMS 5km 0.68 6.5 10 · −14 ǫ and σRMS 1km 0.94 7.2 10 | | · −12 ǫ and σRMS 3km 0.94 2.7 10 | | · −10 ǫ and σRMS 5km 0.93 5.4 10 | | ·

2016] occurred within the Eastern California Shear Zone on faults systems with > 3 km ∼ cumulative offsets [Klinger, 2010, Lin et al., 2017]. Recalling that paleoseismic trenching and bedrock offsets imply cumulative offsets of 250–500 m and 850–1,900 m for Hinagu ∼ ∼ and Futagawa faults [Lin et al., 2017, Toda et al., 2016], the Landers and Hector Mine earthquakes occurred on somewhat more structurally mature faults than the Kumamoto earthquake. The 2010 Mw 7.2 El Mayor-Cucapah earthquake [Lajoie et al., 2018] in Baja California, Mexico ruptured across a disconnected suite of probably slow slip rate faults with variable structural maturities [Fletcher et al., 2014]. The 2013 Mw 7.7 Balochistan earth- quake [Vallage et al., 2015] ruptured the Hoshab fault, Pakistan, which exhibits offsets of 11 km [Zinke et al., 2014], making it by far the most structurally mature of the faults in ∼ this analysis.

Figure 2.7 shows σRMS as a function of measurement lengthscale for all five earthquakes, with the El Mayor-Cucapah earthquake plotted by individual fault segment. In contrast with

Kumamoto, σRMS–lengthscale trends for the other four earthquakes exhibit subtle curves or

31 inflections, indicating that H and D change somewhat with observation scale. We compute

HRMS for linear portions of each curve, finding values of 0.37 for Landers, 0.39 for Hector ∼ ∼ Mine, and 0.75 for Balochistan, compared with 0.26 for Kumamoto. Visually, it is clear ∼ ∼ that the Balochistan slip distribution is least rough, with the lowest values of σRMS) across all measured length scales, and that the relative roughnesses of other earthquakes varies according to the observation length scale. For example, Kumamoto is roughest (has highest values of σRMS) at length scales of 500 m to 1.5 km, but is surpassed by both Landers and ∼ Hector Mine at larger length scales. Therefore, the most structurally mature fault appears to be least rough in this analysis, with a more complicated, scale dependent relationship between the relative roughnesses of less mature faults. This appears to fit the hypothesis that roughness decreases with increasing cumulative offset [e.g Brodsky et al., 2011]. The approximate linearity of roughness scaling across length scales reflects a finding that the roughness of fault (and fracture) surfaces is stationary over many length scales [e.g. Bouchaud et al., 1990, Candela et al., 2012]. However, we find that the roughness scaling (H) values for slip distributions vary significantly from the range of 0.6–0.8 predicted for fault and fracture surface topography [e.g. Bouchaud et al., ∼ 1990, Candela et al., 2012, Power & Tullis, 1991, Schmittbuhl et al., 2006], and also from H 0.2 0.1 for initial and final stress distributions along a fault assuming elastic asperity ∼− ± squeeze [Candela et al., 2011]. These differences suggest that fault surface roughness alone cannot explain slip roughness along an earthquake rupture, but the fractal scaling still hints at a link between the two.

2.7 Conclusions

We find that the surface slip distribution in the 2016 Kumamoto earthquake correlates strongly with fault trace complexity, and show how offset magnitudes vary as slip is trans- ferred from one fault strand to another. Surface slip roughness also varies spatially, with lateral slip magnitude and variability (i.e. surface strains) increasing at the merging of two discrete fault segments, and remaining high after the merge. Nevertheless, the average slip

32 roughness is comparable to values calculated for other large earthquakes hosted on similarly immature fault systems [Milliner et al., 2016], but higher than values for large earthquakes on more mature faults. This result supports the hypothesis that faults become progressively smoother with accumulated slip [e.g. Brodsky et al., 2011, Wesnousky, 1988], unless the calculated slip distribution does not directly reflect fault roughness.

2.8 Acknowledgments

This research was supported by a grant from the Southern California Earthquake Center (SCEC project number 14101), a Pakiser Fellowship for L. J. L., and Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 2017-04029 and a Canada Research Chair for E. N. We are grateful to Asia Air Survey, Co. for making the pre- and post-event lidar data available through the NSF-supported Open Topography facility (awards EAR1557484, EAR1557319 and EAR1557330). Some of the figures in this paper were plotted using the NSF-supported Generic Mapping Tools software [Wessel et al., 2013].

33 CHAPTER 3 EXTENT OF LOW-ANGLE NORMAL SLIP IN THE 2010 EL MAYOR-CUCAPAH (MEXICO) EARTHQUAKE FROM DIFFERENTIAL LIDAR

A paper published in Journal of Geophysical Research1 Lia J. Lajoie2, Edwin Nissen2,3, Kendra L. Johnson4, J Ram´on Arrowsmith5, Craig L. Glennie6, Alejandro Hinojosa-Corona7, and Michael E. Oskin8

Abstract

We investigate the 4 April 2010 Mw 7.2 El Mayor-Cucapah (Mexico) earthquake using three-dimensional surface deformation computed from preevent and postevent airborne lidar topography. By profiling the E–W, N–S, and vertical displacement fields at densely sampled ( 300 m) intervals along the multisegment rupture, and computing fault offsets in each com- ∼ ponent, we map the slip vector along strike. Because the computed slip vectors must lie on the plane of the fault, whose local strike is known, we calculate how fault dip changes along the rupture. A principal goal is to resolve the discrepancy between field-based inferences of widespread low-angle (<30◦) oblique-normal slip beneath the Sierra Cucapah, and geodetic and/or seismological models which support steeper (50◦–75◦) faulting in this area. Our re- sults confirm that low-angle slip occurred along a short ( 2 km) stretch of the Paso Superior ∼ fault — where the three-dimensional rupture trace is also best fit by gently-inclined planes — as well as along shorter ( 1 km) section of the Paso Inferior fault. We also characterize ∼ an 8 km fault crossing the Puerta accommodation zone as dipping 60◦ NE with slip of ∼ ∼ 1 c 2018. American Geophysical Union. All Rights Reserved. For citation, see Lajoie et al. [2018] 2Department of Geophysics, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401, USA 3School of Earth and Ocean Sciences, University of Victoria, Victoria, BC, Canada 4Global Earthquake Model, Via Ferrata 1, 27100 Pavia, Italy 5School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA 6Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204, USA 7Divisi´onde Ciencias de la Tierra, Centro de Investigaci´onCient´ıfica y de Educaci´onSuperior de Ensenada (CICESE), Ensenada, Mexico 8UC Davis Earth and Planetary Sciences, Davis, CA 95616, USA

34 2 m. These results indicate that within the northern Sierra Cucapah, deep-seated rup- ∼ ture of steep faults (resolved by coarse geodetic models) transfers at shallower depths onto low-angle structures. We also observe a statistically-significant positive correlation between fault dip and slip, with slip pronounced along steep sections of fault and inhibited along low-angle sections. This highlights the important role of local structural fabric in controlling the surface expression of large earthquakes.

3.1 Introduction

We investigate fault zone surface deformation and the subsurface fault geometry of the

4 April 2010 Mw 7.2 El Mayor-Cucapah earthquake in northern Baja California, Mexico (Figure 3.1a and Figure 3.1b). This earthquake involved failure of several discrete dextral and dextral-normal faults with differing structural characteristics, making it a type example of a cascading, multifault rupture [Fletcher et al., 2014]. However, in spite of an abundance of field measurements, terrestrial and airborne lidar imagery, and satellite geodetic data [e.g., Bariˇsin et al., 2015, Fletcher et al., 2014, Gold et al., 2013, Huang et al., 2017, Oskin et al., 2012, Teran et al., 2015, Wei et al., 2011], there remain key discrepancies between models that seek to describe the underlying fault geometry. In particular, field observations in the northern rupture zone have been interpreted as indicating widespread oblique normal slip along low-angle ( 20◦–40◦-dipping) normal faults underlying the Sierra Cucapah [Fletcher ∼ et al., 2014, Teran et al., 2015], whereas several independent earthquake source models based on space geodesy and/or seismology all support steeper ( 50◦–70◦-dipping) faulting in this ∼ area [Fialko et al., 2010, Hauksson et al., 2011, Huang et al., 2017, Uchide et al., 2013, Wei et al., 2011, Zheng et al., 2012]. We seek to resolve this discrepancy by analyzing fault zone deformation in the El Mayor Cucapah earthquake mapped from preearthquake and postearthquake airborne lidar topog- raphy [Glennie et al., 2014]. These near-field geodetic data help bridge a gap between offsets surveyed in the field and those determined over larger apertures from satellite imagery and — in revealing fault zone displacements in three dimensions — provide an unusual opportunity

35 Superstition a Hills fault c Seismological models d Fialko et al. (2010) First motions: 56o E Elsinore fault Imperial fault o (Uchide et al. 2013) 71 NE

Yuha o Imperial High rate GPS: 77 NE Desert 79o NE Valley (Zheng et al. 2012)

United States USGS W-phase: 77o NE 89o SW Mexico o USGS CMT: 82o NE 59 SW Figures 2, 3 20 km Laguna Salada fault GCMT: 88o NE Sierra CucapahMexicali Valley e Wei et al. (2011) vertical strike-slip o + and residual: 50o NE 50 NE (Haukkson et al. 2011) o Sierra Juarez 75 NE Sierra fault system Laguna Juarez Salada 45o E 32˚20' 32˚40' Cañada David detachment SCSN epicenter

Sierra El Mayor o Colorado River 60 SW

Cerro Prieto fault 20 km

−120o −115o −110o Indiviso fault North America f Huang et al. (2017) o CA Plate 35 56o NE o AZ 59 NE a 50o NE 32˚00' Figure 1 62o NE 69o NE o MX 30 40o E 66o SW Pacific Colorado River Delta Plate 53o SW 20 km 50o SW b 20 km

−116˚00' −115˚40' −115˚20' −115˚00'

Figure 3.1: (a) Tectonic setting of the 4 April 2010 El Mayor-Cucapah earthquake. The red star is the epicenter from the Southern California Seismic Network (SCSN), red lines show the principal surface ruptures from Fletcher et al. [2014], and black lines show other active faults. (b) Inset showing wider tectonic setting with the main Pacific-North America plate boundary in bold. (c) Focal mechanisms from seismology with red numbers indicating the dips of the E or NE-dipping nodal planes, marked in red. (d–f) Finite fault models derived from Interferometric Synthetic Aperture Radar and pixel correlation measurements, from Fialko et al. [2010], Wei et al. [2011], and Huang et al. [2017]. Map extents are the same as in (a) and the red star is the SCSN epicenter. Each gray rectangle is an individual model fault segment, shaded darker down dip and labeled with its dip and dip direction.

36 to test for the involvement of low-angle detachment faulting. This is an important issue for a variety of reasons. First, normal slip along gently- dipping fault planes is mechanically unfavorable [e.g. Anderson, 1905, 1951] and resolving the extent of it in the El Mayor-Cucapah earthquake is thus important for the long-standing debate over whether low-angle normal faults host large earthquakes [e.g. Abers, 1991, Axen, 1999, Jackson & White, 1989, Proffett, 1977, Styron & Hetland, 2014, Wernicke, 1995] and whether multifault ruptures provide a mechanism by which they can do so [Fletcher et al., 2016]. Second, there are regional implications for how oblique extension is accommodated along this section of the Pacific-North America plate boundary [Axen et al., 1999, Fletcher & Spelz, 2009, Mueller et al., 2009, Nagy & Stock, 2000]. Finally, the mechanism of the El Mayor-Cucapah earthquake has an important bearing on stresses transferred to neighboring faults, and thus regional seismic hazard. For instance, widespread oblique slip along a shallow-angle, NE dipping detachment could lead to a significant reduction of normal stresses on the Imperial and Superstition Hills faults to the NE (Figure 3.1a). Previous studies of triggered slip or seismicity rate changes on neighboring faults following the El Mayor- Cucapah earthquake may have estimated Coulomb stresses using model fault geometries that may be inaccurate in light of our work [Meng & Peng, 2014, Wei et al., 2015]. Though a full slip model for this earthquake — and an ensuing Coulomb stress change calculation — lie beyond the scope of this study, we hope that our new constraints on the shallow fault geometry will inform future efforts on this topic.

