| Edition |
Fourth edition. |
| Description |
1 online resource |
|
text txt rdacontent |
|
computer c rdamedia |
|
online resource cr rdacarrier |
| Note |
Includes index. |
|
Online resource; title from PDF title page (EBSCO, viewed April 17, 2018). |
| Contents |
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 |
| Summary |
Annotation This fourth edition maintains the accessible and succinct manner for which the original book is known. It also features the addition of MATLAB examples and problem sets, advanced colour graphics, and much more. |
| Subject |
Geophysics -- Measurement.
|
|
Oceanography -- Measurement.
|
|
Inverse problems (Differential equations) -- Numerical solutions.
|
|
Problèmes inverses (Équations différentielles) -- Solutions numériques.
|
|
SCIENCE -- Earth Sciences -- Geography.
|
|
SCIENCE -- Earth Sciences -- Geology.
|
|
Geophysics -- Measurement
|
|
Inverse problems (Differential equations) -- Numerical solutions
|
|
Oceanography -- Measurement
|
| ISBN |
9780128135563 (electronic bk.) |
|
0128135565 (electronic bk.) |
|
9780128135556 |
| Standard No. |
AU@ 000062228050 |
|
GBVCP 1026057817 |
|
