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Three-Dimensional Deformation and Stress Models: Exploring One-Thousand Years of Earthquake History Along the San Andreas Fault System

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Three-Dimensional Deformation and Stress Models: Exploring One-Thousand Years of Earthquake History Along the San Andreas Fault System Three-dimensional Deformation and Stress Models: Exploring One-Thousand Years of Earthquake History Along the San Andreas Fault System by Bridget Renee Smith UNIVERSITY OF CALIFORNIA, SAN DIEGO SCRIPPS INSTITUTION OF OCEANOGRAPHY 2005 UNIVERSITY OF CALIFORNIA, SAN DIEGO Three-dimensional Deformation and Stress Models: Exploring One-Thousand Years of Earthquake History Along the San Andreas Fault System A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Earth Sciences by Bridget Renee Smith Committee in charge: David T. Sandwell, Chair Bruce Bills Steve Cande Yuri Fialko Catherine Johnson Xanthippi Markenscoff 2005 Copyright Bridget Smith, 2005 All rights reserved. The dissertation of Bridget Renee Smith is approved, and it is acceptable in quality and form for publication on microfilm: _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ University of California, San Diego 2005 iii For my parents – although I have never been a student in your classrooms, you will always be my most treasured teachers of life. iv TABLE OF CONTENTS Signature Page.……………………...……………………………………………………………….iii Dedication.……………………...……………………………………………………………………iv Table of Contents.……………………..……………………………………………………………...v List of Figures and Tables.……………………...………………………………………………….viii Acknowledgements.…………………….………………………………………………………….…x Vita and Publications.…………………….…………………………………………………………xii Abstract……………...………………………………………………………………………………xv Chapter 1. An Introduction to the San Andreas Fault System: Geologic, Geodetic, and Seismic Observations, Fault Modeling Techniques, and Stress Triggering….…....1 1.1 Introduction.………..…………………………………………………………………………...1 1.2 The Earthquake Cycle.………………………………………………………………………….2 1.2.1 Early Observations.…..…..…….………….………………………………………2 1.2.2 Present-day Theory.……..………………...………………………………………4 1.3 The San Andreas Fault Zone.…………………………………………………………………...4 1.3.1 Geologic Observations: 10,000 – 106 yrs.…....……………….………………….4 1.3.2 Geodetic Observations: ~ 1-10 yrs.…….….....……………….………………….6 1.3.3 Seismological Observations: < 1000 s..……………………….………………….8 1.4 Fault Deformation Models: 10 - 10,000 yrs.……….…………………………………………...9 1.4.1 Objectives and Necessary Ingredients.………....…………….…………………..9 1.4.2 Common Approaches: Analytic and Numeric Models.…..…....……………….10 1.4.3 The Hybrid Approach: The Fourier Model.……..…………..….………………10 1.5 Tectonic Stress Triggering.…………………………………………………………………....12 1.5.1 “Earthquake Conversations”.……...…………………………………………….12 1.5.2 Coulomb Failure.…………...……...……………………………………………13 1.6 Thesis Organization.……….…………………………………………………………………15 1.7 Conclusions.…………………………………………………………………………………..16 1.7.1 Summary of Results.…….…..………………………..………………………...16 1.7.2 Avenues of Future Research.…...…..…………………………………………...17 1.8 References.……….…………………………………………………………………………...18 Chapter 2. Coulomb Stress Along the San Andreas Fault System.……..…………………….23 2.1 Introduction.……….……….…...………………………...………………………………….23 2.2 Fourier Solution to 3-D Body Force Model.…...…...….…...………………..………………24 2.3 Modeling the San Andreas Fault Zone.….…....….…………………………………………..25 2.4 Geodetic Inversion.………..……………………………...…………………………………..28 2.5 Results.……….……………………………………………………………………………….30 2.5.1 Horizontal Motion and Locking Depth.………………………………………….30 2.5.2 Far-field Constraint: 40 mm/yr.…………………………………………………30 2.5.3 Vertical Motion.……………………...……………....…………………………..31 2.5.4 Static Coulomb Stress and Seismic Moment Accumulation.….……..………….33 2.6 Discussion.……………………………………….……………………………………………36 2.6.1 Coulomb Stress and Fault Creep.………..……………………………………….36 v 2.6.2 Moment Accumulation Rate.………..…………………………………………36 2.6.3 Coulomb Stress and Earthquake Frequency.………..…………………………37 2.7 Conclusions.………………………………………………………………………………….37 2.8 Acknowledgements.………...………………………………………………………………..39 2.9 References.………..………………………………………………………………………….39 Appendix 2.A Analytic 3-D Body Force Model.………...………………………………………..43 Appendix 2.B Locking Depth Analysis of Individual Fault Segments.…………….…….………48 2.B.1 Profile 1: Segment 1.……….……………………………………………………48 2.B.2 Profile 2: Segments 2 and 4.……….…………………………………………….48 2.B.3 Profile 3: Segments 3 and 5.……….…………………………………………….49 2.B.4 Profile 4: Segment 6.……….……………………………………………………49 2.B.5 Profile 5: Segment 7.……….……………………………………………………49 2.B.6 Profile 6: Segment 8.……..………………………………….…………………..49 2.B.7 Profile 7: Segment 9.…………………………………………………………….49 2.B.8 Profile 8: Segment 10.…………………………………………….……………..50 2.B.9 Profile 9: Segments 11 and 13.……….