The Finite-Difference Modelling of Earthquake Motions

TLDR: In this article, the authors compare 1D and 3D finite-difference (FD) methods applied to seismic-wave propagation problems and propose a 4th-order velocity-stress staggered-grid scheme for 3D problems.

Abstract: Preface Acknowledgements List of symbols 1. Introduction Part I. Mathematical-Physical Model: 2. Basic mathematical-physical model 3. Rheological models of continuum 4. Earthquake source Part II. Time-Domain Numerical Modelling and the Finite-Difference Method: 5. Time-domain numerical methods 6. Introduction to the finite-difference (FD) method 7. 1D problems 8. Basic comparison of the 1D and 3D FD schemes 9. The FD method applied to seismic-wave propagation - a brief historical summary 10. Overview of the FD schemes for 3D problems 11. Velocity-stress staggered-grid scheme for an unbounded heterogeneous viscoelastic medium 12. Velocity-stress staggered-grid schemes for a free surface 13. Discontinuous spatial grid 14. Perfectly matched layer 15. Simulation of the kinematic sources 16. Simulation of the dynamic rupture propagation 17. Other wavefield excitations 18. Memory optimization 19. Complete FD algorithm for a 3D problem based on the 4th-order velocity-stress staggered-grid scheme 20. Finite-element (FE) method 21. TSN modelling of rupture propagation with the adaptive smoothing algorithm 22. Hybrid FD-FE method Part III. Numerical Modelling of Seismic Motion at Real Sites: 23. Mygdonian Basin, Greece 24. Grenoble Valley, France Part IV. Concluding Remarks: Appendix. Time-frequency (TF) misfit and goodness-of-fit criteria for quantitative comparison of time signals Miriam Kristekova, Peter Moczo, Josef Kristek and Martin Galis References Index.