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Theory of Seismic Imaging

  



Theory of Seismic Imaging

File : pdf, 5 MB, 297 pages

TOC

1. Introduction to Seismic Migration
11. The Reflection Seismic Experiment
12. Huygen’s Principle
13. Zero-Ofset Data
14. Exploding Reflector Model
15. Finite Offset
16. Stacking Velocity Analysis
17. Dipping Reflectors
18. Resolution
19. Computer Excersise I

2. Harmonic Analysis and Delta Functions
21. Fourier Series
22. Fourier Transform
23. The Sampling Theorem
24. Discrete Fourier Transform

3. Equations of Motions of the Earth

4. Elastic Wave Equations
41. Gravity Versus Elasticity
42. The Elastic Wave Equation
43. Scalar Wave Equations
44. Reflection
45. Phase Velocity, Group Velocity, and Dispersion
46. A Quantum Mechanical Slant on Waves

5. Ray Theory
51. The Eikonal Equation
52. The Differential Equations of Rays
53. Fermat’s Principle
54. Fermat Redux

6. Kirchhoff Migration
61. The Wave Equation in Disguise
62. Application to Migration
63. Summary of Green Functions

7. Kirchoff Migration/Inversion

8. The Method of Stationary Phase

9. Downward Continuation of the Seismic Wavefield
91. A Little Fourier Theory of Waves
92. WKBJ Approximation
93. Phase-Shift Migration
94. One-Way Wave Equations
95. Paraxial Wave Equations
96. The Factored Two-Way Wave Equation
97. Downward Continuation of Sources and Receivers
98. Time Domain Methods
99. A Surfer’s Guide to Continued Fractions

10. Plane Wave Decomposition of Seismograms
101. The Weyl and Sommerfeld Integrals
102. Reflection of a Spherical Wave from a Plane Boundary
103. Slant-stacks and the Plane Wave Decomposition

11. Numerical Methods for Tracing Rays
111. Finite Difference Methods for Tracing Rays
112. Initial Value Problems
113. Boundary Value Problems
114. Algebraic Methods for Tracing Rays
115. Distilled Wisdom
116. Eikonal Equation Methods

12. Finite Difference Methods for Wave Propagation and Migration
121. Parabolic Equations
122. Hyperbolic Equations
123. The Full Two-Way Wave Equation
124. Absorbing Boundary Conditions
125. Finite Difference Code for the Wave Equation

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