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Full Description
Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
Contents
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 Gális; References; Index.
