Keywords:
Seismology--Mathematics.
;
Electronic books.
Description / Table of Contents:
This book is an introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering, and many other fields. It looks under the hood of current simulation technology and provides guidelines on what to look out for when carrying out sophisticated simulation tasks.
Type of Medium:
Online Resource
Pages:
1 online resource (340 pages)
Edition:
1st ed.
ISBN:
9780191026850
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=4755306
DDC:
551.220151
Language:
English
Note:
Cover -- Computational Seismology: A Practical Introduction -- Copyright -- Dedication -- Preface -- Acknowledgements -- Contents -- 1 About Computational Seismology -- 1.1 What is computational seismology? -- 1.2 What is computational seismology good for? -- 1.3 Target audience and level -- 1.4 How to read this volume -- 1.5 Code snippets -- Further reading -- Part I Elastic Waves in the Earth -- 2 Seismic Waves and Sources -- 2.1 Elastic wave equations -- 2.2 Analytical solutions: scalar wave equation -- 2.3 Rheologies -- 2.3.1 Viscoelasticity and attenuation -- 2.3.2 Seismic anisotropy -- 2.3.3 Poroelasticity -- 2.4 Boundary and initial conditions -- 2.4.1 Initial conditions -- 2.4.2 Free surface and Lamb's problem -- 2.4.3 Internal boundaries -- 2.4.4 Absorbing boundary conditions -- 2.5 Fundamental solutions -- 2.5.1 Body waves -- 2.5.2 Gradient, divergence, curl -- 2.5.3 Surface waves -- 2.6 Seismic sources -- 2.6.1 Forces and moments -- 2.6.2 Seismic wavefield of a double-couple point source -- 2.6.3 Superposition principle, finite sources -- 2.6.4 Reciprocity, time reversal -- 2.7 Scattering -- 2.8 Seismic wave problems as linear systems -- 2.9 Some final thoughts -- Chapter summary -- Further reading -- Exercises -- 3 Waves in a Discrete World -- 3.1 Classification of partial differential equations -- 3.2 Strategies for computational wave propagation -- 3.3 Physical domains and computational meshes -- 3.3.1 Dimensionality: 1D, 2D, 2.5D, 3D -- 3.3.2 Computational meshes -- 3.3.3 Structured (regular) grids -- 3.3.4 Unstructured (irregular) grids -- 3.3.5 Other meshing concepts -- 3.4 The curse of mesh generation -- 3.5 Parallel computing -- 3.5.1 Physics and parallelism -- 3.5.2 Domain decomposition, partitioning -- 3.5.3 Hardware and software for parallel algorithms -- 3.5.4 Basic hardware architectures -- 3.5.5 Parallel programming.
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3.5.6 Parallel I/O, data formats, provenance -- 3.6 The impact of parallel computing on Earth Sciences -- Chapter summary -- Further reading -- Exercises -- Part II Numerical Methods -- 4 The Finite-Difference Method -- 4.1 History -- 4.2 The finite-difference method in a nutshell -- 4.3 Finite differences and Taylor series -- 4.3.1 Higher derivatives -- 4.3.2 High-order operators -- 4.4 Acoustic wave propagation in 1D -- 4.4.1 Stability -- 4.4.2 Numerical dispersion -- 4.4.3 Convergence -- 4.5 Acoustic wave propagation in 2D -- 4.5.1 Numerical anisotropy -- 4.5.2 Choosing the right simulation parameters -- 4.6 Elastic wave propagation in 1D -- 4.6.1 Displacement formulation -- 4.6.2 Velocity-stress formulation -- 4.6.3 Velocity-stress algorithm: example -- 4.6.4 Velocity-stress: dispersion -- 4.7 Elastic wave propagation in 2D -- 4.7.1 Grid staggering -- 4.7.2 Free-surface boundary condition -- 4.8 The road to 3D -- 4.8.1 High-order extrapolation schemes -- 4.8.2 Heterogeneous Earth models -- 4.8.3 Optimizing operators -- 4.8.4 Minimal, triangular, unstructured grids -- 4.8.5 Other coordinate systems -- 4.8.6 Concluding remarks -- Chapter summary -- Further reading -- Exercises -- 5 The Pseudospectral Method -- 5.1 History -- 5.2 The pseudospectral method in a nutshell -- 5.3 Ingredients -- 5.3.1 Orthogonal functions, interpolation, derivative -- 5.3.2 Fourier series and transforms -- 5.4 The Fourier pseudospectral method -- 5.4.1 Acoustic waves in 1D -- 5.4.2 Stability, convergence, dispersion -- 5.4.3 Acoustic waves in 2D -- 5.4.4 Numerical anisotropy -- 5.4.5 Elastic waves in 1D -- 5.5 Infinite order finite differences -- 5.6 The Chebyshev pseudospectral method -- 5.6.1 Chebyshev polynomials -- 5.6.2 Chebyshev derivatives, differentiation matrices -- 5.6.3 Elastic waves in 1D -- 5.7 The road to 3D -- Chapter summary -- Further reading.