3.2 Overview of the El Mayor-Cucapah Earthquake

The Mw 7.2 El Mayor-Cucapah earthquake struck northern Baja California, Mexico (Figure 3.1a) at 22:40 UTC on 4 April 2010, causing major damage to Mexicali and Calexico where four people were killed and more than 100 injured. The epicenter was situated at the intersection of the Sierra El Mayor and Sierra Cucapah mountain ranges, subparallel uplifts composed of Mesozoic igneous and metamorphic rocks and Tertiary volcanics and sediments which separate the Mexicali Valley to the northeast from the Laguna Salada basin to the

37 southwest [Fletcher et al., 2014]. Aftershocks form a 120-km-long, 10-km-wide band that ∼ ∼ extends northwest of the epicenter along the axis of the Sierra Cucapah range to just north of the U. S. border, and southeast of the epicenter across the Colorado river delta [Castro et al., 2011, Hauksson et al., 2011]. Coseismic surface faulting was initially mapped using Interferometric Synthetic Aperture Radar (InSAR) and satellite pixel offsets [Fialko et al., 2010, Wei et al., 2011], later enhanced by more detailed lidar and field-based measurements [Fletcher et al., 2014, Oskin et al., 2012, Teran et al., 2015]. This revealed faulting extending along the full length of the main aftershock zone and encompassing several discrete fault segments. Southeast of the epicenter, the earthquake ruptured the previously unrecognized Indiviso fault within thick (up to 5 km), actively subsiding deltaic deposits of the Colorado River (Figure 3.1a). ∼ Northwest of the epicenter, the earthquake ruptured a left stepping, en echelon array of N to NW striking faults within the Sierra Cucapah — the Laguna Salada, Pescadores, Borrego, and Paso Superior faults — before terminating at the U.S. border (Figure 3.2). A surprising aspect of the earthquake is that it ruptured into stress shadows of recent events on adjacent, subparallel faults [Fialko et al., 2010, Fletcher et al., 2014]. The surface traces of the Paso Superior and Borrego faults lie within 1–2 km of the western Sierra Cuca- pah range front, where the W dipping Laguna Salada fault ruptured in a M 7 earthquake ∼ in 1892 [Hough & Elliot, 2004, Mueller & Rockwell, 1995, Rockwell et al., 2015]. The Indi- viso fault lies 10 km southwest of the Cerro Prieto fault which hosted Mw 7, 6.1 and 5.4 ∼ ∼ earthquakes in 1934, 1980 and 2006, respectively [Su´arez-Vidal et al., 2007]. Faulting in this region collectively accommodates 4–5 cm/year of NW-SE right-lateral shear at this lati- ∼ tude [Gonz´alez-Ortega et al., 2018], but how this strain rate is distributed among individual structures is currently poorly understood.

3.2.1 Seismological Rupture Models

Focal mechanisms derived from seismology characterize the aggregate sense of slip in the earthquake but also provide an indication of the complexity of faulting involved (Figure 3.1c).

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a Indiviso A double-couple solution calculated from P wave first motions, and therefore representative only of initial faulting at the earthquake hypocenter, indicates oblique slip along moderately E dipping (normal/left-lateral) or SW dipping (normal/right-lateral) planes [Uchide et al., 2013]. A double-couple mechanism derived from modeling surface waves recorded by high- rate GPS stations in southern California supports almost pure right-lateral strike slip along a 77◦ NE dipping fault [Zheng et al., 2012]. Mechanisms determined from regional and teleseismic surface waves by the USGS National Earthquake Information Center and Global Centroid Moment Tensor project have similar nodal planes, but contain a large nondouble- couple component, implying source complexity. Hauksson et al. [2011] deconvolved the Global Centroid Moment Tensor solution to show that the non-doublecouple component is consistent with vertical NW–SE trending strike-slip faulting and additional, parallel normal faulting. Most aftershock mechanisms mimic the mainshock moment tensor solutions, though a cluster of events close to the mainshock epicenter involve normal faulting on moderate-angle NE or SW dipping planes [Hauksson et al., 2011]. Most of those that were well-recorded locally have hypocenters shallower than 15 km, with a few at greater depths of up to 30 km ∼ [Castro et al., 2011]. Several thousand aftershocks at the northern end of the rupture, detected and relocated using a temporary seismic deployment in southernmost California, align closely with a series of short, conjugate (NE and NW trending) ruptures mapped in the Yuha desert [Fletcher et al., 2014, Kroll et al., 2013, Ross et al., 2017, Rymer et al., 2011].

3.2.2 Satellite Geodetic Rupture Models

Elastic dislocation modeling of Interferometric Synthetic Aperture Radar (InSAR) line- of-sight displacements, horizontal satellite pixel offsets, and regional GPS velocities have provided more detailed constraints on the subsurface fault geometry that are independent from the seismological solutions. To date, there are four published coseismic fault slip models based on subsets of these data [Fialko et al., 2010, Huang et al., 2017, Wei et al., 2011, Xu et al., 2016]. Though the detailed model fault geometries and slip distributions differ, they

40 are all in agreement on three key aspects of the earthquake: (1) that faulting in the main NW- SE rupture zone is steeply dipping ( 50◦–90◦), consistent with the seismological moment ∼ tensor solutions, (2) that coseismic faulting penetrates to depths of 10–15 km, consistent with the base of the main aftershock zone, and (3) that the greatest slip occurs at depths of 3–6 km such that there is a clear shallow slip deficit. However, we also note that each of these models approximates the en echelon rupture pattern in the northern Sierra Cucapah (described in more detail in section 3.2.3) as a continuous, near-linear trace. These models might be biased toward steeper dip angles in an effort to fit a single plane across the en echelon segments. The InSAR imagery also contains data gaps along the entire surface rupture, where steep phase gradients and/or heavy ground shaking are likely to have caused decorrelation. An initial elastic dislocation model by Fialko et al. [2010] indicates 59◦ and 89◦ SW dips along the southern and northern Indiviso fault, a 79◦ NE dip on the Laguna Salada fault, and 71◦ NE dips on three segments that approximate the Pescadores, Borrego, and Paso Superior faults (Figure 3.1d). This model has since been used as the basis for dynamic rupture simulations [Kyriakopoulos et al., 2017] and modeling of postseismic deformation [Gonz´alez- Ortega et al., 2014]. An alternative model by Wei et al. [2011] shows a 60◦ SW dip on the Indiviso fault, a 60◦ NE dip for a fault segment approximating the Laguna Salada, Pescadores and Borrego faults, and a 50◦ NE dip for the Paso Superior fault (Figure 3.1e). They also invoke slip along a 45◦, E dipping normal fault at the southern end of the Sierra Cucapah, which corresponds to the earthquake hypocenter and accounts for its first motion mechanism. A third slip model, by Xu et al. [2016], involves six steeply-dipping fault segments in a similar arrangement to the Fialko et al. [2010] model, but the exact parameters are not reported and so we do not show the model in Figure 3.1. A fourth, nine-segment slip model by Huang et al. [2017] indicates dips of 50◦–66◦ SW on the Indiviso fault, 62◦–69◦ NE on the Laguna Salada, Pescadores and Borrego faults, 50◦ and 59◦ NE on two segments of the Paso Superior fault (Figure 3.1e). This model also includes a fault at the earthquake epicenter itself, which

41 dips 40◦ E. Kinematic rupture models, which take the fault geometries derived from geodesy and map the progression of slip from seismological data, reveal important additional properties of the earthquake [Uchide et al., 2013, Wei et al., 2011]. Slip initiated along an E-dipping normal segment before progressing bilaterally onto the Indiviso and Laguna Salada faults after 15– 20 s. Strong high-frequency radiation 50 km northwest of the hypocenter after 28 s ∼ ∼ may correspond to the step-over between the Borrego and Paso Superior faults. Finally, rupture ceases simultaneously at the northwestern end of the Paso Superior fault and the southeastern end of the Indiviso fault after 50 s. ∼ 3.2.3 Field Observations of Surface Faulting

The El Mayor–Cucapah earthquake generated 120 km of surface ruptures from the Col- ∼ orado River delta in the SE to the US-Mexico border in the NW. Initial rupture mapping was facilitated by lidar surveys undertaken both before and after the earthquake and by vertical differencing of these data [Oskin et al., 2012]. Subsequently, extensive field measurements have detailed variations in surface slip, slip sense, and fault dip along the primary rupture trace [Fletcher et al., 2014], as well as changes in the width, thickness, and internal strain distribution of a broader fault damage zone [Teran et al., 2015]. These studies also describe the structural and geomorphological context of the surface ruptures. Close to the epicenter, liquefaction features reported by Fletcher et al. [2014] may relate to the E dipping normal fault that hosted initial slip in the earthquake [Uchide et al., 2013, Wei et al., 2011]. Fletcher et al. [2016] pointed out that within the regional stress field this fault is unfavorably oriented for slip; it may have acted as a ‘keystone’ that held more favorably oriented, neighboring faults in place, before eventually failing and causing the entire network of faults to break. Southeast of the epicenter, the newly identified Indiviso fault produced a distributed zone of en echelon fractures and liquefaction within thick deltaic deposits of the Colorado River, but local slip magnitude and rupture geometry are difficult to determine due to the lack of a discrete, laterally continuous surface trace [Fletcher et al.,

42 2014]. The epicentral and Indiviso faults lie outside the area of coherent differential lidar displacements determined by Glennie et al. [2014], and so we do not discuss them further in this study. Northwest of the epicenter, the surface rupture crosses the Sierra Cucapah (Figure 3.1a), a 50-km-long mountain range composed of Mesozoic igneous and metamorphic rocks and ∼ Tertiary volcanics and sediments [Barnard, 1969, Fletcher et al., 2014]. Here it ruptured across a left-stepping, en echelon array of mostly NE dipping faults, as well as two broad accommodation zones containing more distributed deformation, interpreted as structural relays between these faults (Figure 3.2). From southeast to northwest (and hence in the local rupture propagation direction), the main rupture segments comprise the subvertical Laguna Salada fault, the 70◦ NE dipping Pescadores fault, the 40◦ NE dipping Borrego fault, and ∼ ∼ the 20◦ NE dipping Paso Superior fault. The progressive reduction in dip suggested that ∼ these faults form an imbricate stack or fan, with the structurally lowest of them — the Paso Superior fault — the master fault onto which the others sole into at depth [Fletcher et al., 2014]. The Paso Superior fault is a major geological contact juxtaposing Neogene sediments with Mesozoic crystalline basement and appears to be the most structurally mature of the faults that ruptured in the El Mayor-Cucapah earthquake, based on well-developed gouge, breccia, chloritic alteration, and cataclasite. Field measurements of surface slip within the Sierra Cucapah average 2 m but locally ∼ reach 3–4 m on all four main faults [Fletcher et al., 2014]. The slip sense varies locally from pure dextral, through normal-dextral, to pure normal, with the strike- and dip-slip compo- nents sometimes partitioned between neighboring strands. In general, the steeper, southern faults have larger dextral and smaller normal components than the more gently inclined, northern faults. The rupture zone fabric also varies widely, with the broadest damage zones generally associated with the shallowest-dipping Borrego and Paso Superior fault segments [Teran et al., 2015]. At one locality, the latter fault hosted >3 m of oblique surface slip along a plane inclined at just 20◦, and so a primary interest of ours is determining the extent of ∼

43 low-angle slip on this important regional structure. The 10-km-wide Puerta accommodation zone links the Pescadores and Borrego faults ∼ (Figure 3.2). Though only a few scattered ruptures were identified on the ground and surface faulting is hard to discern from lidar elevation changes, satellite pixel tracking indicates a sharp, near-continuous horizontal displacement discontinuity crossing the Puerta accommo- dation zone [Fletcher et al., 2014, Wei et al., 2011]. It is possible either that the surface trace of the rupture is largely obliterated by coseismic mass wasting, or that slip at depth failed to propagate upward all the way to the surface. The 5-km-wide Paso Inferior accommodation ∼ zone, which links the Borrego and Paso Superior faults, contains several short NE-dipping fault scarps and one longer one that dips toward the SW. Lidar elevation changes appear to show kilometer-scale bending across the Paso Inferior accommodation zone, perhaps ac- counting for the extensive ground cracking that was observed even away from these scarps. The rupture terminated in a third zone of distributed deformation just north of the US- Mexico border [Rymer et al., 2011], but these short, scattered fault segments lie outside the bounds of Glennie et al.’s [2014] displacement data set and so are not a focus of this study.

