Preface |
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ix | |
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1 Introduction to the Wave Theory |
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1 | (18) |
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1.1 Wave Motion in Continuous Media |
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2 | (3) |
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5 | (1) |
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1.3 Propagation and Diffusion |
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6 | (2) |
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1.4 Acoustic Wave Equation |
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8 | (3) |
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1.5 Acoustic Wave Equation with Complex Coefficients |
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11 | (5) |
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1.5.1 Complex Elastic Modulus and the Complex Wave Velocity |
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11 | (2) |
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1.5.2 Damping Wave Equations in Viscoelastic Media |
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13 | (1) |
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1.5.3 Viscoelastic Models |
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14 | (2) |
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1.6 Acoustic Wave Equation with Variant Density or Velocity |
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16 | (2) |
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18 | (1) |
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2 Elastic Waves in a Perfect Elastic Solid |
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19 | (28) |
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2.1 Stress Tensor and Strain Tensor |
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20 | (3) |
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2.2 Vector Wave Equation in Fully Elastic Media |
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23 | (4) |
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2.3 Scalar Wave Equations in Fully Elastic Media |
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27 | (3) |
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2.4 Elastic Wave Equation in Two-Dimensional Media |
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30 | (1) |
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2.5 Elastic Wave Equations in Anisotropic Media |
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31 | (3) |
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2.6 Boundary Conditions for Elastic Wave Equations |
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34 | (3) |
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2.7 Elastic Wave Velocities of Rocks |
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37 | (10) |
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3 From Elastic Waves to Seismic Waves |
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47 | (36) |
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3.1 On Acoustic Wave Equations with Variant Coefficients |
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48 | (6) |
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3.2 Seismic Reflection Records and Corresponding Equations |
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54 | (4) |
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3.2.1 Wave Equations for Marine Reflection Records |
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54 | (1) |
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3.2.2 Wave Equations for Land Single-Component Records |
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55 | (1) |
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3.2.3 Wave Equations for Land Three-Component Records |
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55 | (3) |
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3.3 Elastic Waves in Horizontally Multilayered Media |
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58 | (8) |
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3.3.1 Elastic Wave Equations in a Cylindrical Coordinate System |
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58 | (5) |
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3.3.2 Boundary Conditions |
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63 | (1) |
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3.3.3 Acoustic Wave Propagation in Layered Half Space |
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64 | (2) |
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3.4 Elastic Waves in Fluid-Saturated Solid (I): Gassmann's Model |
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66 | (5) |
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66 | (3) |
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3.4.2 The Generalized Gassmann Model |
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69 | (2) |
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3.5 Elastic Waves in Fluid-Saturated Solid (II): Biot's Theory |
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71 | (6) |
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3.5.1 Low-Frequency Elastic Waves in a Fluid-Saturated Porous Solid |
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72 | (4) |
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3.5.2 All Frequency Elastic Waves in a Fluid-Saturated Porous Solid |
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76 | (1) |
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3.6 Tracking Reservoirs with the Gassmann Model |
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77 | (6) |
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4 Wave Equation Reduction with Reflection Seismic Data Processing |
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83 | (24) |
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4.1 The Statics of Land Seismic Data |
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84 | (3) |
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4.2 Muting and Deghost Filtering |
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87 | (1) |
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4.3 Shear Wave Decoupling Process |
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88 | (1) |
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4.4 Suppression of Multiples Generated by the Ocean Bottom |
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89 | (2) |
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91 | (4) |
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4.6 The One-Way Wave Equation and the Wave Migration Equations |
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95 | (4) |
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99 | (6) |
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105 | (2) |
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5 Integral Solutions of the Wave Equation with Boundary and Initial Value Conditions |
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107 | (28) |
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5.1 Integral Solutions for Mixed Cauchy Boundary Value Problems |
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109 | (3) |
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5.2 The Kirchhoff Integral Formula for the Boundary Value Wave Equation Problems |
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112 | (5) |
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5.3 The Green's Function of Boundary Value Problems for Wave Motion |
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117 | (7) |
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5.3.1 The Green's Function Method |
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117 | (2) |
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5.3.2 Green's Function for the Wave Equation with Zero Initial Value Problems |
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119 | (3) |
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5.3.3 Green's Function of the Wave Equation in Half Space with a Point Source |
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122 | (2) |
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5.4 The Green's Function in Medium with Linear Velocity |
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124 | (3) |
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5.5 The Eikonal Equation and the Transport Equations |
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127 | (4) |
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5.6 The Second-Type Green's Function with Nonhomogeneous Boundary Conditions |
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131 | (2) |
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133 | (2) |
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6 Decomposition and Continuation of Seismic Wave Field |
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135 | (36) |
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6.1 The Equations of Acoustic Upgoing and Downgoing Waves |
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137 | (3) |
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6.2 Kirchhoff Migration of the Prestack Seismic Data |
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140 | (3) |
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6.3 Downward Continuation of the Reflective Seismic Wave Field in Homogenous Media |
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143 | (5) |
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6.4 Downward Continuation of Seismic Wave Field in Vertically Inhomogeneous Media |
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148 | (3) |
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6.5 The Pseudo-Differential Operator and Fourier Integral Operator |
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151 | (10) |
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6.5.1 Analysis of the Boundary Value Problem of Wave Equation with Variant Coefficients |
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151 | (2) |
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6.5.2 The Oscillatory Integral |
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153 | (3) |
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6.5.3 The Fourier Integral Operator |
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156 | (3) |
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6.5.4 Decomposition of Fourier Integral Operator |
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159 | (2) |
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6.6 Downward Continuation of the Seismic Wave Field in Inhomogeneous Medium |
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161 | (4) |
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6.7 Decomposition of Body Waves in Reflection Seismic Wave Field |
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165 | (4) |
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169 | (2) |
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171 | (44) |
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7.1 Introduction to Inverse Problems in Seismology |
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172 | (8) |
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7.1.1 Inverse Problems in Seismic Exploration |
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172 | (2) |
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7.1.2 The Generalized Solutions |
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174 | (3) |
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7.1.3 Linearized Iterative Seismic Inversion |
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177 | (1) |
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7.1.4 Nonlinear Stochastic Inversions |
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178 | (2) |
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7.2 Born Approximation Inversion by Inverse Scattering |
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180 | (7) |
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7.3 Acoustic Wave Equation Inversion in Vertically Inhomogeneous Background Media |
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187 | (3) |
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7.4 Acoustic Inverse Scattering Problems in Variant Velocity Media |
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190 | (8) |
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7.4.1 Acoustic Generalized Radon Transformation |
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190 | (2) |
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7.4.2 The Inverse Acoustic Generalized Radon Transformation |
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192 | (4) |
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7.4.3 Some Supplements about Inverse Scattering Procedures |
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196 | (2) |
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7.5 Linearized Iterative Inversion of Seismic Reflection Data |
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198 | (9) |
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7.6 The Maximum Entropy Inversion and Inversion for Reservoir Parameters |
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207 | (5) |
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7.6.1 Bayes' Theorem and Maximum Entropy Inversion |
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207 | (3) |
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7.6.2 Probability Density Inversion Based on Statistical Estimation of Rock Physical Properties |
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210 | (2) |
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212 | (3) |
Appendix: Finite difference method for solving the acoustic wave equation with velocity and density variant media |
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215 | (30) |
References |
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245 | (4) |
Index |
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249 | |