This book is the second monograph of the earth science specializing in computational, observational and interpretational seismology and geophysics, containingthe full-3D waveform tomography method and its application; beamlets andcurvelets method for wavefield representation, propagation and imaging; twoway coupling of solid-fluid with discrete element model and lattice Boltzmannmodel; fault-zone trapped wave observations and 3-D finite-difference synthetics for high-resolution imaging subsurface rupture zone segmentation and bifurcation; fault rock damage and heal associated with earthquakes in Californiaand New Zealand; characterization of pre-shock accelerating moment releasewith careful considerations in processing and analysis of seismicity using earthquake catalogues; and statistical modeling of earthquake occurrences based onthe ultra-low frequency ground electric signals. Each chapter in this book includes the detailed discussion of the state-of-the-art method and technique withtheir applications in case study. The editor approaches this as a broad interdisciplinary effort, with well-balanced observational, metrological and numericalmodeling aspects. Linked with these topics, the book highlights the importancefor imaging the crustal complex structures and internal fault-zone rock damageat seismic depths that are closely related to earthquake occurrence and physics.
Researchers and graduate students in geosciences will broaden their horizonsabout advanced methodology and technique applied in seismology, geophysicsand earthquake science. This book can be taken as an expand of the first bookin the series, and covers multi-disciplinary topics to allow readers to grasp thenew methods and skills used in data processing and analysis as well as numericalmodeling for structural, physical and mechanical interpretation of earthquakephenomena, and to strengthen their understanding ofearthquake occurrence andhazards, thus helping readers to evaluate potential earthquake risk in seismogenicregions globally. Readers of this book can make full use of the present knowledgeand techniques to serve the reduction of earthquake disasters.