3.3 Data and Methods 3.3.1 Three-Dimensional Surface Displacement Field From Differential Lidar

We analyzed the El Mayor-Cucapah rupture geometry using the 100-m-resolution surface deformation data set of Glennie et al. [2014], which was calculated by aligning 100-m windows of preevent and postevent lidar point clouds using the Iterative Closest Point (ICP) algorithm [Nissen et al., 2012, 2014]. The preevent lidar data belong to a regional survey by the Instituto Nacional de Estadistica y Geografia (INEGI) flown in August 2006, and have an average density of 0.013 points/m2. The postevent data were collected by the National Center for ∼ Airborne Laser Mapping in August 2010, 4 months after the earthquake. They are higher density than the preevent data, averaging 10 points/m2, but cover a relatively narrow ( 3– ∼ ∼ 5 km-wide) swath centered on the surface rupture. This pair of data sets were first analyzed by Oskin et al. [2012], who mapped coseismic elevation changes by subtracting preevent from

44 postevent gridded digital terrain models. However, this strategy does not account for lateral displacements and so cannot directly resolve surface displacements. Elevation changes are also of limited value in parts of the rupture zone characterized by rugged topography and where horizontal motions exceed vertical ones. In contrast, by aligning windowed lidar point clouds using ICP, Glennie et al. [2014] captured the surface displacement vectors in three dimensions, as well as three rotation components. Bariˇsin et al. [2015] produced a similar data set by correlating in two dimen- sions preevent satellite photographs with the postevent lidar, correcting digital elevation models for these horizontal shifts and subtracting for the vertical component, but the re- sulting displacement fields are noticeably noisier than those of Glennie et al. [2014] and so we choose to work with the latter. Figure 3.3a–c shows the resulting x axis (E-W), y axis (N-S) and z axis (up-down) displacements, and Figure 3.3d shows the y axis rotations. In Figure 3.3d, pixels containing large eastward (positive) or westward (negative) tilts, respec- tively, illuminate the various E and W dipping fault scarps, but we do not otherwise utilize the cell rotations, focusing here on the displacement fields. These exhibit coherent defor- mation throughout much of the coverage area, but there are nevertheless some important limitations. First, Glennie et al. [2014] found that there was insufficient relief within the Colorado River delta and Laguna Salada basin to resolve coherent horizontal displacements in these areas. Second, initial results were hampered by large N-S trending artifacts related to errors in the preevent survey data. Reprocessing of the preevent lidar has reduced but not entirely eliminated these artifacts from the displacement fields [Glennie et al., 2014], and we find that they are particularly problematic within the Puerta accommodation zone.

3.3.2 Estimating Dault Dip From the 3-D Surface Displacement Field

To analyze the subsurface geometry of the El Mayor-Cucapah faults, we first mapped offsets in each component of the displacement field at regular intervals along the length of the surface rupture. The x, y, and z offset at any point on a fault represents the local Cartesian slip vector, which must lie in the plane of the fault, so we can then use knowledge of the local

45 bu the about ftePs neiracmoainzn i h ot)adth and north) ICP the For (in zone south). fault the accommodation annotated Inferior The Paso the east). of the toward tilt (i.e., direction al oesi,aeidctdb lc ie [Teran lines black by indicated are slip, zone fault n pad epciey ao utrs oal accommo locally ruptures, Major respectively. upward, and iue32adUMzn 1codnts aes()t c hwtr show (c) to (a) Panels of coordinates. size 11 cell the zone a in for UTM results and Point 3.2 Closest Figure Iterative 3.3: Figure

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0000853 Positive lineartrends 0000063 0000853 0000063 E-dipping scarps E-dipping

tilt westwards radians meters tilt eastwards northward southward 000026 000026−1 0 1 −2 −1 0 1 2 tal. et r h ogs,Wdpigstrand dipping W longest, the are s 05.Pnl()sosrotations shows (d) Panel 2015]. , W-dipping scarpsW-dipping Negative lineartrends: b d dating 0 ,wt a xet sin as extents map with m, 100 y y ipn org al (in fault Borrego dipping E e -axis displacement -axis rotation Figure 4b > bu h oiieaxis positive the about 0 ftecumulative the of 30% 000046 000046 nlto components anslation adteE N, E, the ward 000066 000066 fault strike to compute the fault dip. Geometrically, this is done by projecting the slip vector onto a vertical plane orthogonal to the local fault strike and calculating its inclination. We also measure rake by taking the dot product of the strike and slip vectors. An important limitation to this method arises along faults with horizontal slip vectors that parallel the fault strike – in other words, where the rake is purely strike slip. In this instance, any plane with the fault strike contains the slip vector, making fault dip impossible to resolve. We discuss this limitation as it applies to the oblique normal-dextral El Mayor-Cucapah rupture in section 3.4. To determine robust slip vectors, we developed and applied a semi-automated procedure for extracting offsets from fault trace-perpendicular swath profiles through the x, y, and z surface displacement fields. The swath profiles are centered at 300 m intervals along Fletcher et al.’s [2014] digitized fault surface trace (exact centerpoint locations are shown in Supplementary Figures S2–S6) and extend orthogonally on either side of the fault to the edge of the lidar double coverage. After testing, we found that a swath width of 300 m is the narrowest that still provides a sufficient number of data points to ensure a robust result. All points within the swath were projected onto the central profile line. Offsets were measured separately in each of the x, y and z displacement fields using straight-line, least squares fits through the data points on each side of the fault, projecting to the fault, and computing the line separation at the fault [Milliner et al., 2015]. We similarly calculated, projected, and differenced 1σ uncertainties, in order to determine the error in each slip vector measurement. In our implementation, the user can define for each profile the limits for curve fitting on either side of the fault, allowing for some human discretion in avoiding artifacts and accounting for the variable width (tens to hundreds of meters) of the near-fault damage zone. We were particularly careful analyzing profiles that straddled or partially straddled the N–S-trending displacement artifacts, so as to avoid including the artifact in the measured offset. By using linear displacement trends recorded hundreds of meters from the fault, we avoided complications from off-fault damage zone deformation or free surface effects, and

47 so we consider that the resulting measurements sample faulting at depths of 10s to 100s of meters [Nissen et al., 2014, Scott et al., 2018]. In this way, we analyzed the four main Sierra Cucapah faults identified by Fletcher et al. [2014]: the Paso Superior fault, which we divided into two segments, the Borrego fault, and the Pescadores and Laguna Salada faults, which we treated as one continuous structure. In addition, we studied the longest of the faults within the Paso Inferior accommodation zone as well as a sixth fault crossing the Puerta accomodation zone to link the Borrego and Pescadores faults. The Puerta accommodation zone contains no continuous mapped surface rupture, but — consistent with the pixel tracking results of Wei et al. [2011] and Bariˇsin et al. [2015] — there is a clear discontinuity in the x, y and z displacement fields, which is kinked or undulating in map view but which we approximated as a single, linear trace (Figure 3.4a–c).

3.3.3 Estimating Fault Dip From the 3-D Surface Rupture Trace

For an independent check on the dip along the reported lowest-dip angle rupture section — the Paso Superior fault — we adopted a method for computing fault dip using only the high-resolution postearthquake lidar topography [Zhou et al., 2016]. By fitting planes through the 3-D rupture trace, which is the intersection of the underlying fault plane with topography, we can estimate the fault dip representative of the shallow depths (tens to hundreds of meters) sampled by the local relief. We estimated the fault dip separately for four segments of the Paso Superior fault and avoided estimating it across the segment boundaries where plane fitting is unlikely to produce meaningful results. We digitized simplified surface traces of the four segments, guided jointly by Fletcher et al.’s [2014] principal rupture trace and the ICP surface displacement fields (whose major discontinuity generally lies a short distance to the southwest). Each digitized rupture trace comprised roughly 100 vertices at ∼ 5-m point spacing. Following Zhou et al. [2016], we computed the dip, θ, of each segment by ∼ minimizing least-squares residual distances di between the fault trace vertices, xi, yi, and zi,

48 wt rfie r lte nmpve nFgr 5i h suppor the in S5 Figure in view map in plotted are profiles swath ybaklns ihtoeaccommodating pro the those of with endpoints the lines, are black B by and A Points zone. accomodation iue34 ac trtv lss Point Closest Iterative (a–c) 3.4: Figure i of dip al. et uraacmoainzn.Bcueo h togright-lat the strong only consider the we of trace, surface Because fault 1 oversimplified zone. with accommodation line, red Puerta the line) by blue connected the by connect centerpoints, swath displacement 05.()Aogsrk rfie ffutdp(ml blue/wh (small dip fault of profiles Along-strike (d) 2015]. , ∼

60 total slip (m) 3585000 3590000 3585000 3590000 ◦ 0 1 2 3 4 W S 2− 2m 1 0 −1 −2 2m 1 0 −1 −2 8 7 6 5 4 3 2 1 0 Eadsi of slip and NE NW A A 300640000 635000 640000 635000 d displacement displacement N E Puerta accommodationPuerta zone b a y x B B ∼ -axis -axis srbs.Tecnepit fidvda displacement individual of centerpoints The robust. as — m 2 distance alongsimplifiedfaulttrendA-B(km)

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x Cascabel fault Cascabel , > y 49 0 fcmltv tanlbldi c [Teran (c) in labeled strain cumulative of 30% A and , up z xsdslcmnswti h Puerta the within displacements axis average c 000536 z -axis displacement n lp(ml e/ht squares, red/white (small slip and eut o hsfut—afault a — fault this for results rlsi opnn n the and component slip eral l n() alsaemarked are Faults (d). in file t qae akindividual mark squares ite iginformation. ting B

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dip (degrees) and a plane defined by the plane equation coefficients, A, B, C, and D (Equations 3.1–3.3):

A x + B y + C z + D =0 (3.1) · · ·

A xi + B yi + C zi + D di = | · · · | (3.2) √A2 + B2 + C2 π C θ = tan−1 (3.3) 2 − √A2 + B2 To ensure robust segment dip values, we additionally performed a bootstrapping statis- tical analysis to minimize the impact of erroneous points incorrectly identified as lying upon the primary surface rupture. In each iteration, we found the planar fit to a randomly selected 70% of the scarp points, repeating this test 1,000 times to yield a distribution of planar fits from which uncertainties were calculated.

