| Description |
1 online resource : illustrations |
| Series |
Methods in geochemistry and geophysics ; volume 36 |
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Methods in geochemistry and geophysics.
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| Contents |
Front Cover; Inverse Theory and Applications in Geophysics; Copyright; Dedication; Contents; Preface to the Second Edition; Preface; Part I: Introduction to Inversion Theory; Chapter 1: Forward and Inverse Problems in Science and Engineering; 1.1 Formulation of Forward and Inverse Problems for Different Physical Fields; 1.1.1 Gravity Field; 1.1.2 Magnetic Field; 1.1.3 Electromagnetic Field; 1.1.4 Seismic Wavefield; 1.2 Existence and Uniqueness of the Inverse Problem Solutions; 1.2.1 Existence of the Solution; 1.2.2 Uniqueness of the Solution; 1.2.3 Practical Uniqueness |
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1.3 Instability of the Inverse Problem Solution References; Chapter 2: Ill-Posed Problems and the Methods of Their Solution; 2.1 Sensitivity and Resolution of Geophysical Methods; 2.1.1 Formulation of the Inverse Problem in General Mathematical Spaces; 2.1.2 Sensitivity; 2.1.3 Resolution; 2.2 Formulation of Well-Posed and Ill-Posed Problems; 2.2.1 Well-Posed Problems; 2.2.2 Conditionally Well-Posed Problems; 2.2.3 Quasi-Solution of the Ill-Posed Problem; 2.3 Foundations of Regularization Methods of Inverse Problem Solution; 2.3.1 Regularizing Operators; 2.3.2 Stabilizing Functionals |
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2.3.3 Tikhonov Parametric Functional2.4 Family of Stabilizing Functionals; 2.4.1 Stabilizing Functionals Revisited; 2.4.2 Representation of a Stabilizing Functional in the Form of a Pseudo-Quadratic Functional; 2.5 Definition of the Regularization Parameter; 2.5.1 Optimal Regularization Parameter Selection; 2.5.2 L-Curve Method of Regularization Parameter Selection; References; Part II: Methods of the Solution of Inverse Problems; Chapter 3: Linear Discrete Inverse Problems; 3.1 Linear Least-Squares Inversion; 3.1.1 The Linear Discrete Inverse Problem |
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3.1.2 Systems of Linear Equations and Their General SolutionsMinimization of the misfit functional; 3.1.3 The Data Resolution Matrix; 3.2 Solution of the Purely Underdetermined Problem; 3.2.1 Underdetermined System of Linear Equations; 3.2.2 The Model Resolution Matrix; 3.3 Weighted Least-Squares Method; 3.4 Applying the Principles of Probability Theory to a Linear Inverse Problem; 3.4.1 Some Formulae and Notations from Probability Theory; 3.4.2 Maximum Likelihood Method; 3.4.3 Chi-Square Fitting; 3.5 Regularization Methods; 3.5.1 The Tikhonov Regularization Method |
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3.5.2 Application of SLDM Method in Regularized Linear Inverse Problem Solution3.5.3 Integrated Sensitivity; 3.5.4 Definition of the Weighting Matrices for the Model Parameters and Data; 3.5.5 Controlled Sensitivity; 3.5.6 Approximate Regularized Solution of the Linear Inverse Problem; 3.5.7 The Levenberg-Marquardt Method; 3.5.8 The Maximum a Posteriori Estimation Method (the Bayes Estimation); 3.6 The Backus-Gilbert Method; 3.6.1 The Data Resolution Function; 3.6.2 The Spread Function; 3.6.3 Regularized Solution in the Backus-Gilbert Method; References |
| Summary |
Geophysical Inverse Theory and Applications, Second Edition, brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. It's the first book of its kind to treat many kinds of inversion and imaging techniques in a unified mathematical manner. The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. Unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, it represents an exhaustive treatise on inversion theory. Written by one of the world's foremost experts, this work is widely recognized as the ultimate researcher's reference on geophysical inverse theory and its practical scientific applications |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed July 22, 2015) |
| Subject |
Inversion (Geophysics)
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Geophysics -- Measurement
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Functional analysis.
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Mathematical optimization.
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SCIENCE -- Earth Sciences -- General.
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SCIENCE -- Physics -- Geophysics.
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Functional analysis
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Geophysics -- Measurement
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Inversion (Geophysics)
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Mathematical optimization
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| Form |
Electronic book
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| ISBN |
9780444627124 |
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044462712X |
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