Seismic Imaging, Fault Damage and Heal: An Overview 1

References 10

1 Applications of Full-Wave Seismic Data Assimilation (FWSDA) 15

1.1 Numerical Solutions of Seismic Wave Equations 16

      1.1.1 Stable Finite-Difference Solutions on Non-Uniform, Discontinuous Meshes 18

      1.1.2 Accelerating Finite-Difference Methods Using GPUs 22

      1.1.3 The ADER-DG Method 26

      1.1.4 Accelerating the ADER-DG Method Using GPUs 29

1.2 Automating the Waveform Selection Process for FWSDA 41

      1.2.1 Seismogram Segmentation 42

      1.2.2 Waveform Selection 49

      1.2.3 Misfit Measurement Selection 50

      1.2.4 Fr´ echet Kernels for Waveforms Selected in the Wavelet Domain 51

1.3 Application of FWSDA in Southern California 55

      1.3.1 Waveform Selection on Ambient-Noise Green’s Functions 57

      1.3.2 Waveform Selection on Earthquake Recordings 59

      1.3.3 Inversion Results after 18 times Adjoint Iteration 60

1.4 Summary and Discussion 63

References 65

2 Wavefield Representation, Propagation and Imaging Using Localized Waves: Beamlet, Curvelet and Dreamlet 73

2.1 Introduction 74

2.2 Phase-Space Localization and Wavelet Transform 77

      2.2.1 Time-Frequency Localization 78

      2.2.2 Time-Scale Localization 81

      2.2.3 Extension and Generalization of Time-Frequency, Time-Scale Localizations 82

2.3 Localized Wave Propagators: From Beam to Beamlet 85

      2.3.1 Frame Beamlets and Orthonormal Beamlets 87

      2.3.2 Beamlet Spreading, Scattering and Wave Propagation in the Beamlet Domain 90

      2.3.3 Beam Propagation in Smooth Media with High-Frequency Asymptotic Solutions 96

      2.3.4 Beamlet Propagation in Heterogeneous Media by the Local Perturbation Approach 101

2.4 Curvelet and Wave Propagation 106

      2.4.1 Curvelet and Its Generalization 106

      2.4.2 Fast Digital Transforms for Curvelets and Wave Atoms 110

      2.4.3 Wave Propagation in Curvelet Domain and the Application to Seismic Imaging 110

2.5 Wave Packet: Dreamlets and Gaussian Packets 112

      2.5.1 Physical Wavelet and Wave-Packets 112

      2.5.2 Dreamlet as a Type of Physical Wavelet 116

      2.5.3 Seismic Data Decomposition and Imaging/Migration Using Dreamlets 119

      2.5.4 Gaussian Packet Migration and Paraxial Approximation of Dreamlet 123

2.6 Conclusions 130

Acknowledgement 131

References 132

3 Two-way Coupling of Solid-fluid with Discrete Element Model and Lattice Boltzmann Model 143

3.1 Introduction 143

3.2 Discrete Element Method and the ESyS-Particle Code 146

      3.2.1 A Brief Introduction to the Open Source DEM Code: The ESyS-Particle 147

      3.2.2 The Basic Equations 147

      3.2.3 Contact Laws and Particle Interaction 148

      3.2.4 Fracture Criterion 150

3.3 Lattice Boltzmann Method 151

      3.3.1 The Basic Principle of LBM 151

      3.3.2 Boundary Conditions of LBM 152

      3.3.3 A Brief Introduction to the Open Source LBM Code: OpenLB 156

3.4 Two-way Coupling of DEM and LBM 156

      3.4.1 Moving Boundary Conditions 157

      3.4.2 Curved Boundary Conditions 157

      3.4.3 Implementation of Darcy Flow in LBM 160

3.5 Preliminary Results 161

      3.5.1 Bonded Particles Flow in Fluid 161

      3.5.2 Fluid Flow in the Fractures 162

      3.5.3 Hydraulic Fracture Simulation 164

3.6 Discussion and Conclusions 166

Acknowledgement 167

References 167

4 Co-seismic Damage and Post-Mainshock Healing of Fault Rocks at Landers, Hector Mine and Parkfield, California Viewed by Fault-Zone Trapped Waves 173

4.1 Introduction 173

4.2 Rock Damage and Healing on the Rupture Zone of the 1992 M7.4 Landers Earthquake 176

      4.2.1 Landers Rupture Zone Viewed with Fault-Zone Trapped Waves 176

      4.2.2 Fault Healing at Landers Rupture Zone 183

      4.2.3 Additional Damage on the Landers Rupture Zone by the Nearby Hector Mine Earthquake 192

4.3 Rock Damage and Healing on the Rupture Zone of the 1999 M7.1 Hector Mine Earthquake 194

      4.3.1 Hector Mine Rupture Zone Viewed with FZTWs 194

      4.3.2 Fault Healing at Hector Mine Rupture Zone 204

4.4 Rock Damage and Healing on the San Andreas Fault Associated with the 2004 M6 Parkfield Earthquake 208

      4.4.1 Low-Velocity Damaged Structure of the San Andreas Fault at Parkfield from Fault Zone Trapped Waves 209

      4.4.2 Seismic Velocity Variations on the San Andreas Fault Caused by the 2004 M6 Parkfield Earthquake 218

      4.4.3 Discussion 237

4.5 Conclusion 239

Acknowledgment 242

References 242

5 Subsurface Rupture Structure of the M7.1 Darfield and M6.3 Christchurch Earthquake Sequence Viewed with Fault-Zone Trapped Waves 249

5.1 Introduction 250

5.2 The Data and Waveform Analyses 256

      5.2.1 The FZTWs Recorded for Aftershocks along Darfield/Greendale Rupture Zone 264

      5.2.2 The FZTWs Recorded for Aftershocks along Christchurch/Port Hills Rupture Zone 277

5.3 Subsurface Damage Structure Viewed with FZTWs 288

5.4 3-D Finite-Difference Simulations of Observed FZTWs 294

5.5 Conclusion and Discussion 306

Acknowledgment 314

References 314

6 Characterizing Pre-shock (Accelerating) Moment Release: A Few Notes on the Analysis of Seismicity 323

6.1 Introduction 323

6.2 The ‘Interfering Events’ and the ‘Eclipse Method’ 325

6.3 Comparing with Linear Increase: The BIC Criterion 327

6.4 The Time-Space-M C Mapping of the Scaling Coefficient, m(T, R, M C ) 328

6.5 Removal of Aftershocks and the ‘De-clustered Benioff Strain’ 331

6.6 ‘Crack-like’ Spatial Window for Great Earthquakes: The 2008 Wenchuan Earthquake 335

6.7 Looking into a Finite Earthquake Rupture: The 2004 Sumatra-Andaman Earthquake 338

6.8 Using Seismic Moment Tensors to Investigate the Moment Release: AM ij R before the 2011 Tohoku Earthquake? 340

6.9 Concluding Remarks and Discussion 344

6.10 Appendix: The Magnitude Conversion Problem, and the Completeness of an Earthquake Catalogue 345

6.10.1 Magnitudes 345

      6.10.2 Conversion of Magnitudes 346

      6.10.3 Completeness of an Earthquake Catalogue 347

References 347

7 Statistical Modeling of Earthquake Occurrences Based on External Geophysical Observations: With an Illustrative Application to the Ultra-low Frequency Ground Electric Signals Observed in the Beijing Region 351

7.1 Introduction 352

7.2 The Data 354

7.3 Model Description 357

7.4 Results for Circles around the Individual Stations 359

7.5 Results for the 300 km Circle around Beijing 364

7.6 Results from the Tangshan Region 369

7.7 Probability Gains from Forecasts Based on Electrical Signals 371

7.8 Effect of Changes in the Background Seismicity 373

7.9 Conclusions 374

References 375

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