3.4 Results

Along-fault slip and dip profiles are shown in Figure 3.4d (Puerta accommodation zone) and Figure 3.5 (other faults). An important general observation is that where the rake approaches 180◦ (pure right lateral), our computed dip values are highly variable. This reflects the fact that where the slip vector is both subhorizontal and subparallel to local fault strike, small errors in measured x and y offsets translate into large errors in dip (section 3.3.2). Consequently, we have filtered from our results all dip measurements for which our computed rake is less than 20◦ from pure right lateral; this includes the entire southern half of the Pescadores-Laguna Salada section (Figure 3.5e). Below, we discuss our detailed results in geographical order, starting at the northern end of the rupture (and, thus, in reverse order of rupture propagation). The Paso Superior fault is of particular interest as it encompasses some of the key field localities in which low-angle slip was observed on the ground [Fletcher et al., 2014, Teran et al., 2015]. Figure 3.5a–b shows our displacement field-derived estimates of fault dip (blue line) and slip vector magnitude (red line, with pink shading indicating 1σ error); our independent scarp trace-derived estimates for fault dip (four horizontal blue lines, with blue

50 4 90 5 90 3 90 5 90 a Paso Sup- b Paso Superior South c Paso Inferior W-dip d Borrego erior North strand 75 4 75 75 4 75 3 60 60 2 60 60 3 3 2 45 45 45 45 2 2 30 30 1 30 30 1 15 1 15 15 1 15

0 0 0 0 0 0 0 0 01201234560123 0123456 7 90 e Large scatter in computed dip Pescadores/Laguna Salada as rake approaches ~180 o total slip (m) 6 75

5 Pescadores Laguna Salada dip (degrees) 60 4 45 3 30 2

1 15

0 0 012345678910 11 12 13 14 15 16 17 18 19 20 distance along fault (km)

Figure 3.5: Along-strike profiles of fault dip (small blue/white squares mark individual dis- placement swath center points, connect by blue lines) and slip (red/white squares, connected by red lines, with 1σ uncertainties in pink) for (a, b) the Paso Superior fault, (c) the longest, W-dipping strand of the Paso Inferior accommodation zone, (d) the Borrego fault, and (e) the Pescadores and Laguna Salada faults. The NW end of each fault is at 0 km distance on the x axis. Corresponding field measurements of dip (blue diamonds) and slip (red circles) are from Fletcher et al. [2014]. In (a) and (b), horizontal blue lines show auxiliary dip esti- mates from plane fitting through four short sections of the Paso Superior fault trace, with blue boxes indicating standard errors. In (e), the short section of dip measurements toward the SW is marked dashed. The center points of individual displacement swath profiles are plotted in map view in Figures S2–S4 and S6 in the supporting information.

51 shading for 1σ errors); and, for comparison, field measurements of fault dip (blue circles) and total slip (red circles with vertical error bars) from Fletcher et al. [2014]. These are plotted as a function of distance along the curved fault traces. Our dip estimates are mostly consistent with the lower end of the field measurements and exhibit significantly less short-wavelength scatter; our slip measurements also vary more smoothly along strike than those of the field survey, though generally agree within error. This likely reflects that the fault geometry and slip exposed at the primary rupture trace are often influenced by surficial effects, including off fault deformation, shallow branching, refraction (steepening) of the fault toward the Earth free surface, and the tendency for unconsolidated surficial materials to fail in tension [Fletcher et al., 2014, Teran et al., 2015]. The lidar measurements, in spanning apertures of hundreds of meters, are insensitive to these effects and constrain the underlying fault. We observe moderate profile-derived dips of 60◦ at both ends of the Paso Superior fault, ∼ but much gentler dips of 0◦–30◦ along a 2 km middle section (Figure 3.5a–b). Supplemental ∼ estimates from scarp trace-fitting exhibit a similar pattern, with mean dips and standard errors of 39◦ 2◦, 11◦ 8◦, 15◦ 2◦ and 37◦ 1◦ in N-S order. The lowest dip angles ± ± ± ± can be confirmed visually from the raw displacement fields (Figure 3.3): this section of fault forms only a faint discontinuity in the vertical displacement field, reflecting small amounts of throw, but is much more prominent in the horizontal displacement fields, reflecting larger amounts of heave. The steeper dips along the outer segments are within the range of 50◦– 71◦ estimated from coarse-scale geodetic modeling in this area (Figure 3.1e), but the central structures have much shallower dips that agree within error with the 20◦ dip of the Paso ∼ Superior fault recorded by Fletcher et al. [2014]. Within the Paso Inferior accommodation zone, we only inspect the longest ( 4 km), ∼ W dipping strand. West and south of this strand, a set of shorter and highly distributed E dipping scarps, which are thought to belong to a 20◦–45◦ NE dipping detachment, may be the locally more important structure but they are too discontinuous to form part of our analysis. Measurements of the W dipping strand are hampered by noise, which is relatively large due

52 to smaller slip values of 1–2 m compared to the other faults analyzed here (Figure 3.5c). Nevertheless, we observe systematic variations in both fault dip — with very shallow (up to subhorizontal) inclinations along the northernmost 1 km of the fault, steepening abruptly ∼ to 60◦–90◦ along the southern 3 km — and total slip, which increases from 1m to 2m ∼ ∼ ∼ concordantly. Our slip estimates always exceed those of Fletcher et al. [2014], implying that much of the deeper slip is lost to off-fault deformation in the near-surface. Additionally, where we calculate shallow dip angles of <30◦ (from 0–1 km on Figure 3.5c), field dip ∼ measurements are consistently 60◦. This discrepancy might reflect steepening (refraction) ∼ of the fault toward the free surface, but we caution that the low signal to noise in offset measurements along this section (which sum to <1.2 m in total slip) might give rise to large errors in computed dip. The abrupt change in fault dip, if genuine, would imply that this fault strand is a relatively minor structure confined to shallow depths, consistent with its short length and subdued topographic signature. Pronounced short-wavelength scatter in dip at the northern end of the Borrego fault (Fig- ure 3.5d) most likely reflects that the rake here approaches 180◦, indicating predominantly right lateral slip (two of the measurements are above the cut off of 160◦). Nevertheless, dip measurements cluster between 60◦ and 80◦ along the northern half of the fault, and between 40◦ and 60◦ along the southern half, mimicking a trend in the field measurements. In con- trast, satellite geodetic models approximate the Borrego fault as a single plane with a dip ranging from 50◦ to 75◦ (Figure 3.1d–f). The Borrego fault is highly curvilinear, perhaps indicating linkages between diverse, shorter fault segments [Fletcher et al., 2014], and so we regard the southward reduction in dip angle captured in the field and lidar data as real. However, whereas field measurements of surface slip are extremely heterogeneous, our com- puted slip varies smoothly, increasing from 1 m in the north to 3 m in the south. Where ∼ ∼ our computed slip values disagree within error from field measurements (most notably from 2.5–3.5 km on Figure 3.5d), the field measurements are the smaller of the two. ∼

53 We resolve a continuous fault trend across the Puerta accommodation zone, although there are particularly bad striping artifacts in this area [Glennie et al., 2014] that make it challenging to determine accurate slip vectors (Figure 3.4a–c). Consequently our slip estimates display short-wavelength along-strike scatter in the order of 1 m (Figure 3.4d). ± Estimates of dip are further hampered by a strongly right-lateral rake that often exceeds our 160◦ cutoff, as well as our gross simplification of the fault strike, which may vary considerably across this region of steep, mountainous topography. Consequently, we consider that only the average results for this section — a northeastward dip of 60◦ and slip of 2 m — are ∼ ∼ robust. There are no field estimates of fault dip to compare against, but our estimated dip of 60◦ is consistent with values of 50◦–75◦ from coarse space geodetic models (Figure 3.1d– ∼ f). The moderate dip angle, coupled with the local rugged topography, may explain why the surface trace of the displacement discontinuity appears undulating in map view (mostly clearly evident in Figure 3.4c). Finally, computed dip angles along the Pescadores and Laguna Salada faults in the south- ernmost Sierra Cucapah are highly variable, reflecting the predominantly right-lateral sense of slip; in fact, all dip values along the southern half of this section are filtered from Fig- ure 3.5e due to rake exceeding 160◦. Nevertheless, along the northern Pescadores fault our average dip of 70◦ is in agreement with field measurements [Fletcher et al., 2014], geodetic ∼ models (Figure 3.1d–f), and estimates based on planar-fitting of the fault trace using lidar topography [Zhou et al., 2016]. However, our computed slip measurements differ from those of Fletcher et al. [2014]. We observe an isolated peak of 6 m on the central Pescadores fault ∼ where, locally, Fletcher et al. [2014] measure only 2 m. We also consistently resolve larger ∼ values of slip than Fletcher et al.’s along the southern half of this fault and the neighboring Laguna Salada fault (ours average 3 m, theirs 2 m). This likely indicates a significant ∼ ∼ shallow slip deficit along these faults.

54 3.5 Discussion

Over a 2-km section of the Paso Superior fault, our results confirm that the field-based ∼ observations and inferences of low-angle (<30◦) oblique-normal coseismic slip [Fletcher et al., 2014] are not merely surficial phenomena but are also characteristic of the larger apertures sampled by the lidar. Because we do not observe any major inflections in the displacement field within the 3-km-wide differential lidar swath, we contend that the low-angle slip must ∼ extend over a distance of at least 1–2 km from the fault surface trace, and therefore probably at least several hundred meters into the subsurface. We also observe gentle dip angles of 30◦ along a shorter ( 1 km) section of the W dipping Paso Inferior fault. ∼ ∼ Throughout the central and northern Sierra Cucapah, satellite geodetic models of the earthquake yield much steeper dip estimates (50◦–75◦) than lidar and field measurements along the same stretches of fault. These models also oversimplify the complex surface rup- ture in this area, by amalgamating several left-stepping, en echelon faults onto a continuous, nearly linear trace. This oversimplification, and the resulting modeling trade-offs with fault surface trace location and strike, may account for why these models fail to capture an im- portant signal of shallow-angle slip [Fialko et al., 2010, Huang et al., 2017, Wei et al., 2011, Xu et al., 2016]. Conversely, these coarse geodetic models — together with the various seismological solutions for the El Mayor-Cucapah earthquake (Figure 3.1c) — are likely to characterize best the deeper part of the fault zone, which is poorly sampled by the narrow differential lidar footprint. We note that aftershock locations and mechanisms also appear inconsistent with deep slip along a possible northeastward extension of the shallowly dipping Paso Superior fault beneath the Mexicali Valley [Hauksson et al., 2011]. We therefore envis- age that deep-seated slip along subvertical faulting transfers onto shallow, low-angle faulting in the northern Sierra Cucapah, perhaps because no more favorably-oriented structure is available for reactivation in this area (though we have not confirmed this with structural observations in the field).

