Front Matter
 Seismic Imaging, Fault Damage and Heal: An Overview
  References
 1 Applications of Full-Wave Seismic Data Assimilation (FWSDA)
  1.1 Numerical Solutions of Seismic Wave Equations
   1.1.1 Stable Finite-Difference Solutions on Non-Uniform,Discontinuous Meshes
   1.1.2 Accelerating Finite-Difference Methods Using GPUs
   1.1.3 The ADER-DG Method
   1.1.4 Accelerating the ADER-DG Method Using GPUs
  1.2 Automating the Waveform Selection Process for FWSDA
   1.2.1 Seismogram Segmentation
   1.2.2 Waveform Selection
   1.2.3 Misfit Measurement Selection
   1.2.4 Fr´echet Kernels for Waveforms Selected in the Wavelet Domain
  1.3 Application of FWSDA in Southern California
   1.3.1 Waveform Selection on Ambient-Noise Green’s Functions
   1.3.2 Waveform Selection on Earthquake Recordings
   1.3.3 Inversion Results after 18 times Adjoint Iteration
   1.4 Summary and Discussion
  References
 2 Wavefield Representation, Propagation and Imaging Using Localized Waves: Beamlet, Curvelet and Dreamlet
  2.1 Introduction
  2.2 Phase-Space Localization and Wavelet Transform
   2.2.1 Time-Frequency Localization
   2.2.2 Time-Scale Localization
   2.2.3 Extension and Generalization of Time-Frequency, Time-Scale Localizations
  2.3 Localized Wave Propagators: From Beam to Beamlet
   2.3.1 Frame Beamlets and Orthonormal Beamlets
   2.3.2 Beamlet Spreading, Scattering and Wave Propagation in the Beamlet Domain
   2.3.3 Beam Propagation in Smooth Media with High-Frequency Asymptotic Solutions
   2.3.4 Beamlet Propagation in Heterogeneous Media by the Local Perturbation Approach
  2.4 Curvelet and Wave Propagation
   2.4.1 Curvelet and Its Generalization
   2.4.2 Fast Digital Transforms for Curvelets and Wave Atoms
   2.4.3 Wave Propagation in Curvelet Domain and the Application to Seismic Imaging
  2.5 Wave Packet: Dreamlets and Gaussian Packets
   2.5.1 Physical Wavelet and Wave-Packets
   2.5.2 Dreamlet as a Type of Physical Wavelet
   2.5.3 Seismic Data Decomposition and Imaging/Migration Using Dreamlets
   2.5.4 Gaussian Packet Migration and Paraxial Approximation of Dreamlet
  2.6 Conclusions
  Acknowledgement
  References
 3 Two-way Coupling of Solid-fluid with Discrete Element Model and Lattice Boltzmann Model
  3.1 Introduction
  3.2 Discrete Element Method and the ESyS-Particle Code
   3.2.1 A Brief Introduction to the Open Source DEM Code: The ESyS-Particle
   3.2.2 The Basic Equations
   3.2.3 Contact Laws and Particle Interaction
   3.2.4 Fracture Criterion
  3.3 Lattice Boltzmann Method
   3.3.1 The Basic Principle of LBM
   3.3.2 Boundary Conditions of LBM
   3.3.3 A Brief Introduction to the Open Source LBM Code: OpenLB
  3.4 Two-way Coupling of DEM and LBM
   3.4.1 Moving Boundary Conditions
   3.4.2 Curved Boundary Conditions
   3.4.3 Implementation of Darcy Flow in LBM
  3.5 Preliminary Results
   3.5.1 Bonded Particles Flow in Fluid
   3.5.2 Fluid Flow in the Fractures
   3.5.3 Hydraulic Fracture Simulation
  3.6 Discussion and Conclusions
  Acknowledgement
  References
 4 Co-seismic Damage and Post-Mainshock Healing of Fault Rocks at Landers, Hector Mine and Parkfield, California Viewed by Fault-Zone Trapped Waves
  4.1 Introduction
  4.2 Rock Damage and Healing on the Rupture Zone of the1992 M7.4 Landers Earthquake
   4.2.1 Landers Rupture Zone Viewed with Fault-Zone Trapped Waves
   4.2.2 Fault Healing at Landers Rupture Zone
   4.2.3 Additional Damage on the Landers Rupture Zone by the Nearby Hector Mine Earthquake
  4.3 Rock Damage and Healing on the Rupture Zone of the1999 M7.1 Hector Mine Earthquake
   4.3.1 Hector Mine Rupture Zone Viewed with FZTWs
   4.3.2 Fault Healing at Hector Mine Rupture Zone
  4.4 Rock Damage and Healing on the San Andreas Fault Associated with the 2004 M6 Parkfield Earthquake
   4.4.1 Low-Velocity Damaged Structure of the San Andreas Fault at Parkfield from Fault Zone Trapped Waves
   4.4.2 Seismic Velocity Variations on the San Andreas Fault Caused by the 2004 M6 Parkfield Earthquake
   4.4.3 Discussion
  4.5 Conclusion
  Acknowledgment
  References
 5 Subsurface Rupture Structure of the M7.1 Darfield and M6.3 Christchurch Earthquake Sequence Viewed withFault-Zone Trapped Waves
  5.1 Introduction
  5.2 The Data and Waveform Analyses
   5.2.1 The FZTWs Recorded for Aftershocks along Darfield/Greendale Rupture Zone
   5.2.2 The FZTWs Recorded for Aftershocks along Christchurch/Port Hills Rupture Zone
  5.3 Subsurface Damage Structure Viewed with FZTWs
  5.4 3-D Finite-Difference Simulations of Observed FZTWs
  5.5 Conclusion and Discussion
  Acknowledgment
  References
 6 Characterizing Pre-shock (Accelerating) Moment Release: A Few Notes on the Analysis of Seismicity
  6.1 Introduction
  6.2 The ‘Interfering Events’ and the ‘Eclipse Method’
  6.3 Comparing with Linear Increase: The BIC Criterion
  6.4 The Time-Space-MC Mapping of the Scaling Coefficient,m(T,R,MC)
  6.5 Removal of Aftershocks and the ‘De-clustered Benioff Strain’
  6.6 ‘Crack-like’ Spatial Window for Great Earthquakes:The 2008 Wenchuan Earthquake
  6.7 Looking into a Finite Earthquake Rupture:The 2004 Sumatra-Andaman Earthquake
  6.8 Using Seismic Moment Tensors to Investigate the Moment Release:AMijR before the 2011 Tohoku Earthquake?
  6.9 Concluding Remarks and Discussion
  6.10 Appendix: The Magnitude Conversion Problem, and theCompleteness of an Earthquake Catalogue
   6.10.1 Magnitudes
   6.10.2 Conversion of Magnitudes
   6.10.3 Completeness of an Earthquake Catalogue
  References
 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
  7.1 Introduction
  7.2 The Data
  7.3 Model Description
  7.4 Results for Circles around the Individual Stations
  7.5 Results for the 300 km Circle around Beijing
  7.6 Results from the Tangshan Region
  7.7 Probability Gains from Forecasts Based on Electrical Signals
  7.8 Effect of Changes in the Background Seismicity
  7.9 Conclusions
  References
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