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1 About Computational Seismology |
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1 | (12) |
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1.1 What is computational seismology? |
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1 | (1) |
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1.2 What is computational seismology good for? |
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2 | (3) |
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1.3 Target audience and level |
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5 | (1) |
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1.4 How to read this volume |
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6 | (1) |
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7 | (6) |
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8 | (5) |
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Part I Elastic Waves in the Earth |
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2 Seismic Waves and Sources |
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13 | (36) |
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2.1 Elastic wave equations |
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17 | (2) |
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2.2 Analytical solutions: scalar wave equation |
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19 | (3) |
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22 | (3) |
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2.3.1 Viscoelasticity and attenuation |
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22 | (1) |
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23 | (1) |
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24 | (1) |
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2.4 Boundary and initial conditions |
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25 | (3) |
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25 | (1) |
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2.4.2 Free surface and Lamb's problem |
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26 | (1) |
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2.4.3 Internal boundaries |
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27 | (1) |
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2.4.4 Absorbing boundary conditions |
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27 | (1) |
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2.5 Fundamental solutions |
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28 | (3) |
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28 | (1) |
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2.5.2 Gradient, divergence, curl |
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28 | (1) |
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29 | (2) |
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31 | (8) |
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31 | (2) |
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2.6.2 Seismic wavefield of a double-couple point source |
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33 | (3) |
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2.6.3 Superposition principle, finite sources |
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36 | (2) |
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2.6.4 Reciprocity, time reversal |
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38 | (1) |
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39 | (3) |
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2.8 Seismic wave problems as linear systems |
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42 | (1) |
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43 | (6) |
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44 | (1) |
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45 | (1) |
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45 | (4) |
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3 Waves in a Discrete World |
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49 | (26) |
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3.1 Classification of partial differential equations |
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49 | (2) |
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3.2 Strategies for computational wave propagation |
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51 | (2) |
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3.3 Physical domains and computational meshes |
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53 | (5) |
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3.3.1 Dimensionality: 1D, 2D, 2.5D, 3D |
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53 | (1) |
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3.3.2 Computational meshes |
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54 | (1) |
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3.3.3 Structured (regular) grids |
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55 | (1) |
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3.3.4 Unstructured (irregular) grids |
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56 | (1) |
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3.3.5 Other meshing concepts |
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57 | (1) |
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3.4 The curse of mesh generation |
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58 | (1) |
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59 | (9) |
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3.5.1 Physics and parallelism |
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61 | (1) |
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3.5.2 Domain decomposition, partitioning |
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62 | (1) |
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3.5.3 Hardware and software for parallel algorithms |
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62 | (1) |
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3.5.4 Basic hardware architectures |
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63 | (1) |
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3.5.5 Parallel programming |
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64 | (3) |
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3.5.6 Parallel I/O, data formats, provenance |
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67 | (1) |
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3.6 The impact of parallel computing on Earth Sciences |
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68 | (7) |
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69 | (1) |
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70 | (1) |
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70 | (5) |
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Part II Numerical Methods |
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4 The Finite-Difference Method |
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75 | (41) |
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75 | (2) |
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4.2 The finite-difference method in a nutshell |
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77 | (1) |
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4.3 Finite differences and Taylor series |
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78 | (4) |
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79 | (2) |
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4.3.2 High-order operators |
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81 | (1) |
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4.4 Acoustic wave propagation in 1D |
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82 | (8) |
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87 | (1) |
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4.4.2 Numerical dispersion |
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88 | (1) |
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89 | (1) |
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4.5 Acoustic wave propagation in 2D |
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90 | (5) |
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4.5.1 Numerical anisotropy |
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91 | (1) |
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4.5.2 Choosing the right simulation parameters |
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92 | (3) |
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4.6 Elastic wave propagation in 1D |
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95 | (6) |
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4.6.1 Displacement formulation |
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95 | (1) |
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4.6.2 Velocity-stress formulation |
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96 | (2) |
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4.6.3 Velocity-stress algorithm: example |
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98 | (1) |
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4.6.4 Velocity-stress: dispersion |
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99 | (2) |
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4.7 Elastic wave propagation in 2D |
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101 | (2) |
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101 | (1) |
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4.7.2 Free-surface boundary condition |
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102 | (1) |
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103 | (13) |
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4.8.1 High-order extrapolation schemes |
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103 | (2) |
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4.8.2 Heterogeneous Earth models |
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105 | (1) |
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4.8.3 Optimizing operators |
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105 | (2) |
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4.8.4 Minimal, triangular, unstructured grids |
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107 | (1) |
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4.8.5 Other coordinate systems |
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108 | (1) |
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109 | (1) |
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109 | (1) |
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110 | (1) |
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111 | (5) |
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5 The Pseudospectral Method |
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116 | (37) |
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117 | (1) |
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5.2 The pseudospectral method in a nutshell |
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118 | (1) |
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119 | (8) |
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5.3.1 Orthogonal functions, interpolation, derivative |
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119 | (2) |
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5.3.2 Fourier series and transforms |
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121 | (6) |
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5.4 The Fourier pseudospectral method |
