Seismic Imaging, Fault Damage and Heal (eBook)

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Yong-Gang Li,University of Southern California, Los Angeles, CA, USA.

Seismic Imaging, Fault Damage and Heal: An Overview 11
References 20
1 Applications of Full-Wave Seismic Data Assimilation (FWSDA) 25
1.1 Numerical Solutions of Seismic Wave Equations 26
1.1.1 Stable Finite-Difference Solutions on Non-Uniform, Discontinuous Meshes 28
1.1.2 Accelerating Finite-Difference Methods Using GPUs 32
1.1.3 The ADER-DG Method 36
1.1.4 Accelerating the ADER-DG Method Using GPUs 39
1.2 Automating the Waveform Selection Process for FWSDA 51
1.2.1 Seismogram Segmentation 52
1.2.2 Waveform Selection 59
1.2.3 Misfit Measurement Selection 60
1.2.4 Fréchet Kernels for Waveforms Selected in the Wavelet Domain 61
1.3 Application of FWSDA in Southern California 65
1.3.1 Waveform Selection on Ambient-Noise Green’s Functions 67
1.3.2 Waveform Selection on Earthquake Recordings 69
1.3.3 Inversion Results after 18 times Adjoint Iteration 70
1.4 Summary and Discussion 73
References 75
2 Wavefield Representation, Propagation and Imaging Using Localized Waves: Beamlet, Curvelet and Dreamlet 83
2.1 Introduction 84
2.2 Phase-Space Localization and Wavelet Transform 87
2.2.1 Time-Frequency Localization 88
2.2.2 Time-Scale Localization 91
2.2.3 Extension and Generalization of Time-Frequency, Time-Scale Localizations 92
2.3 Localized Wave Propagators: From Beam to Beamlet 95
2.3.1 Frame Beamlets and Orthonormal Beamlets 97
2.3.2 Beamlet Spreading, Scattering and Wave Propagation in the Beamlet Domain 100
2.3.3 Beam Propagation in Smooth Media with High-Frequency Asymptotic Solutions 106
2.3.4 Beamlet Propagation in Heterogeneous Media by the Local Perturbation Approach 111
2.4 Curvelet and Wave Propagation 116
2.4.1 Curvelet and Its Generalization 116
2.4.2 Fast Digital Transforms for Curvelets and Wave Atoms 120
2.4.3 Wave Propagation in Curvelet Domain and the Application to Seismic Imaging 120
2.5 Wave Packet: Dreamlets and Gaussian Packets 122
2.5.1 Physical Wavelet and Wave-Packets 122
2.5.2 Dreamlet as a Type of Physical Wavelet 126
2.5.3 Seismic Data Decomposition and Imaging/Migration Using Dreamlets 129
2.5.4 Gaussian Packet Migration and Paraxial Approximation of Dreamlet 133
2.6 Conclusions 140
Acknowledgement 141
References 142
3 Two-way Coupling of Solid-fluid with Discrete Element Model and Lattice Boltzmann Model 153
3.1 Introduction 153
3.2 Discrete Element Method and the ESyS-Particle Code 156
3.2.1 A Brief Introduction to the Open Source DEM Code: The ESyS-Particle 157
3.2.2 The Basic Equations 157
3.2.3 Contact Laws and Particle Interaction 158
3.2.4 Fracture Criterion 160
3.3 Lattice Boltzmann Method 161
3.3.1 The Basic Principle of LBM 161
3.3.2 Boundary Conditions of LBM 162
3.3.3 A Brief Introduction to the Open Source LBM Code: OpenLB 166
3.4 Two-way Coupling of DEM and LBM 166
3.4.1 Moving Boundary Conditions 167
3.4.2 Curved Boundary Conditions 167
3.4.3 Implementation of Darcy Flow in LBM 170
3.5 Preliminary Results 171
3.5.1 Bonded Particles Flow in Fluid 171
3.5.2 Fluid Flow in the Fractures 172
3.5.3 Hydraulic Fracture Simulation 174
3.6 Discussion and Conclusions 176
Acknowledgement 177
References 177
4 Co-seismic Damage and Post-Mainshock Healing of Fault Rocks at Landers, Hector Mine and Parkfield, California Viewed by Fault-Zone Trapped Waves 183
4.1 Introduction 183
4.2 Rock Damage and Healing on the Rupture Zone of the 1992 M7.4 Landers Earthquake 186
4.2.1 Landers Rupture Zone Viewed with FaultZone Trapped Waves 186
4.2.2 Fault Healing at Landers Rupture Zone 193
4.2.3 Additional Damage on the Landers Rupture Zone by the Nearby Hector Mine Earthquake 202
4.3 Rock Damage and Healing on the Rupture Zone of the 1999 M7.1 Hector Mine Earthquake 204
4.3.1 Hector Mine Rupture Zone Viewed with FZTWs 204
4.3.2 Fault Healing at Hector Mine Rupture Zone 214
4.4 Rock Damage and Healing on the San Andreas Fault Associated with the 2004 M6 Parkfield Earthquake 218
4.4.1 LowVelocity Damaged Structure of the San Andreas Fault at Parkfield from Fault Zone Trapped Waves 219
4.4.2 Seismic Velocity Variations on the San Andreas Fault Caused by the 2004 M6 Parkfield Earthquake 228
4.4.3 Discussion 247
4.5 Conclusion 249
Acknowledgment 252
References 252
5 Subsurface Rupture Structure of the M7.1 Darfield and M6.3 Christchurch Earthquake Sequence Viewed with Fault-Zone Trapped Waves 259
5.1 Introduction 260
5.2 The Data and Waveform Analyses 266
5.2.1 The FZTWs Recorded for Aftershocks along Darfield/Greendale Rupture Zone 274
5.2.2 The FZTWs Recorded for Aftershocks along Christchurch/Port Hills Rupture Zone 287
5.3 Subsurface Damage Structure Viewed with FZTWs 298
5.4 3-D Finite-Difference Simulations of Observed FZTWs 304
5.5 Conclusion and Discussion 316
Acknowledgment 324
References 324
6 Characterizing Pre-shock (Accelerating) Moment Release: A Few Notes on the Analysis of Seismicity 333
6.1 Introduction 333
6.2 The ‘Interfering Events’ and the ‘Eclipse Method’ 335
6.3 Comparing with Linear Increase: The BIC Criterion 337
6.4 The Time-Space-MC Mapping of the Scaling Coefficient, m(T, R,MC) 338
6.5 Removal of Aftershocks and the ‘De-clustered Benioff Strain’ 341
6.6 ‘Crack-like’ Spatial Window for Great Earthquakes: The 2008 Wenchuan Earthquake 345
6.7 Looking into a Finite Earthquake Rupture: The 2004 Sumatra-Andaman Earthquake 348
6.8 Using Seismic Moment Tensors to Investigate the Moment Release: AMijR before the 2011 Tohoku Earthquake? 350
6.9 Concluding Remarks and Discussion 354
6.10 Appendix: The Magnitude Conversion Problem, and the Completeness of an Earthquake Catalogue 355
6.10.1 Magnitudes 355
6.10.2 Conversion of Magnitudes 356
6.10.3 Completeness of an Earthquake Catalogue 357
References 357
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 361
7.1 Introduction 362
7.2 The Data 364
7.3 Model Description 367
7.4 Results for Circles around the Individual Stations 369
7.5 Results for the 300 km Circle around Beijing 374
7.6 Results from the Tangshan Region 379
7.7 Probability Gains from Forecasts Based on Electrical Signals 381
7.8 Effect of Changes in the Background Seismicity 383
7.9 Conclusions 384
References 385