55 Figure 3.5a–c reveals an apparent correlation between fault dip and slip magnitude along the Paso Superior and Paso Inferior faults. We test these relations statistically, calculating correlation coefficients (R) of 0.911 for the northern Paso Superior fault segment, 0.647 for the southern segment, and 0.618 for the Paso Inferior fault (Figure 3.6a–c). Correlations for all three fault segments are maximized at zero lag. We use a p test to determine correla- tion significance – testing the null hypothesis that there is no relationship between observed phenomena. We find that we can reject the null hypothesis – and confirm statistical corre- lation between dip and slip magnitude – at the 95% confidence level. Similar analyses for the remaining faults yields R values of 0.305, 0.208, and 0.065 for the Borrego, Puerta, − and northern Pescadores faults, respectively, with p tests indicating no correlation or weak correlation along these faults (Figure 3.6d–f). Overall, these results suggest that along the northernmost fault strands, fault dip is providing a first-order control on slip magnitude. For normal faults, with the maximum principal stress oriented vertically, Andersonian mechanics predicts optimally-oriented fault dip angles of 60◦; the less favorably-oriented the fault is, the more difficult it is to slip ∼ [Anderson, 1905, 1951]. The low-angle central Paso Superior fault appears to depress surface slip, whereas steeper sections of faulting to the north and south permit slip to break the surface relatively uninhibited. Similar relations hold for the Paso Inferior fault, with lidar- derived fault slip depressed according to the misalignment of the fault dip from the ideal Andersonian case. The northwestward decrease in dip angle along the Paso Inferior fault may have even prompted the northwestward propagating rupture to jump onto the neighboring, steeper southern Paso Superior fault (Figure 3.5b, c). In summary, building upon earlier observations by Fletcher et al. [2014] and Teran et al. [2015], we demonstrate the importance of inherited structures in guiding the surface rupture trace of the El Mayor-Cucapah earthquake and controlling variations in shallow slip magni- tude along it. This work adds to a growing number of studies that highlight the first order role of geological fabric in governing the surface expression of large earthquakes, as well as

56 a b c 90 Paso Superior North 90 Paso Superior South 90 Paso Inferior W-dip strand

60 60 60

30 30 30

dip (degrees) R = 0.911 dip (degrees) R = 0.647 dip (degrees) R = 0.618 p = 0.002 p = 0.002 p = 0.018 0 0 0 0 2 4 6 0 2 4 6 0 2 4 6 total slip (m) total slip (m) total slip (m)

d e f 90 Borrego 90 Puerta accomodation zone 90 Northern Pescadores

60 60 60

30 30 30

dip (degrees) R = 0.305 dip (degrees) R = 0.208 dip (degrees) R = -0.065 p = 0.147 p = 0.279 p = 0.711 0 0 0 0 2 4 6 0 2 4 6 0 2 4 6 total slip (m) total slip (m) total slip (m)

Figure 3.6: Slip and dip measurements (blue circles) with best fit linear trends (red lines) for (a, b) the Paso Superior fault, (c) the longest, W dipping strand of the Paso Inferior accommodation zone, (d) the Borrego fault, (e) the Puerta accomodation zone, and (f) the northern Pescadores fault. We do not include the southern Pescadores or Laguna Salada faults in this analysis because our dip calculation method fails (i.e. produces largely uncon- strained results) for this stretch of fault due to rake values that approach pure strike slip (e.g., 0◦ or 180◦ / -180◦). We therefore only plot results here for the northern section of the Pescadores fault: from 0 to 10.2 km in Figure 3.5e.

57 the importance of high-resolution imagery and imaging geodesy in resolving this behavior [e.g. Avouac et al., 2006, Choi et al., 2018, Lee et al., 2002, Vallage et al., 2016, Yue et al., 2005].

3.6 Conclusions

Three-dimensional surface displacements from differential lidar provide a new means of characterizing shallow faulting in large earthquakes, bridging an observational gap between far-field deformation imaged by traditional satellite geodesy and surface slip measured in the field. We use differential lidar to map the slip vector distribution and shallow fault geometry along the northern half of the 2010 El Mayor-Cucapah earthquake rupture. We observe subsurface low-angle (<30◦) oblique-normal slip along a 2 km section of the Paso ∼ Superior fault, consistent with local field measurements, as well as along a 1 km section ∼ of the neighboring Paso Inferior fault. Geodetic models that characterize the earthquake at the scale of the seismogenic layer indicate steep faulting throughout this region, and the low angle faults are thus probably reactivated only within the upper few kilometers. Nevertheless, this earthquake is among the first well-documented examples of seismic slip along a continental low-angle normal fault during the instrumental period, and justifies the interpretation that these are relevant active tectonic structures in regions of continental extension. As such, these structures should be considered as possible seismic sources in regional seismic hazard analyses and Coulomb stress change calculations. We also observe that slip along the low-angle structures is depressed relative to adjacent, steeper sections of faulting, with a statistically-significant correlation between displacement magnitude and fault dip. At one fault segment boundary, rupture appears to have jumped from a low-angle structure onto a steeper neighboring faults. This suggests that fault dip provided a first order control both on the path of the surface rupture and on the amount of localized surface slip.

58 3.7 Acknowledgments

This research was funded primarily through a Pakiser fellowship from Colorado School of Mines to L. J. L. and a United States Geological Survey (USGS) grant G12AC20042 to E. N., who also acknowledges ongoing support from the Natural Sciences and Engineering Research Council of Canada (NSERC) through Discovery Grant 2017-04029, the Canada Foundation for Innovation (CFI), the British Columbia Knowledge Development Fund (BCKDF), and the Canada Research Chair program. In addition, initial work on this earthquake was sup- ported by the National Science Foundation (NSF) through award EAR1148319, and earlier work on lidar differencing by NSF through EAR1461574 and by the Southern California Earthquake Center (SCEC) through award 14101. The authors thank the Instituto Na- cional de Estadistica y Geografia (INEGI) for making the preevent lidar survey available, the NSF supported National Center for Airborne Laser Mapping (NCALM, award EAR1339015) for the postearthquake survey, and the NSF supported Open Topography facility (awards EAR1557484, EAR1557319 and EAR1557330) for publicly hosting both data sets [Open- Topography, 2010, 2013]. All maps in this paper were plotted using the NSF-supported Generic Mapping Tools software [Wessel et al., 2013]. We are grateful to Brandon Dugan, Yvette Kuiper and Paul Sava for discussing this work and Tom Rockwell and Rob Zinke for thoughtful reviews.

59 CHAPTER 4 SUB-METER RESOLUTION SURFACE RUPTURE TOPOGRAPHY FROM LEGACY AIR-PHOTOS – A TEST CASE FROM THE 1992 LANDERS EARTHQUAKE

pending submission to Bulletin of the Seismological Society of America Lia J. Lajoie1 Edwin Nissen1,2, Kendra L. Johnson3, Kenneth R. Lajoie4

Abstract The 1992 Mw 7.3 Landers earthquake in the Mojave Desert of southern Cali- fornia provided unparalleled observations of surficial fault and fracture patterns of a large earthquake. The entire rupture length was photographed by the United States Geological Survey in a 1:6,000 aerial survey within days of the earthquake, and a small segment was photographed at 1:1,000. Recent advances in Structure from Motion (SfM) photogrammetry allow for these legacy datasets to be re-analyzed quantitatively in a way that was not pre- viously possible. In this proof-of-concept study, we generate a high-resolution, georectified point cloud ( 10 points/m2) over nearly the entire 85 km rupture length, and process a ∼ ∼ smaller area to a resolution of 40 points/m2. We validate our point cloud accuracy and ∼ utility in two separate tests. First, we confirm the geometric accuracy of our point cloud by comparing it against a modern (2008) terrestrial lidar survey. Second, make 173 vertical offset measurements within a small, structurally complex pull-apart basin and find statistical similarity with the 21 field measurements in that same area. These two tests demonstrate that point clouds generated from legacy aerial surveys and generic geographic referencing information can improve our understanding of even the best-studied earthquakes. Successful implementation of offset calculations from legacy aerial photographs has the potential to vastly expand our database of slip measurements in historical earthquakes.

1Department of Geophysics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, USA. 2School of Earth and Ocean Sciences, University of Victoria, Victoria, BC, Canada 3Global Earthquake Model, Via Ferrata 1, 27100 Pavia, Italy 4[Retired] United States Geological Survey, 345 Middlefield Road, Menlo Park, CA 94025, USA.

60 4.1 Introduction

The 28 June 1992 Mw 7.3 Landers dextral strike-slip earthquake generated a 85 km-long ∼ surface rupture distributed across five major and numerous minor faults within the East- ern California Shear Zone (Figure 4.1). From south to north, the earthquake sequentially ruptured the Johnson Valley, Kickapoo, Homestead Valley, Emerson, and Camp Rock faults (Figure 4.2a). Few of these faults were well characterized before the earthquake, and the Kickapoo fault had not been recognized as an active fault at all. The intricate and almost perfectly exposed surface rupture was surveyed aerially by the United States Geological Sur- vey (USGS) within days of the earthquake, resulting in 1:6,000 black and white photographs covering the entire rupture length, and 1:1,000 over a smaller section. Initially, the pho- tographs were primarily used as the basis for field rupture mapping, assisting in numerous, detailed studies of the surface rupture [Arrowsmith & Rhodes, 1994, Aydin & Du, 1995, Kaneda & Rockwell, 2009, McGill & Rubin, 1999, Sieh et al., 1993, Spotila & Sieh, 1995, Zachariasen & Sieh, 1995]. However, recent advances in optical image analysis allow for new applications of these legacy datasets. Structure from motion (SfM) is a method of generating three-dimensional point clouds from optical images taken at various viewing angles over the same target area or object [James & Robson, 2012, Snavely et al., 2008, Westoby et al., 2012]. Unlike classical stereophotogrammetry, image locations and camera parameters do not need to be known a priori, but are solved for along with surface topography in a ‘bundle adjustment’. This raises the possibility of reconstructing landscapes at high spatial resolution using archived photosets lacking in detailed metadata [Bakker & Lane, 2017, Derrien et al., 2015, Gomez et al., 2015, Midgley & Tonkin, 2017]. In this study, we explore the possibilities and limita- tions of using legacy aerial photography surveys to produce scientifically relevant topographic data along historical earthquake ruptures. Starting around a decade ago, airborne lidar topography has transformed our means of detecting subtle tectonic landforms, extracting fault offset measurements, and characterizing

61 Nevada California

Garlock fault

35˚ Eastern California Shear Zone

San Andreas fault North American Plate

34˚ San Jacinto fault

Elsinore fault

33˚ Pacific Plate USA Mexico

−118˚ −117˚ −116˚ −115˚

Figure 4.1: Tectonic setting of the 1992 Landers earthquake. The 1992 rupture trace (red line) and other late Quaternary faults (black) are from the USGS Quaternary Fault and Fold Database. The 1992 focal mechanism and epicenter (red star) are also from the USGS.

62 a Camp Rock fault b c

34˚40' Emerson fault

-116˚ 30’

34˚30' d Data coverage area Figures 3 and 4

Kickapoo Homestead Valley fault fault

-116˚ 20’

1992 epicenter Data coverage area Johnson Valley fault Figures 5, 6, 9

34˚10' fault Burnt Hill

Eureka Peak fault 10 km

Figure 4.2: (a) Overview of the 1992 Landers surface rupture. (b) 10 points/m2 full rupture point cloud. The orange polygon outlines the 17-image higher-resolution∼ point cloud used to make detailed fault measurements of the pull-apart basin in the second test area (Figure 4.5, Figure 4.6, and Figure 4.9). (c) Oblique view of the higher resolution point cloud showing five ground control points. Blue squares indicate camera positions, and black lines their look angles. This point cloud has 329 106 points and covers 8 km2 with an average point density of 40 points/m2. (d) Zoom∼ in· of full-rupture point cloud∼ showing two test sites. ∼

63 slip rate and trenching sites [Meigs, 2013, Zielke et al., 2015]. For such applications, lidar has been exploited in southern California perhaps more than anywhere else [e.g. Blisniuk et al., 2012, DeLong et al., 2010, Frankel et al., 2007, Hudnut et al., 2002, Oskin et al., 2007, Oskin et al., 2008, Salisbury et al., 2012, Zielke et al., 2010]. Most major known faults in California now have airborne lidar coverage, but conspicuously and perhaps surprisingly, the majority of the Landers rupture has never been scanned (Figure 4.1). The absence of high resolution digital imagery has limited further analysis of its surface rupture characteristics and may explain the near absence of Late Quaternary slip rate estimates along its constitutive faults [Oskin et al., 2008]. Landers and its aftershocks place high up the list of the most important earthquakes for the advancement of earthquake seismology, geodesy and geology. These were the first earthquakes ever imaged with InSAR [Massonnet et al., 1993, 1994] and were well-recorded by regional seismic and GPS stations. Regionally, they sparked renewed interest in the tectonics of the Eastern California Shear Zone (ECSZ) and its interplay with the San Andreas fault [e.g. Dolan et al., 2007, Rockwell et al., 2000, Sauber et al., 1994]. Globally, they provided vital insights into rupture dynamics [e.g. Cohee & Beroza, 1994, Ji et al., 2002, Olsen et al., 1997, Wald & Heaton, 1994], the roles of static, visco-elastic and dynamic stress triggering and shadowing [e.g. Freed & Lin, 2001, Gomberg et al., 2001, Hardebeck et al., 1998, Kilb et al., 2000, King et al., 1994], including at regional and remote distances [e.g. Anderson et al., 1994, Bodin et al., 1994, Hill et al., 1993], and the visco- and poro-elastic response of the crust and upper mantle [e.g. Deng et al., 1998, Masterlark & Wang, 2002, Peltzer et al., 1998, Pollitz et al., 2000, Savage & Svarc, 1997, Shen et al., 1994]. We exploit this wealth of data to validate our point clouds and show that high-resolution topography has the potential to advance our understanding of even the most well-studied earthquakes. We begin by constructing a high-resolution point cloud and digital elevation model (DEM) from the 1:6,000 USGS aerial images, which covers nearly the entire 85 km ∼ rupture trace. The only archived geographical information are approximate corner and center

64 points of the photographs, which provide limited and imprecise information for properly registering the photographs and derivative products. However, we show that modern, freely available satellite imagery provide an alternative means of georeferencing our data. This study presents a proof-of-concept approach for generating georectified high-resolution topographic datasets using legacy photographs and generic geographical information. Simi- lar overlapping aerial photosets likely exist for numerous modern and historic earthquakes, and we show that these data can be used to create high-resolution topographic models that rival state-of-the-art lidar in resolution and accuracy.

