Description 
1 online resource 
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 MixedDetermined 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 BackusGilbert Spread Function; 4.9 The BackusGilbert Generalized Inverse for the Underdetermined Problem; 4.10 Including the Covariance Size; 4.11 The TradeOff 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 ChiSquare Test for the Compatibility of the Prior and Posterior Error; 5.7 The Ftest 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 
Notes 
Includes index 

Online resource; title from PDF title page (EBSCO, viewed April 17, 2018) 
Subject 
Geophysics  Measurement.


Inverse problems (Differential equations)  Numerical solutions.


Oceanography  Measurement.

Form 
Electronic book

ISBN 
0128135565 (electronic bk.) 

9780128135563 (electronic bk.) 
