Website Search
Find information on spaces, staff, and services.
Catalog Search
Books
Geophysical data analysis : discrete inverse theory
- Author / Creator
- Available as
- Online
Details
- Creator
- William Menke
- Format
- Books
- Language
- English
- Publication
-
- Fourth edition
- London, United Kingdom : Elsevier Limited : Academic Press, [2018]
- Physical Details
-
- 1 online resource
- ISBNs
- 0128135565, 9780128135556, 0128135557, 9780128135563
- OCLC
- on1031373802
- Includes index.
- Intro; Title page; Table of Contents; Copyright; Preface; Introduction; I.1 Forward and Inverse Theories; I.2 MATLAB as a Tool for Learning Inverse Theory; I.3 A Very Quick MATLAB Tutorial; I.4 Review of Vectors and Matrices and Their Representation in MATLAB; I.5 Useful MatLab Operations; Chapter 1: Describing Inverse Problems; Abstract; 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; Abstract; 2.1 Noise and Random Variables
- 2.2 Correlated Data2.3 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; Abstract; 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 Solution3.7 The Purely Underdetermined Problem; 3.8 Mixed-Determined Problems; 3.9 Weighted Measures of Length as a Type of Prior Information; 3.10 Other Types of Prior 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; Abstract; 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 Inverses4.6 Measures of Goodness of Resolution and Covariance; 4.7 Generalized Inverses With Good Resolution and Covariance; 4.8 Sidelobes and the Backus-Gilbert Spread Function; 4.9 The Backus-Gilbert Generalized Inverse for the Underdetermined Problem; 4.10 Including the Covariance Size; 4.11 The Trade-Off of Resolution and Variance; 4.12 Checkerboard Tests; 4.13 Problems; Chapter 5: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods; Abstract; 5.1 The Mean of a Group of Measurements
- 5.2 Maximum Likelihood Applied to Inverse Problem5.3 Model Resolution in the Presence of Prior Information; 5.4 Relative Entropy as a Guiding Principle; 5.5 Equivalence of the Three Viewpoints; 5.6 Chi-Square Test for the Compatibility of the Prior and Posterior Error; 5.7 The F-test of the Error Improvement Significance; 5.8 Problems; Chapter 6: Nonuniqueness and Localized Averages; Abstract; 6.1 Null Vectors and Nonuniqueness; 6.2 Null Vectors of a Simple Inverse Problem; 6.3 Localized Averages of Model Parameters; 6.4 Relationship to the Resolution Matrix; 6.5 Averages Versus Estimates