4.2 Data

We exploit a detailed airborne photographic survey flown over almost the entire 85 km ∼ Landers rupture trace soon after the earthquake. Black-and-white photographs were col- lected by the USGS at 1:6,000 and 1:12,000, with some targeted fault segments and step- overs collected at 1:1,000. Images were collected at a time of day that casts shadows across the more prevalent east-side-up scarps. This helps highlight the majority of the primary rupture, while antithetic scarps are nearly invisible. Our analysis is based on 365 high- resolution scans of negatives from the 1:6,000 images. Though the corner and center point of each photographs are archived, their accuracy cannot be verified; since this information is not essential to the SfM processing, we simply disregard this information. We also attempted to produce a pre-event topographic point cloud using 51 black and white images collected in about nine different aerial surveys between August 1947 and June 1975 at scales ranging from 1:30,000 to 1:136,000. These images were downloaded from the USGS ‘Earth Explorer’ data portal (http://earthexplorer.usgs.gov/). We excluded a number of other images available on this website, that we deemed unsuable due to poor resolution or cloud cover. A pre-1992 topographic model of the rupture area might allow us to compute the three-dimensional (3-D) surface deformation field for the Landers earthquake, and more accurately assess fault slip and coseismic surface displacements [e.g. Lajoie et al., 2018, Nissen et al., 2014]. Unfortunately, the noise level of the resulting point cloud was greater

65 than the expected signal, and was therefore useless for any quantitative purposes. However, we do note that pre- and post-earthquake photographic imagery were successfully used to determine the Landers coseismic displacement field in two dimensions [Milliner et al., 2015]. The accuracy and utility of our point clouds are assessed via comparisons against two extant datasets. First, we determine that our point clouds are properly georectified by comparing a subset of our SfM point cloud to a 2008 terrestrial lidar scanning (TLS) survey covering a small ( 200 m by 250 m, or 0.04 km2) portion of the central Emerson fault ∼ ∼ ∼ (Figure 4.2a, d). The TLS point cloud was scanned from 11 positions using a tripod-mounted Riegl LPM 321 terrestrial laser scanner. A total of 8.8 106 are reported with point densities · ranging from 1 to 38 104 points/m2, and an average of 231 points/m2. Eighteen Global ∼ ∼ · ∼ Positional System (GPS) ground control points allowed the survey to be reprojected into the 2008 UTM Zone 11 N NAD83 coordinate system with a <10 cm uncertainty in network adjustments. Vertical measurements are referenced to the WGS84 ellipsoid. These data are publicly available on the OpenTopography portal (https://opentopography.org) under collection identification OT.072011.32611.2. Secondly, we address the question of whether or not legacy datasets can be used to make meaningful fault offset measurements by comparing displacements measured from the SfM point clouds against field measurements of vertical offset. McGill & Rubin [1999] mapped a 5.6 km length of the central Emerson fault, aided by the 1:6,000 USGS aerial photography survey described previously, and made 60 offset measurements across the main fault zone and another 200 across secondary structures. Offset measurements were made with a ∼ steel tape. For this stretch of fault, right lateral slip measurements vary between 150 and 530 cm along the main rupture, with vertical separations reaching up to 175 cm east-side- up. (Even though all measurements have an oblique-normal sense of offset, we use the east- or west-side-up nomenclature to maintain continuity with field measurements). McGill & Rubin [1999] note high spatial variability of slip over short distances along strike. Field mapping focused on fractures with 10 cm of slip, though smaller offsets were measured ≥

66 where they occurred on structures that hosted large slip in other localities. We reanalyze a 700 m segment of McGill & Rubin’s mapping area, focusing on a structurally rich stretch ∼ of fault at a prominent stepover (Figure 4.2d). Here, 21 measurements of total right lateral displacement across the main rupture zone vary between 9 and 434 cm, with a maximum vertical separation of 100 cm east-side-up.

4.3 Point Cloud Generation

We use Structure-from-Motion (SfM) to reconstruct the post-earthquake surface topog- raphy, generating high-resolution point clouds – x, y, and z coordinates — of the ground surface with coregistered texture (color). SfM computes the structure of a scene by trian- gulating the positions of features recognized in multiple images. Importantly, “structure” refers to both the geometry of the imaged feature (topography, for aerial surveys) as well as camera parameters such as location (relative to the scene), orientation, and focal length – and so SfM can be used even when no survey metadata exist, making it ideally suited for use with legacy datasets where such information is crude or lacking. The feature recognition algorithm employed by SfM [Scale Invariant Feature Transform; Lowe, 2004, Snavely et al., 2008] can also accomodate irregular and/or unknown image acquisition geometries. Following the work of Johnson et al. [2014], we construct SfM point clouds using the commercial software Photoscan Pro created by Agisoft LLC. While the workflow is largely automated within Photoscan, the lack of geographic image metadata requires that ground control be added manually. We approximate seventy-five ground control points (GCPs) throughout the coverage area of the 1:6,000 aerial survey by coupling Google Earth imagery with the National Elevation Dataset (NED) to determine x, y, and z locations of recog- nizable features such as bushes and boulders. Ideally, all geographic information would be hosted in a single source, but NED image resolution is insufficient to locate small features despite having much higher elevation data resolution than Google Earth. Google Earth in- corporates smoothed elevation data from the 30 meter Shuttle Radar Topography Mission (SRTM); the NED elevation are resolved at 1/3 arc second (about 10 meters at the latitude

67 of California). Conveniently, geographic coordinates for both datasets are referenced to the WGS-84 ellipsoid. We determine UTM easting and northing coordinates of GCPs using Google Earth, and then obtain corresponding elevation values using a bulk point query to the NED. We choose GCPs located in broad, flat areas to minimize uncertainties in elevation data smoothing; those sited in topographically high areas and placed in the flattest locations possible. We estimated lateral uncertainties for the GPS of 1 m; the vertical uncertainty ∼ is harder to assess quantitatively, and likely exceeds 1 m. ∼ At this point, it is worth nothing that modern ground control can be imported into Pho- toscan Pro even without visual reference. GPS measurements, for example, can be uploaded and used to manually rescale, rotate, and translate a point cloud. While we acknowledge that this is might provide more accurate ground control in areas where such acquisitions are possible, we elect to use only georeferencing data that is readily available for any geographic locality to expand the applicability of this proof-of-concept test. Furthermore, we feel that our results in Section 4.4 support this approach. Due to large file sizes (averaging 60 Mb), the 365 1:6,000 images are divided into 8 ∼ separate subsets and merged later. Each photo subset is processed with the feature matching algorithm (dense point cloud generation) set at Photoscan’s “medium accuracy” setting, since the higher accuracy settings increase computation time and become prohibitive for such large datasets. Accuracy in this case refers to the number, not the quality, of matched features and affects only the resolution of the point cloud. The raw point cloud was very roughly de-noised using the Photoscan “gradual selection” tool on each of the sparse point clouds. This tool calculates the reprojection error between the estimated and real location of a point in a pixel and is a metric of the quality of the camera alignment and subsequent feature extraction. The cleaned, full-rupture-length point cloud is shown in plan view in Figure 4.2b and has an average density of 10.3 points/m2. ∼ To test the higher-resolution capabilities of this method, we also generate a smaller point cloud with a subset of 17 images that encompasses the southern study area (the orange

68 polygon in Figure 4.2b–d). For this region, we place 5 GCPs with 1 m accuracy and process ∼ with Photoscan’s feature matching algorithm set to “high”. The resulting point cloud has 329 million points and covers 8 km2 with an average point density of 40.1 points/m2, ∼ ∼ ∼ a four-fold increase in spatial resolution over the full-rupture point cloud (Figure 4.5).

4.4 Point Cloud Accuracy

A scientifically useful dataset must properly represent the geometry of the original sur- face, with both the shape and scale accurately rendered. Ideally, geographic referencing is also accurate, though meaningful measurements can be made without absolute geographic location provided that the geometry is correct. In this section, we assess the geometric accuracy of the full-rupture point cloud by comparing a small subset to a colocated 2008 TLS survey. This comparison serves as a rough proxy for the accuracy of the point cloud as a whole, acknowledging that variations in topography and image coverage will affect local point cloud quality. The TLS point uncertainties are <10 cm, and so for the purpose of this assessment, we treat the TLS scan (with 18 GPS ground control points) as a “ground truth” representation of the target surface. Accuracy is quantified by computing closest point distances from the SfM point cloud to the TLS point cloud; very small residual distances between topographically complex surfaces require that the SfM point cloud is both properly scaled and geometrically rendered. For perfectly planar surfaces, however, very small dis- tances between point clouds can be achieved even despite large horizontal registration errors and scale discrepancies, and so we caution that the distance between registered point clouds is only a relevant metric of similarity for topographically varied surfaces.

4.4.1 Methods

We calculate the distance between the SfM and TLS point clouds using the open-source point cloud modelling software CloudCompare (https://www.danielgm.net/cc/). We begin by trimming the SfM point cloud to the same extent as the TLS survey (Figure 4.3). The TLS coverage is sparse in areas of steep topography, and so we additionally remove points from

69 the SfM cloud in this area, leaving 7.3 105 points in the SfM cloud. To remove any effects ∼ · of geographic misregistration between the two surveys, we first finely register the two point clouds to each other using an implementation of the iterative closest point (ICP) algorithm in Photoscan Pro (the “fine registration” tool). ICP iteratively rotates and translates the SfM point cloud until closest point distances to the TLS cloud are minimized – in this case requiring 2.3 m, 4.1 m, and -10.5 m x, y, and z translations, respectively. All rotations are negligible, in no case exceeding 3 10−3 degrees. The ICP transformations likely represents ∼ · differences in geographic projections for ground control between the two surveys. After registration, we compute the distance from our SfM cloud to a meshed surface of the TLS survey using the CloudCompare ‘cloud-to-mesh’ (C2M) tool.

