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Imaging,Modeling and Assimilation in Seismology:An Overview 1

References 11

Chapter 1 Full-Wave Seismic Data Assimilation:A Unified MethodologyforSeismicWaveformInversion 19

1.1 Introduction 19

1.2 Generalized Inverse 21

1.2.1 Prior Probability Densities 22

1.2.2 Bayes'Theorem 25

1.2.3 Euler-Lagrange Equations 26

1.3 Data Functionals 31

1.3.1 Differential Waveforms 32

1.3.2 Cross-correlation Measurements 33

1.3.3 Generalized Seismological Data Functionals (GSDF) 34

1.4 The Adjoint Method 38

1.4.1 An Example of Adjoint Travel-Time Tomography 39

1.4.2 Review of Some Recent Adjoint Waveform Tomography 41

1.5 The Scattering-Integral(SI)Method 42

1.5.1 Full-Wave Tomography Based on SI 44

1.5.2 Earthquake Source Parameter Inversion Based on SI 46

1.6 Discussion 54

1.6.1 Computational Challenges 55

1.6.2 Nonlinearity 57

1.7 Summary 58

References 59

Chapter 2 One-Return Propagators and the Applications in Modeling and Imaging 65

2.1 Introduction 66

2.2 Primary-Only Modeling and One-Return Approximation 67

2.3 Elastic One-Return Modeling 72

2.3.1 Local Born Approximation 73

2.3.2 The Thin Slab Approximation 75

2.3.3 Small-Angle Approximation and the Screen Propagator 77

2.3.4 Numerical Implementation 80

2.3.5 Elastic,Acoustic and Scalar Cases 81

2.4 Applications of One-Return Propagators in Modeling,Imaging and Inversion 81

2.4.1 Applications to Modeling 81

2.4.2 One-Return Propagators Used in Migration Imaging 85

2.4.3 Calculate Finite-Frequency Sensitivity Kernels Used in Velocity Inversion 88

2.5 Other Development of One-Return Modeling 93

2.5.1 Super-Wide Angle One-Way Propagator 93

2.5.2 One-Way Boundary Element Method 95

2.6 Conclusion 99

References 100

Chapter 3 Fault-Zone Trapped Waves:High-Resolution Characterization of the Damage Zone of the Parkfield San Andreas Fault at Depth 107

3.1 Introduction 107

3.2 Fault-Zone Trapped Waves at the SAFOD Site 109

3.2.1 The SAFOD Surface Array 111

3.2.2 The SAFOD Borehole Seismographs 116

3.2.3 Finite-Difference Simulation of Fault-Zone Trapped Waves at SAFOD Site 124

3.3 Fault-Zone Trapped Waves at the Surface Array near Parkfield Town 132

3.4 Conclusion and Discussion 135

Acknowledgements 138

References 138

Appendix:Modeling Fault-Zone Trapped SH-Love Waves 143

Chapter 4 Fault-Zone Trapped Waves at a Dip Fault:Documentation of Rock Damage on the Thrusting Longmen-Shan Fault Rupturedinthe 2008 M8 WenchuanEarthquake 151

4.1 Geological Setting and Scientific Significance 152

4.2 Data and Results 154

4.2.1 Data Collection 154

4.2.2 Examples of Waveform Data 157

4.3 3-D Finite-Difference Investigations of Trapping Efficiency at the Dipping Fault 164

4.3.1 Effect of Fault-Zone Dip Angle 166

4.3.2 Effect of Epicentral Distance 169

4.3.3 Effect of Source Depth 171

4.3.4 Effect of Source away from Vertical and Dip Fault Zones 172

4.3.5 Effect of Fault-Zone Width and Velocity Reduction 175

4.4 3-D Finite-Difference Simulations of FZTWs at the South Longmen-Shan Fault 175

4.5 Fault Rock Co-Seismic Damage and Post-Mainshock Heal 180

4.6 Conclusion and Discussion 186

Acknowledgements 190

References 190

Appendix 196

Chapter 5 Ground-Motion Simulations with Dynamic Source CharacterizationandParallelComputing 199

5.1 Introduction 199

5.2 The Spontaneous Rupture Model 200

5.3 EQdyna:An Explicit Finite Element Method for Simulating Spontaneous Rupture on Geometrically Complex Faults and Wave Propagation in Complex Geologic Structure 203

5.4 Two Examples of Ground-Motion Related Applications of EQdyna 206

5.4.1 Sensitivity of Physical Limits on Ground Motion on Yucca Mountain 206

5.4.2 Effects of Faulting Style Changes on Ground Motion 209

5.5 Hybrid MPI/OpenMP Parallelization of EQdyna and Its Application to a Benchmark Problem 210

5.5.1 Element-size Dependence of Solutions 211

5.5.2 Computational Resource Requirements and Performance Analysis 215

5.6 Conclusions 215

Acknowledgements 216

References 216

Chapter 6 Load-Unload Response Ratio and Its New Progress 219

6.1 Introduction 219

6.2 The Status of Earthquake Prediction Using LURR 223

6.3 Peak Point ofthe LURR and Its Significance 224

6.4 Earthquake Cases in 2008-2009 226

6.5 Improving the Prediction of Magnitude M and T2-Application of Dimensional Method 227

6.5.1 Location 227

6.5.2 Magnitude 227

6.5.3 Occurrence time(T2) 231

6.6 Conclusions 232

Acknowledgements 232

References 232

Chapter 7 Discrete Element Method and Its Applications inEarthquake and Rock Fracture Modeling 235

7.1 Introduction 235

7.2 A BriefIntroduction to the Esys_Particle 237

7.3 Theoretical and Algorithm Development 238

7.3.1 The Equations of Particle Motion 238

7.3.2 Contact Laws,Particle Interactions and Calculation of Forces and Torques 239

7.3.3 Calibration of the Model 242

7.3.4 Incorporation of Thermal and Hydrodynamic Effects 243

7.3.5 Parallel Algorithm 245

7.4 Some Numerical Results Obtained by Using the Esys_Particle 245

7.4.1 Earthquakes 245

7.4.2 Rock fracture 251

7.5 Coupling of Multiple Physics 254

7.5.1 Thermal-Mechanical Coupling 254

7.5.2 Hydro-Mechanical Coupling 255

7.5.3 Full Solid-Fluid Coupling 255

7.6 Discussion and Conclusions 256

Acknowledgements 258

References 258