Nonlinear Inversion and Tomography – Lecture Notes
File : pdf, 1.7 MB, 164 pages
by James G. Berryman
TOC
1. Introduction to the Traveltime Inversion Problem
1.1 Wave Slowness models
1.2 Fermat’s Principle and Traveltime Functionals
1.3 Snell’s Law
1.4 Seismic Inversion and Tomography
1.5 Backprojection for Bent Rays
1.6 Diffraction Tomography and Full Wave Inversion
1.7 Linear vs Nonlinear Inversion and Tomography
2. Feasibility Analysis for Traveltime Inversion
2.1 Feasibility Constraints Defined
2.2 Quick Review of Convexity
2.3 Properties of Traveltime Functionals
2.4 Feasibility Sets
2.5 Convex Programming for Inversion
3. Least-Squares Methods
3.1 Normal Equations
3.2 Scaled Least-Squares Model
3.3 Nonlinear Least-Squares Models
3.4 Damped Least-Squares Model
3.5 Physical Basis for Weighted Least-Squares
3.6 Partial Corrections Using Backprojection
4. Algorithms for Linear Inversion
4.1 More-Penrose Pseudoinverse and SVD
4.2 Scaling Methods
4.3 Weighted Least-Squares, Regularization, and Effective Resolution
4.4 Sequential and Iterative Method
5. Fast Ray Tracing Methods
5.1 Why Not Straight Ray?
5.2 Variational Derivation of Snell’s law
5.3 Ray Equations and Shooting Methods
5.4 The Eikonal Equation
5.5 Vidale’s Method
5.6 Bending Method
5.7 Comparison
6. Ghost in Traveltime Inversion and Tomography
6.1 Feasibility Constraints and Ghosts
6.2 Types of Ghosts
6.3 Eliminating Ghosts (Ghostbusting)
6.4 Significance of Ghosts
7. Nonlinear Seismic Inversion
7.1 Linear and Nonlinear Programming
7.2 More about Weighted Least-Squares
7.3 Stable Algorithm for Nonlinear Crosswell Tomography
7.4 Using Relative Traveltimes
8. Other Nonlinear Inversion Problems
8.1 Electrical Impedance Tomography
8.2 Inverse Eigenvalue Problems
8.3 General Structure for Convex Inversion Problems
8.4 Nonconvex Inversion Problems with Feasibility Constraints
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