4.4.2 Results

True morphological differences between the two surveys are represented by a map of cloud- to-mesh distance from the registered SfM point cloud to the meshed TLS survey (Figure 4.4). The average cloud-to-mesh distance is 2.1 cm with a standard deviation of 14 cm. In ∼ detail, positive cloud-to-mesh values highlight the scarp and stream channels, areas that were likely eroded in the sixteen years between survey acquisitions. Indeed, repeat topographic surveys and ground stereoscopic photography at this locality in the 11 months following the earthquake found as much as 50 cm of lateral scarp knick-point migration in that first year alone, due largely to heavy rainfall in the winter of 1992–1993 [Arrowsmith & Rhodes, 1994]. We can therefore attribute some of the morphological difference between the 1992 SfM cloud and the 2008 TLS cloud to erosion, rather than to geometrical errors in either point cloud. The minimal cloud-to-mesh distances and ability to observe erosional patterns confirm that our SfM point cloud is a properly scaled and geometrically accurate representation of the true surface topogrpahy.

70 northing (m)

100 m 3821850 3821900 3821950 3822000 3822050 3822100

540900 540950 541000 541050 541100 easting (m)

Figure 4.3: Colored SfM-derived point cloud over the first test area. The displayed data are a 9.2 105 point subset of the full rupture-length point cloud (Figure 4.2), cropped to the same∼ coverage· area as a 2008 TLS survey.

71 0.90 0.60 0.30 0 -0.30 -0.60 -0.90 Cloud-to-mesh signed distances (m) northing (m)

100 m 3821850 3821900 3821950 3822000 3822050 3822100

540900 540950 541000 541050 541100 easting (m)

Figure 4.4: Results of cloud-to-mesh (C2M) distance calculations for the first test area. The 7.3 105 point SfM surface from Figure 4.3 is finely registered to, then differenced against ∼a meshed· surface of the 2008 TLS survey. With 18 GPS ground control points, we treat the TLS survey as a “ground truth” representation of the target surface. The average C2M distance is 2 cm with a standard deviation of 14 cm, confirming that our SfM point cloud is geometrically∼ accurate. This C2M distance∼ map outlines (in red) areas of erosion between the 1992 aerial photographic survey and the 2008 TLS acquisition, including both the fault scarp (parallel with the long axis of the differenced cloud) and stream channels (perpendicular to the long axis).

72 4.5 Vertical Offset Measurements

We also assess the utility of our point clouds by attempting to replicate field measure- ments made after the earthquake. For this, we use the smaller, higher resolution point cloud, and choose for our test area a site rich in structural complexity with dense field measure- ments (Figure 4.2d, Figure 4.5 and Figure 4.6). At this location, the northward propagating right-lateral rupture steps right to form a small (up to 100 m wide) pull-apart basin. We ∼ exploit 21 field offset measurements from 200 m south to 200 m north of the pull-apart ∼ ∼ structure [McGill & Rubin, 1999]. While field data for the entire rupture have been digitized and compiled by Liu et al. [2003], we find substantial geographic misregistration between their measurements and our surfaces, and so we opt instead to manually digitize field mea- surement locations from McGill & Rubin [1999]. However, McGill & Rubin [1999] note high spatial variability in their slip measurements, and so even small errors in location could cause significant differences in measured vertical offset. Instead, we opt to measure offset at regular intervals along the fault and determine statistically whether the two sets of measurements are from the same population.

4.5.1 Methods

We measure vertical fault offsets from 68 evenly-spaced swath profiles through our SfM point cloud along the pull-apart (Figure 4.6b). We approximate the fault using 3 generalized segments, with the central segment cutting diagonally across the pull-apart basin. Profiles are oriented perpendicular to the closest fault segment and are centered at 10 m increments along the generalized fault trace. Each profile extends 150 m from end to end and is 1 m wide. Offsets are measured by regressing linear least-squares fits through point cloud profiles on either side of scarps, extrapolating the best-fit lines to the vertical center point of the scarp, and computing the vertical separation between intersection points. We semi-automate the process in Matlab, allowing us to dictate both scarp locations and the lateral intervals over which lines are fit to the point cloud. This allows for human interpretation as well as

73 3820600 A’

B’

A C’ B D’ C 3820400 3820500 E’ D

F’ northing (m) E

F 3820200 3820300

100 m 3820100

542400 542500 542600 542700 542800 542900 easting (m)

Figure 4.5: Colored SfM point cloud of the second test area. This is a subset of the higher- resolution point cloud generated from seventeen 1:6,000 aerial images. Green lines give locations of six profiles that outline the structure of the pull-apart basin (Figure 4.7).

74 discretion in avoiding artifacts (most notably bushes). Previous studies have found a correlation between offset in the 1992 earthquake and pre-existing topography; the eastern side of the pull-apart basin is flanked by tectonically uplifted alluvial terraces that have retreated away from the fault [e.g. Bull, 1996, McGill & Rubin, 1999]. It is imperative that measurements are made of only the 1992 earthquake scarps, and that older surfaces are not used in this analysis. However, scarp degradation studies at this site suggest that large scarps would take about 10 kyr to erode to an uniden- tifiable state [Arrowsmith & Rhodes, 1994], and nearby paleoseismic trenching dated the most recent faulting event to 9 ka [Rubin & Sieh, 1997]. Therefore, the alluvial surface ∼ within and immediately surrounding the pull-apart basin was likely essentially undeformed immediately before the earthquake. We submit that our profiles are essentially measuring only deformation from the 1992 Landers earthquake, and not previous events.

4.5.2 Results

Figure 4.6b–c shows the locations, magnitudes, and polarities, of both field and point cloud vertical offset measurements superimposed on a hillshaded SfM topography basemap and projected onto a N–S profile. To the 21 field measurements we are able to add another 173 point cloud offsets that detail deformation patterns both within and adjacent to the pull-apart basin. Point cloud offset measurements clearly delineate the intricate network of normal faults mapped by field teams and visible in the hillshaded SfM DEM (Figure 4.6a). Profiles advancing from north to south across the basin clearly highlight the large oblique- normal displacements along the western margin of the basin that were not captured by field measurements (Figure 4.7). Just as importantly, profiles also show significant block rotations within the basin, with tilting of the basin floor towards the closest bounding scarps. Visually, the field and point cloud-derived scarp offsets are generally in good agreement, given uncertainties in the precise co-location of the two sets of measurements (Figure 4.6b–c). A histogram of vertical offsets for both datasets (Figure 4.8) shows a bimodal distribution of point cloud offsets, with peaks around -10–20 cm (i.e., west side up) and +20 cm (east side

75 a 3820600 3820400 3820500 3820200 3820300 3820100 Vertical scarp offset (cm) 542400 542500 542600 542700 542800 542900 -100 -50 0 50 100

b West SfM offsets East c side field offsets side up up -80-400 40 80 120 3820600 3820600 A’ Vertical scarp offset (cm) Main strands (>100 m) B’ Simplified fault trace

A C’ B D’ 3820400 3820500 C 3820400 3820500 E’ D F’ E

F 3820200 3820300 3820200 3820300

West East 100 m side side 3820100 3820100 up up

542400 542500 542600 542700 542800 542900 -100 -50 0 50 100

Figure 4.6: SfM DEM for the coverage area in Figure 4.5, hillshaded at incidence angle 60◦ and azimuth 055◦. (a) Uninterpreted image displaying fine fault structure across the pull- apart basin. (b) Vertical offsets derived from the point cloud (small circles) and from the field (larger squares), colored by magnitude with positive values indicating east side up. Longer (>100 m) scarps are joined by solid black lines; the dotted black line is the generalized fault trace along which perpendicular profiles are used to determine vertical offsets. Green lines give locations of the six profiles shown in Figure 4.7. (c) Offsets projected onto a N–S profile, with traces of the longer segments joined by solid black lines as in (b).

76 895 A A’ D D’ 896 894 895 893 894 892 891 893

B B’ E E’ 898 894 896 892 894 890 elevation (m)

895 C C’ F F’ 900 894 893 898 892 891 896 -75 -50 -25 0 25 50 75 -75 -50 -25 0 25 50 75

Figure 4.7: Example topographic profiles along the cross-sections shown in Figure 4.5, Fig- ure 4.6b, and Figure 4.9 detailing the morphology of the pull-apart basin from north (A–A’) to south (F–F’). Dotted black lines show the center point of each profile, which is the gen- eralized, three segment fault trace in Figure 4.6b. Red dashed lines indicate locations of vertical offset measurements. Note that these profiles have significant vertical exaggeration — the flat-lying alluvial surface (e.g. the surface at negative distances in profile A–A’) dips 2◦ at true scale. These profiles highlight a number of important features of the pull-apart basin:∼ (1) all scarps dip inward toward the basin center, and are thus normal faults; (2) there is significant rotation of the ground surface inside the pull-apart basin, generally towards the nearest normal fault; and (3) there is significant vertical offset associated with the western flank of the basin at negative profile distances.

77 up). Figure 4.6c and Figure 4.8 hint at a tendancy towards slightly greater field offsets than point cloud offsets; this may simply indicate that field measurements were taken where the scarps were clearest, likely coinciding with local peaks in surface slip. Nevertheless, a two- sided Kolmogorov-Smirnov test is unable to reject the null hypothesis that the two datasets are from the same continuous distribution (or identical distributions) at the 5% significance level, confirming in a statistical sense that our point cloud profiling method yields offsets comparable to field measurements. A histogram of vertical offsets for both datasets (Figure 4.8) shows a bimodal distribution of point cloud offsets, with peaks around -20 cm (i.e., east side up) and 10-20 cm (west side up). A two-sided Kolmogorov-Smirnov test is unable to reject the null hypothesis that the two datasets are from the same continuous distribution (or identical distributions) at the 5% significance level, confirming that our point cloud and profiling method are able to measure offsets comparable to field measurements.

25 173 point cloud offsets 20 21 field offsets

15

counts 10

5

0 -150 -100 -50 0 50 100 150 west side up measured fault offset (cm) east side up

Figure 4.8: Histogram of vertical offset measurements (from the locations shown in Fig- ure 4.6b) with 10 cm bin size. Blue bars give bin counts for 173 measurements made through the SfM point cloud; red bars show 21 field measurements [McGill & Rubin, 1999]. A two- sided Kolmogorov-Smirnov test can not reject the null hypothesis that these two datasets are from the same continuous distribution at the 5% significance level, indicating that point cloud-derived measurements are statistically similar to field measurements.

78 Our rupture offset mapping also confims a peculiar pattern in the field measurements – that the scarp immediately south of the pull-apart basin is west-side-up. This behavior only persists for 300 m south of the pull-apart according to field measurements [McGill ∼ & Rubin, 1999], reverting back to east-side-up further south, and just outside of our test area. We also confirm that vertical offset magnitudes are significantly higher north of the pull-apart than south of it, therefore increasing over the step-over as the rupture propagated northward.

4.6 Pull-Apart Basin Morphology

Having confirmed to first order the accuracy of our point cloud, we now use it to further explore the structure of the pull-apart basin. In Section 4.5.1, we explained that the flat-lying alluvial surface around the pull-apart basin (excluding older tectonically uplifted alluvial terraces) was probably underformed before the 1992 earthquake [Arrowsmith & Rhodes, 1994, Bull, 1996, McGill & Rubin, 1999, Rubin & Sieh, 1997]. Disregarding low-relief stream channels, the surrounding surface can be approximated as a gently-dipping plane. This approximation allows us to calculate the deflection of the SfM point cloud from that idealized plane, and thus generate a rough estimate for coseismic vertical deformation.

4.6.1 Methods

The surface adjacent to the pull-apart basin is characterized by a very gently sloping plain, surrounded in places by older, raised alluvial surfaces. We isolate the adjacent surface by masking out the older surfaces, as well as a thin, highly deformed strip 10 m either side ∼ of the principal 1992 surface rupture trace. The remaining points define a mostly planar surface that CloudCompare fits with a plane dipping 2◦ towards an azimuth of 038◦. The point cloud deviation from this surface is computed for the complete (unmasked) point cloud using the cloud-to-mesh calculation tool in CloudCompare.

