Geophysical Data Analysis: Discrete Inverse Theory, Volume 45

3rd Edition

MATLAB Edition

Print ISBN: 9780128100486
eBook ISBN: 9780123977847
Imprint: Academic Press
Published Date: 21st June 2012
Page Count: 330
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Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new edition maintains the accessible and succinct manner for which it is known, with the addition of:

  • MATLAB examples and problem sets
  • Advanced color graphics
  • Coverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervals
  • Online data sets and MATLAB scripts that can be used as an inverse theory tutorial.

Table of Contents




Chapter 1. Describing Inverse Problems

1.1 Formulating Inverse Problems

1.2 The Linear Inverse Problem

1.3 Examples of Formulating Inverse Problems

1.4 Solutions to Inverse Problems

1.5 Problems


Chapter 2. Some Comments on Probability Theory

2.1 Noise and Random Variables

2.2 Correlated Data

2.3 Functions of Random Variables

2.4 Gaussian Probability Density Functions

2.5 Testing the Assumption of Gaussian Statistics

2.6 Conditional Probability Density Functions

2.7 Confidence Intervals

2.8 Computing Realizations of Random Variables

2.9 Problems


Chapter 3. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method

3.1 The Lengths of Estimates

3.2 Measures of Length

3.3 Least Squares for a Straight Line

3.4 The Least Squares Solution of the Linear Inverse Problem

3.5 Some Examples

3.6 The Existence of the Least Squares Solution

3.7 The Purely Underdetermined Problem

3.8 Mixed-Determined Problems

3.9 Weighted Measures of Length as a Type of A Priori Information

3.10 Other Types of A Priori Information

3.11 The Variance of the Model Parameter Estimates

3.12 Variance and Prediction Error of the Least Squares Solution

3.13 Problems


Chapter 4. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses

4.1 Solutions Versus Operators

4.2 The Data Resolution Matrix

4.3 The Model Resolution Matrix

4.4 The Unit Covariance Matrix

4.5 Resolution and Covariance of Some Generalized Inverses

4.6 Measures of Goodness of Resolution and Covariance

4.7 Generalized Inverses with Good Resolution and Covariance

4.8 Sidelobes and


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