Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. The Finite-Difference Modelling of Earthquake Motions offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, The Finite-Difference Modelling of Earthquake Motions 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.
List of symbols
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 â 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 Gãlis
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Peter Moczo is a professor of physics and Chair of the Department of Astronomy, Physics of the Earth, and Meteorology at Comenius University, Bratislava. He is the main author of several monographs and extended articles on the finite-difference method (including the highly-respected Acta Physica Slovaca article which partly forms the basis of this book). Professor Moczo is a member of the Learned Society of the Slovak Academy of Sciences, and his awards include the Prize of the Slovak Academy of Sciences for Infrastructure, the Silver Medal of the Faculty of Mathematics, Physics and Informatics of Comenius University, and the Dionyz Stur Medal of the Slovak Academy of Sciences for Achievements in Natural Sciences. Along with his two co-authors, Professor Moczo is a leading member of the (informal) NuQuake research group, studying numerical modelling of seismic wave propagation and earthquake motion, at Comenius University and the Slovak Academy of Science in Bratislava. As part of this group, all three authors were major contributors to the elaboration of the finite-difference method and hybrid finite-difference/finite-element method.
Jozef Kristek is an associate professor of physics at the Department of Astronomy, Physics of the Earth, and Meteorology at Comenius University, Bratislava. His research, as part of the NuQuake group, focuses on the development of numerical-modelling methods for seismic wave propagation and earthquake motion in structurally complex media. Dr Kristek has been awarded the Prize of the Slovak Academy of Sciences for Infrastructure and the Dean's Prize for Science for his work in this area.
Martin Gális is a postdoctoral researcher at the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Dr Gális' research also focuses on the development of numerical-modelling methods for seismic wave propagation and earthquake motion in structurally complex media. He has also been awarded the Prize of the Slovak Academy of Sciences for Infrastructure.