79 4.6.2 Results

Figure 4.9 shows the cloud-to-mesh distances computed from the SfM point cloud to the best fit plane. This deflection map is consistent with the general fault behavior observed in field measurements. The deflection magnitude is low to zero at the southern edge of the test area, increasing northward with west-side-up sense of offset, and the fault emerges from the northern end of the basin with strongly east-side-up offset. Farther from the fault trace, surface deflections reflect the non-planar nature of the surface, the planar approximation being an oversimplification that is only useful for qualitative assessments. Nonetheless, large magnitude deflections inside of the pull-apart basin are robust and show that the basin is deepest slightly westward from a bisecting line through the long axis of the basin, closer to the large west-side-up offsets than the smaller east-side-up offsets measured in Section 4.5.

4.7 Discussion

In one 500 m 500 m test area, we were able to add 173 vertical offset measurements ∼ × to the 21 field measurements collected by McGill & Rubin [1999]. A Kolmogorov-Smirnov test suggests that these data may all be from the same statistical distribution, and so we treat our point cloud derived measurements as a supplement to the field data. Looking at only field data, fault offset appears much greater along the eastern wall of the pull-apart, and a reasonable hypothesis might be that the northward-propagating rupture elected to primarily exploit that branch as it navigated the right step over (Figure 4.6b). Such a scenario is unsurprising considering the eastern branch of the pull-apart basin is in the tensional quadrant of a northward propagating, right-lateral rupture and might be the kinematic preference. The basin itself, then, would form primarily due to subsidence associated with oblique slip on that fault branch. Our additional measurements and surface deflection map (Figure 4.9) offer data to sup- port a different interpretation – that both strands of the fault were activated dynamically, likely along a well-defined pre-existing structure. Contrary to the limited view afforded by

80 2

3820600 1 A’

B’ 0

A C’ -1 B D’ C

3820400 3820500 -2 E’ D

F’

Cloud-to-mesh signed distances (m) -3 E

F 3820200 3820300

100 m 3820100

542400 542500 542600 542700 542800 542900

Figure 4.9: Surface deflection of the 1992 topography from plane fit to the gently-sloping alluvial surface. The older tectonically uplifted alluvial surfaces and the fault are masked out before plane fitting. Red hues show positive deviations from the best fit plane, and blue hues show negative deflections. The dashed black line shows the generalized fault trace along which fault-perpendicular profiles were extracted, and green lines give locations of six profiles that outline the structure of the pull-apart basin (Figure 4.7). This map corroborates measurements (Figure 4.6b) that show west-side-up oblique normal slip south of the pull- apart and east-side-up north of it. Within the pull-apart basin, detailed fault strands are clear, with the maximum negative deflection slightly west of a line bisecting the long axis of the basin.

81 sparse field measurements, our deflection map shows that there is slightly more net subsi- dence on the southwest side of the pull-apart basin. Profiles furthermore indicate almost symmetrical rotation of blocks within the basin on either side of a long-axis bisecting line. These observations suggest instead that the fault dynamically ruptured along both branches of the pull-apart basin, imparting large amounts of deformation on both walls. The point cloud offsets also corroborate field data that show a change in offset polarity north and south of the pull-apart. Though much of the rupture produced east-side-up oblique-normal scarps, a 300 m stretch of fault immediately south of the pull-apart basin ∼ displays west-side-up oblique-normal displacements. This suggests that the change in offset polarity is due to a change in dip direction of the causative faults, as opposed to a short- wavelength change in absolute vertical motion along the fault. We posit that the eastward dip of the fault south of the pull-apart basin is related to the evolution of the pull-apart basin. It is clear from the shape of tectonically uplifted older alluvial terraces proximal to the fault [Bull, 1996, McGill & Rubin, 1999] that the bend at this locality has persisted over multiple earthquake cycles. As displacement has accumulated across the step-over, the east-dipping bounding fault appears to have developed into a structurally important feature, and the main strand of the fault has rotated from west-dipping to east-dipping immediately south of the fault to accomodate it.

4.8 Conclusions

In this paper, we show that it is possible to make accurate and scientifically relevant topographic point clouds by applying Structure-from-Motion to legacy airphotosets georef- erenced with generic, freely available remotely sensed data. We use the 1992 Landers rupture — one of few major faults in California currently lacking in airborne lidar coverage — to il- lustrate. There are only slight morphological differences between our Structure-from-Motion point cloud and a GPS-georeferenced terrestrial lidar survey. Additionally, we are able to reproduce field measurements of vertical offset within statistical significance. We demon- strate that these point clouds have the potential to add to our understanding of even the

82 best-studied historic earthquakes. This is illustrated within a small pull-apart basin, where our point cloud measurements prompt a reassessment of the rupture dynamics and fault structure. In our new interpretation, both bounding branches of the pull-apart basin were coseismically activated.

4.9 Acknowledgments

This research was primarily supported by the Southern California Earthquake Center through grant 15189. L. J. L. was supported by a Pakiser Fellowship from Colorado School of Mines, and E. N. by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 2017-04029 and a Canada Research Chair.

83 CHAPTER 5 CONCLUSIONS

In the three chapters of this thesis, I use various techniques to measure surficial fault slip during large, surface-rupturing earthquakes at high spatial density. The resulting slip distributions reveal a number of characteristics of the causative faults. For the Mw 7.0 Ku- mamoto, Japan earthquake, slip distribution, strain, strain gradient, and roughness correlate strongly with fault structure, and slip transfers from one segment to another by maintaining a constant amount of right-lateral slip across the step-over. The slip distribution for the

Mw 7.2 El Mayor-Cucapah earthqauke allows for dip calculations that confirm low angle normal faults in Sierra Cucapah were coseismically acticated during rupture, and that dip appears to control the magnitude of slip locally along the fault. Finally, for the Mw 7.3 Landers, California earthquake, I show that it is possible to generate accurate point clouds for historic earthquakes using Structure-from-Motion, using a small pull-apart basin to show that high-resolution topography can be used to determine the path the propagating rupture takes across structurally complex features. Slip distributions for all three earthquakes also support the nascent hypothesis that fault surfaces become progressively less rough with ac- cumulated displacement across them. Each of these conclusions feeds into active debates about fault and earthquake behavior. It is an ongoing point of debate among earthquake scientists whether slip magnitude and strain scale together across all earthquakes. My work on the Kumamoto earthquake shows a correlation between the two across all observable length scales, and suggests that this link does indeed exist. However, this presents an interesting problem: if strain (and therefore strain drop) scales with slip, then stress drop should also scale with slip. This is not borne out observationally, although datapoints such as my slip distributions will help clarify the matter in the future. Additionally, I find a striking agreement with the average

84 strain from my calculated slip distribution and the strain drop I estimate by converting from a stress drop of 4.5 MPa[Oth et al., 2017] – 1.4 10−4 and 1.5 10−4. This raises the question · · of whether strain is consistent across all depth levels of the fault. If that is so, there are strong implications for fault zone structure and behavior at depth. For example, if fault zones are wider at the surface than at depth, conserving shear strain requires that fault offsets (cumulative across the fault zone) be higher at the surface than at depth as well, even though our current understanding of fault behavior contradicts this. Alternatively, the agreement of strain values could be pure coincidence, with little significance. Coseismic activation of normal faults is also highly controversial, with little evidence that it is mechanically possible. My work on the El Mayor-Cucapah earthquake demonstrates for the first time that these structures were coseismically activated and may present a non- trivial seismic hazard where low angle structures are observed. Additionally, this paper shows that not only does a simple mechanical model (Andersonian mechanics) describe when fault sytems will fail, it also governs slip magnitude locally along faults. I show that slip is supressed along fault segments deviating from the optimal 30◦ alignment relative to the maximum principal stress. All of this work is done using relatively inexpensive software and methodologies, mak- ing it broadly accessible to researchers and applicable to a wide range of earthquakes and datasets. Studies such as these will become commonplace in the near future, aided by rapidly evolving technologies that will permit point clouds and optical dataset to be collected rapidly and inexpensively. Drone advances allow steadily increasing payloads, while lidar systems become progressively smaller. Lidar surveys will not only be deployed more rapidly and broadly after future earthquakes, but this should allow for greatly expanded point cloud coverage over Earths surface in the intermediate future. As the spatial resolution and cover- age of topographic data improves, so does the temporal aperature between remotely sensed datasets. Shoebox satellite constellations promise to collect optical imagery for every point on Earths surface daily. For any given earthquake, multi-temporal pixel tracking results

85 will be achievable in 1-day increments in the near future. Not only will this improve dis- placement estimates by limiting non-seismic deformation between image pairs, it will also allow for precise afterslip monitoring in large earthquakes. And with steady improvements in optical image resolution, these satellite constellations also raise the possibility of being able to generate fully three-dimensional point clouds using Structure-from-Motion for any location on Earth, on almost any day (subject to weather conditions). Technological ad- vances raise the possibility of near-ubiquitous point cloud coverage over Earths surface in the intermediate future, allowing scientists to assess surface deformation associated with not only earthquakes, but other natural hazards such as landslides and volcanic activity. This thesis presents a brief summary of what is currently possible in surface deformation studies for large earthquakes, as well as a glimpse of future possibilites and promises.

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101 APPENDIX SUPPORTING INFORMATION FOR “EXTENT OF LOW-ANGLE NORMAL SLIP IN THE 2010 EL MAYOR-CUCAPAH (MEXICO) EARTHQUAKE FROM DIFFERENTIAL LIDAR”

This supplemental file provides ICP results for x, y, and z axis rotations (Figure A.1) (x, y, and z axis translations, as well as y axis rotations, are given in main text), along with maps showing the calculated dip values and vertical displacement fields for each of the six faults analyzed (Figure A.2 – Figure A.6). Please see the main text for details of the computational techniques, and for the related citations.

A.1 ICP Rotations

Figure A.1

A.2 Dip Maps

Figure A.2 Figure A.3 Figure A.4 Figure A.5 Figure A.6

102 iueA1 aes()t c hwrttosaotthe about rotations show (c) to (a) Panels A.1: Figure a iw(ae ) at fte21 utr rc r easily are trace rupture 2010 the of results. co Parts rotation rotations axis axis c). z (panel positive south; view b); the map (panel towards east tilt the axi towards indicate positive tilt values the positive about a), (panel rotations clockwise indicate values

0000853 0000063 0000853 0000063 0000853 0000063

radians radians radians 000026 000026 −1 0 1 000026−1 0 1 −1 0 1 b a c positive axisdirection) about (positive isclockwise y positive axisdirection) about (positive isclockwise x positive axisdirection) about (positive isclockwise z -axis rotation -axis rotation -axis rotation 103 000046 000046 000046 x , y and , rsodt lcws oain in rotations clockwise to rrespond ieto.Frxai rotations axis x For direction. s oiieyai oain indicate rotations axis y positive 000066 000066 000066 z dnial nteyadz and y the in identifiable xs epciey Positive respectively. axes, Figure A.2: Fault dips calculated along the Paso Superior fault (northern and southern segments) using the calculated x, y, and z offsets in the corresponding ICP displacement fields. Dip values are indicated next to the measurement locations (black circles), and black bars indicate dip direction and magnitude. Magnitudes are displayed as 90◦-dip, such that longer bars indicate shallower dip. The base map displayed gives the magnitude of the vertical ICP displacement field, allowing for rough, visual assessment of how throw varies along the fault. Also shown is the fault trace (red line, from Fletcher et al. [2014]) along which the fault profiles are extracted. Dip values are plotted for every other profile.

104 Figure A.3: Same as Figure A.2, but displaying results for the Paso Inferior fault.

105 Figure A.4: Same as Figure A.2, but displaying results for the Borrego fault. Dip values are plotted for every other profile.

106 Figure A.5: Same as Figure A.2, but displaying results for the Puerta accomodation zone. Dip values are plotted for every other profile.

107 Figure A.6: Same as Figure A.2, but displaying results for the Pescadores and Laguna Salada faults. Dip values are plotted for every third profile.

108