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 Frechet 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 ...................................... 152
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 Darfleld 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-Mc Mapping of the Scaling Coefficient,
m(T,R,MC) ................................................ 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: AMijR 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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