Computational seismology : a practical introduction / Heiner Igel.

Format:

Book

Author/Creator:

Igel, Heiner, author.

Language:

English

Subjects (All):

Seismology--Mathematics.

Seismology.

Seismology--Data processing.

Physical Description:

xv, 323 pages : illustrations (some color) ; 25 cm

Edition:

First edition.

Place of Publication:

Oxford, United Kingdom : Oxford University Press, 2017.

Summary:

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. The physical problem of elastic wave propagation in 1D serves as a model system with which the various numerical methods are introduced and compared. The theoretical background is presented with substantial graphical material supporting the concepts. The results can be reproduced with the supplementary electronic material provided as python codes embedded in Jupyter notebooks. The book starts with a primer on the physics of elastic wave propagation, and a chapter on the fundamentals of parallel programming, computational grids, mesh generation, and hardware models. The core of the book is the presentation of numerical solutions of the wave equation with six different methods: 1) the finite-difference method;2) the pseudospectral method (Fourier and Chebyshev); 3) the linear finite-element method; 4) the spectral-element method; 5) the finite-volume method; and 6) the discontinuous Galerkin method. Each chapter contains comprehension questions, theoretical, and programming exercises. The book closes with a discussion of domains of application and criteria for the choice of a specific numerical method, and the presentation of current challenges. Book jacket.

Contents:

1 About Computational Seismology 1

1.1 What is computational seismology? 1

1.2 What is computational seismology good for? 2

1.3 Target audience and level 5

1.4 How to read this volume 6

1.5 Code snippets 7

Further reading 8

Part I Elastic Waves in the Earth

2 Seismic Waves and Sources 13

2.1 Elastic wave equations 17

2.2 Analytical solutions: scalar wave equation 19

2.3 Rheologies 22

2.3.1 Viscoelasticity and attenuation 22

2.3.2 Seismic anisotropy 23

2.3.3 Poroelasticity 24

2.4 Boundary and initial conditions 25

2.4.1 Initial conditions 25

2.4.2 Free surface and Lamb's problem 26

2.4.3 Internal boundaries 27

2.4.4 Absorbing boundary conditions 27

2.5 Fundamental solutions 28

2.5.1 Body waves 28

2.5.2 Gradient, divergence, curl 28

2.5.3 Surface waves 29

2.6 Seismic sources 31

2.6.1 Forces and moments 31

2.6.2 Seismic wavefield of a double-couple point source 33

2.6.3 Superposition principle, finite sources 36

2.6.4 Reciprocity, time reversal 38

2.7 Scattering 39

2.8 Seismic wave problems as linear systems 42

2.9 Some final thoughts 43

Chapter summary 44

Further reading 45

Exercises 45

3 Waves in a Discrete World 49

3.1 Classification of partial differential equations 49

3.2 Strategies for computational wave propagation 51

3.3 Physical domains and computational meshes 53

3.3.1 Dimensionality: 1D, 2D, 2.5D, 3D 53

3.3.2 Computational meshes 54

3.3.3 Structured (regular) grids 55

3.3.4 Unstructured (irregular) grids 56

3.3.5 Other meshing concepts 57

3.4 The curse of mesh generation 58

3.5 Parallel computing 59

3.5.1 Physics and parallelism 61

3.5.2 Domain decomposition, partitioning 62

3.5.3 Hardware and software for parallel algorithms 62

3.5.4 Basic hardware architectures 63

3.5.5 Parallel programming 64

3.5.6 Parallel I/O, data formats, provenance 67

3.6 The impact of parallel computing on Earth Sciences 68

Chapter summary 69

Further reading 70

Exercises 70

Part II Numerical Methods

4 The Finite-Difference Method 75

4.1 History 75

4.2 The finite-difference method in a nutshell 77

4.3 Finite differences and Taylor series 78

4.3.1 Higher derivatives 79

4.3.2 High-order operators 81

4.4 Acoustic wave propagation in 1D 82

4.4.1 Stability 87

4.4.2 Numerical dispersion 88

4.4.3 Convergence 89

4.5 Acoustic wave propagation in 2D 90

4.5.1 Numerical anisotropy 91

4.5.2 Choosing the right simulation parameters 92

4.6 Elastic wave propagation in 1D 95

4.6.1 Displacement formulation 95

4.6.2 Velocity-stress formulation 96

4.6.3 Velocity-stress algorithm: example 98

4.6.4 Velocity-stress: dispersion 99

4.7 Elastic wave propagation in 2D 101

4.7.1 Grid staggering 101

4.7.2 Free-surface boundary condition 102

4.8 The road to 3D 103

4.8.1 High-order extrapolation schemes 103

4.8.2 Heterogeneous Earth models 105

4.8.3 Optimizing operators 105

4.8.4 Minimal, triangular, unstructured grids 107

4.8.5 Other coordinate systems 108

4.8.6 Concluding remarks 109

Chapter summary 109

Further reading 110

Exercises 111

5 The Pseudospectral Method 116

5.1 History 117

5.2 The pseudospectral method in a nutshell 118

5.3 Ingredients 119

5.3.1 Orthogonal functions, interpolation, derivative 119

5.3.2 Fourier series and transforms 121

5.4 The Fourier pseudospectral method 127

5.4.1 Acoustic waves in 1D 127

5.4.2 Stability, convergence, dispersion 130

5.4.3 Acoustic waves in 2D 131

5.4.4 Numerical anisotropy 132

5.4.5 Elastic waves in 1D 133

5.5 Infinite order finite differences 134

5.6 The Chebyshev pseudospectral method 138

5.6.1 Chebyshev polynomials 139

5.6.2 Chebyshev derivatives, differentiation matrices 144

5.6.3 Elastic waves in 1D 146

5.7 The road to 3D 147

Chapter summary 148

Further reading 149

Exercises 149

6 The Finite-Element Method 153

6.1 History 154

6.2 Finite elements in a nutshell 155

6.3 Static elasticity 156

6.3.1 Boundary conditions 160

6.3.2 Reference element, mapping, stiffness matrix 160

6.3.3 Simulation example 162

6.4 1D elastic wave equation 164

6.4.1 The system matrices 167

6.4.2 Simulation example 169

6.5 Shape functions in 1D 173

6.6 Shape functions in 2D 175

6.7 The road to 3D 177

Chapter summary 178

Further reading 179

Exercises 179

7 The Spectral-Element Method 182

7.1 History 183

7.2 Spectral elements in a nutshell 184

7.3 Weak form of the elastic equation 185

7.4 Getting down to the element level 188

7.4.1 Interpolation with Lagrange polynomials 191

7.4.2 Numerical integration 193

7.4.3 Derivatives of Lagrange polynomials 196

7.5 Global assembly and solution 197

7.6 Source input 199

7.7 The spectral-element method in action 199

7.7.1 Homogeneous example 199

7.7.2 Heterogeneous example 204

7.8 The road to 3D 205

Chapter summary 206

Further reading 207

Exercises 208

8 The Finite-Volume Method 211

8.1 History 212

8.2 Finite volumes in a nutshell 213

8.3 The finite-volume method via conservation laws 214

8.4 Scalar advection in 1D 220

8.5 Elastic waves in 1D 223

8.5.1 Homogeneous case 225

8.5.2 Heterogeneous case 228

8.5.3 The Riemann problem: heterogeneous case 231

8.6 Derivation via Gauss's theorem 233

8.7 The road to 3D 234

Chapter summary 235

Further reading 236

Exercises 236

9 The Discontinuous Galerkin Method 239

9.1 History 240

9.2 The discontinuous Galerkin method in a nutshell 242

9.3 Scalar advection equation 243

9.3.1 Weak formulation 245

9.3.2 Elemental mass and stiffness matrices 247

9.3.3 The flux scheme 249

9.3.4 Scalar advection in action 251

9.4 Elastic waves in 1D 255

9.4.1 Fluxes in the elastic case 257

9.4.2 Simulation examples 260

9.5 The road to 3D 262

Chapter summary 264

Further reading 264

Exercises 265

Part III Applications

10 Applications in Earth Sciences 269

10.1 Geophysical exploration 271

10.2 Regional wave propagation 273

10.3 Global and planetary seismology 275

10.4 Strong ground motion and dynamic rupture 278

10.5 Seismic tomography-waveform inversion 281

10.6 Volcanology 285

10.7 Simulation of ambient noise 287

10.8 Elastic waves in random media 288

Chapter summary 289

Exercises 290

11 Current Challenges in Computational Seismology 291

11.1 Community solutions 291

11.2 Structured vs. unstructured: homogenization 292

11.3 Meshing 293

11.4 Nonlinear inversion, uncertainties 294.

Notes:

Includes bibliographical references and index.

ISBN:

9780198717409

0198717407

9780198717416

0198717415

OCLC:

966965398

Publisher Number:

99970600584