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Exercises -- 6 The Finite-Element Method -- 6.1 History -- 6.2 Finite elements in a nutshell -- 6.3 Static elasticity -- 6.3.1 Boundary conditions -- 6.3.2 Reference element, mapping, stiffness matrix -- 6.3.3 Simulation example -- 6.4 1D elastic wave equation -- 6.4.1 The system matrices -- 6.4.2 Simulation example -- 6.5 Shape functions in 1D -- 6.6 Shape functions in 2D -- 6.7 The road to 3D -- Chapter summary -- Further reading -- Exercises -- 7 The Spectral-Element Method -- 7.1 History -- 7.2 Spectral elements in a nutshell -- 7.3 Weak form of the elastic equation -- 7.4 Getting down to the element level -- 7.4.1 Interpolation with Lagrange polynomials -- 7.4.2 Numerical integration -- 7.4.3 Derivatives of Lagrange polynomials -- 7.5 Global assembly and solution -- 7.6 Source input -- 7.7 The spectral-element method in action -- 7.7.1 Homogeneous example -- 7.7.2 Heterogeneous example -- 7.8 The road to 3D -- Chapter summary -- Further reading -- Exercises -- 8 The Finite-Volume Method -- 8.1 History -- 8.2 Finite volumes in a nutshell -- 8.3 The finite-volume method via conservation laws -- 8.4 Scalar advection in 1D -- 8.5 Elastic waves in 1D -- 8.5.1 Homogeneous case -- 8.5.2 Heterogeneous case -- 8.5.3 The Riemann problem: heterogeneous case -- 8.6 Derivation via Gauss's theorem -- 8.7 The road to 3D -- Chapter summary -- Further reading -- Exercises -- 9 The Discontinuous Galerkin Method -- 9.1 History -- 9.2 The discontinuous Galerkin method in a nutshell -- 9.3 Scalar advection equation -- 9.3.1 Weak formulation -- 9.3.2 Elemental mass and stiffness matrices -- 9.3.3 The flux scheme -- 9.3.4 Scalar advection in action -- 9.4 Elastic waves in 1D -- 9.4.1 Fluxes in the elastic case -- 9.4.2 Simulation examples -- 9.5 The road to 3D -- Chapter summary -- Further reading -- Exercises -- Part III Applications.
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10 Applications in Earth Sciences -- 10.1 Geophysical exploration -- 10.2 Regional wave propagation -- 10.3 Global and planetary seismology -- 10.4 Strong ground motion and dynamic rupture -- 10.5 Seismic tomography-waveform inversion -- 10.6 Volcanology -- 10.7 Simulation of ambient noise -- 10.8 Elastic waves in random media -- Chapter summary -- Exercises -- 11 Current Challenges in Computational Seismology -- 11.1 Community solutions -- 11.2 Structured vs. unstructured: homogenization -- 11.3 Meshing -- 11.4 Nonlinear inversion, uncertainties -- Appendix A Community Software and Platforms in Seismology -- A.1 Wave propagation and inversion -- A.2 Data processing, visualization, services -- A.3 Benchmarking -- A.4 Jupyter Notebooks -- A.5 Supplementary material -- References -- Index.
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