………………………………………….50 2.B.10 Profile 10: Segments 14 and 16.……….………………………….……………..50 2.B.11 Profile 11: Segments 11, 17, and 14.……….……………………………………50 2.B.12 Profile 12: Segments 12, 15, and 18.……….……………………………………51 Chapter 3. A 3-D Semi-Analytic Viscoelastic Model for Time-Dependent Analyses of the Earthquake Cycle.………………………..………………………………………..……….52 3.1 Introduction..……....……………………………………………...…………………………..52 3.2 Fourier 3-D Viscoelastic Model for Fault Deformation.……….…..…………………………55 3.2.1 New Developments to the Analytic Approach.…………………………………..55 3.2.2 3-D Fourier Model Formulation.………………………...……….………………56 3.3 Analytic and Numeric Tests of Layered Viscoelastic Solution.………..…………………….59 3.3.1 2-D Analytic Comparisons.………………………………………………………59 3.3.1.1 Homogeneous elastic half-space.……………………………………….59 3.3.1.2 Layered elastic half-space.……...…………………….………………...59 3.3.1.3 Layered viscoelastic half-space.……….……………………………….60 3.3.2 Boussinesq Analytic Comparisons.………..……………………………………..62 3.3.2.1 Vertical point load on an elastic half-space.…………….……………...62 3.3.2.2 Gravitational restoring force.………...…………………………………62 3.3.2.3 Thin plate flexure approximation.………………………………………65 3.4 3-D Time-Dependent Deformation and Stress.……………...………………………………66 3.4.1 3-D Velocity.……………………………………………………………………..66 3.4.2 Coulomb Stress.…………………………………………………………………..72 3.5 Discussion.…………..………………………………………………………………………..72 3.6 Conclusions.………….…………...…………………………………………………………..73 3.7 Acknowledgements.………….……....……………………………………………………….74 3.8 References.……….…..…………...……………………………………….………………….74 Appendix 3.A Boussinesq Problem for Layered Half-Space.…....………..……………………….77 vi Appendix 3.B Method of Images.…………..…...…………………………………………………84 Appendix 3.C Analytic Treatment of Infinite Sum.…………...……………….…….…………….85 Appendix 3.D Including Time Dependence: The Maxwell Model.……………………………….86 Appendix 3.E Force Couples on a Regular Grid.…………...…...…………………………………90 Chapter 4. A Model for the Earthquake Cycle Along the San Andreas Fault System for the Past 1000 Years.……………..…………………...……………………………………93 4.1 Introduction.…………………………………………………………………………………..93 4.2 Great Earthquakes of the SAF System: 1000 A.D. to Present Day.….….…………………..95 4.2.1 Historical Earthquakes.………...………………………………………………...96 4.2.2 Prehistorical Earthquakes.………..………………………………….………….101 4.3 3-D Viscoelastic Model.………....…………………………………………………………..103 4.4 Application to the San Andreas Fault System.………………………………………………103 4.5 Geodetic Data.………...……..………………………………………………………………107 4.6 Results.………...…………………………………………………………………………….107 4.6.1 Present-day Velocity.………..………………………………………………….108 4.6.2 Present-day Coulomb Stress.…………………………………………………...112 4.7 Discussion.…………………………………………………………………………………...114 4.7.1 Implications of Best-Fit Model Parameters.…………...……………………….114 4.7.2 Temporal and Spatial Deficiencies of GPS Data.………….…………………...115 4.7.3 Present-day Stress Implications and Seismic Hazard…………………………..115 4.8 Conclusions.………….……………………………………………………………………..116 4.9 Acknowledgements.………….……………………………………………………………..117 4.10 References.…………………..………………………………………………...……………117 4.11 Appendix 4.A. 3-D Viscoelastic Body Force Model.…………….….….………………….124 Chapter 5. Accuracy and Resolution of Shuttle Radar Topography Mission Data….………………126 5.1 Introduction.……………………………...………………………………….……………126 5.2 Data Characteristics.………………………………………………….……….…………..127 5.2.1 STRM Data.………...………………………………………………………….127 5.2.2 NED Data.………...……....……………………………………………………127 5.2.3 Hector Mine ALSM Data………….…………………………….……………..127 5.3 Data Preparation.………….………………………………………………………………127 5.4 Cross-Spectral Analyses Results.…………...…………………………………………….129 5.4.1 SRTM vs. NED.………....….………...……………………….………………129 5.4.2 SRTM & NED vs. Hector Mine ALSM….……......…………………………..129 5.4.3 Phase Shift.…….……………………………………...……………………….131 5.4.4 SRTM Filter and Decimation.………....…...………………………………….131 5.5 Acknowledgements.……………..………………………………………………………….132 5.6 References.…………..……………………………………………………………………...132 Computer movie animations on file at Mandeville Special Collections. vii LIST OF FIGURES AND TABLES Chapter 1. Figure 1.1 Fault rupture from the 1906 San Francisco Earthquake..…………………….…………..….2 Figure 1.2 Elastic rebound theory………………...…………..….……………………….………...…...3 Figure 1.3 North American-Pacific Plate boundary history...………….…...…………………………..5 Figure 1.4 San Andreas Fault System tectonics..…………………..…..…………………………….....7 Figure 1.5 Elastic vs. viscoelastic models..…………..………………………………………….…….11 Figure 1.6 Landers-Hector Mine triggered earthquake sequence....…………..…..………….……….13 Figure 1.7 Coulomb failure model.…………………………………………..……………….……….14 Figure 1.8 Coulomb stress for Landers-Big Bear-Hector Mine sequence..……..……….….………...15 Chapter 2. Figure 2.1 San Andreas Fault System model………………………...…..………………….………...26 Figure 2.2 Fault-parallel velocity model
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