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127 | (7) |
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5.4.1 Acoustic waves in 1D |
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127 | (3) |
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5.4.2 Stability, convergence, dispersion |
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130 | (1) |
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5.4.3 Acoustic waves in 2D |
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131 | (1) |
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5.4.4 Numerical anisotropy |
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132 | (1) |
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5.4.5 Elastic waves in 1D |
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133 | (1) |
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5.5 Infinite order finite differences |
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134 | (4) |
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5.6 The Chebyshev pseudospectral method |
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138 | (9) |
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5.6.1 Chebyshev polynomials |
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139 | (5) |
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5.6.2 Chebyshev derivatives, differentiation matrices |
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144 | (2) |
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5.6.3 Elastic waves in 1D |
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146 | (1) |
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147 | (6) |
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148 | (1) |
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149 | (1) |
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149 | (4) |
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6 The Finite-Element Method |
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153 | (29) |
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154 | (1) |
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6.2 Finite elements in a nutshell |
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155 | (1) |
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156 | (8) |
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6.3.1 Boundary conditions |
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160 | (1) |
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6.3.2 Reference element, mapping, stiffness matrix |
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160 | (2) |
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162 | (2) |
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6.4 1D elastic wave equation |
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164 | (9) |
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6.4.1 The system matrices |
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167 | (2) |
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169 | (4) |
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6.5 Shape functions in 1D |
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173 | (2) |
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6.6 Shape functions in 2D |
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175 | (2) |
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177 | (5) |
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178 | (1) |
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179 | (1) |
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179 | (3) |
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7 The Spectral-Element Method |
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182 | (29) |
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183 | (1) |
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7.2 Spectral elements in a nutshell |
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184 | (1) |
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7.3 Weak form of the elastic equation |
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185 | (3) |
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7.4 Getting down to the element level |
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188 | (9) |
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7.4.1 Interpolation with Lagrange polynomials |
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191 | (2) |
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7.4.2 Numerical integration |
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193 | (3) |
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7.4.3 Derivatives of Lagrange polynomials |
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196 | (1) |
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7.5 Global assembly and solution |
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197 | (2) |
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199 | (1) |
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7.7 The spectral-element method in action |
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199 | (6) |
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7.7.1 Homogeneous example |
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199 | (5) |
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7.7.2 Heterogeneous example |
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204 | (1) |
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205 | (6) |
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206 | (1) |
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207 | (1) |
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208 | (3) |
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8 The Finite-Volume Method |
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211 | (28) |
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212 | (1) |
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8.2 Finite volumes in a nutshell |
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213 | (1) |
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8.3 The finite-volume method via conservation laws |
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214 | (6) |
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8.4 Scalar advection in 1D |
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220 | (3) |
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223 | (10) |
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225 | (3) |
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228 | (3) |
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8.5.3 The Riemann problem: heterogeneous case |
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231 | (2) |
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8.6 Derivation via Gauss's theorem |
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233 | (1) |
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234 | (5) |
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235 | (1) |
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236 | (1) |
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236 | (3) |
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9 The Discontinuous Galerkin Method |
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239 | (30) |
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240 | (2) |
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9.2 The discontinuous Galerkin method in a nutshell |
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242 | (1) |
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9.3 Scalar advection equation |
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243 | (12) |
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245 | (2) |
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9.3.2 Elemental mass and stiffness matrices |
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247 | (2) |
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249 | (2) |
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9.3.4 Scalar advection in action |
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251 | (4) |
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255 | (7) |
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9.4.1 Fluxes in the elastic case |
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257 | (3) |
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9.4.2 Simulation examples |
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260 | (2) |
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262 | (7) |
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264 | (1) |
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264 | (1) |
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265 | (4) |
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10 Applications in Earth Sciences |
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269 | (22) |
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10.1 Geophysical exploration |
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271 | (2) |
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10.2 Regional wave propagation |
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273 | (2) |
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10.3 Global and planetary seismology |
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275 | (3) |
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10.4 Strong ground motion and dynamic rupture |
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278 | (3) |
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10.5 Seismic tomography---waveform inversion |
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281 | (4) |
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285 | (2) |
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10.7 Simulation of ambient noise |
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287 | (1) |
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10.8 Elastic waves in random media |
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288 | (3) |
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289 | (1) |
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290 | (1) |
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11 Current Challenges in Computational Seismology |
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291 | (4) |
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291 | (1) |
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11.2 Structured vs. unstructured: homogenization |
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292 | (1) |
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293 | (1) |
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11.4 Nonlinear inversion, uncertainties |
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294 | (1) |
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Appendix A Community Software and Platforms in Seismology |
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295 | (8) |
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A.1 Wave propagation and inversion |
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295 | (2) |
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A.2 Data processing, visualization, services |
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297 | (1) |
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298 | (1) |
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299 | (1) |
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A.5 Supplementary material |
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299 | (4) |
References |
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303 | (18) |
Index |
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321 | |