Geophysical Inverse Theory and Regularization Problems

Michael S. Zhdanov (Eds.)9780444510891, 0444510893

This book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology. The book 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. This text is the first 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. The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods. The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration.This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, andrepresents an exhaustive treatise on inversion theory.

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Table of contents :
Content:
Preface
Pages XIX-XXIII
Michael S. Zhdanov

Chapter 1 Forward and inverse problems in geophysics Original Research Article
Pages 3-28

Chapter 2 Ill-posed problems and the methods of their solution Original Research Article
Pages 29-57

Chapter 3 Linear discrete inverse problems Original Research Article
Pages 61-90

Chapter 4 Iterative solutions of the linear inverse problem Original Research Article
Pages 91-119

Chapter 5 Nonlinear inversion technique Original Research Article
Pages 121-165

Chapter 6 Integral representations in forward modeling of gravity and magnetic fields Original Research Article
Pages 169-176

Chapter 7 Integral representations in inversion of gravity and magnetic data Original Research Article
Pages 177-198

Chapter 8 Foundations of electromagnetic theory Original Research Article
Pages 201-229

Chapter 9 Integral representations in electromagnetic forward modeling Original Research Article
Pages 231-286

Chapter 10 Integral representations in electromagnetic inversion Original Research Article
Pages 287-329

Chapter 11 Electromagnetic migration imaging Original Research Article
Pages 331-360

Chapter 12 Differential methods in electromagnetic modeling and inversion Original Research Article
Pages 361-391

Chapter 13 Wavefield equations Original Research Article
Pages 395-442

Chapter 14 Integral representations in wavefield theory Original Research Article
Pages 443-465

Chapter 15 Integral representations in wavefield inversion Original Research Article
Pages 467-529

Appendix A Functional spaces of geophysical models and data
Pages 531-551

Appendix B Operators in the spaces of models and data
Pages 553-561

Appendix C Functionals in the spaces of geophysical models
Pages 563-568

Appendix D Linear operators and functionals revisited
Pages 569-576

Appendix E Some formulae and rules from matrix algebra
Pages 577-587

Appendix F Some formulae and rules from tensor calculus
Pages 589-592

Bibliography
Pages 593-604

Index
Pages 605-609