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Author Zhdanov, Michael S.

Title Geophysical inverse theory and regularization problems / Michael S. Zhdanov
Published Amsterdam ; Oxford : Elsevier Science, 2002
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Description 1 online resource (xxiii, 609 pages) : illustrations : digital, HTML and PDF files
Series Methods in geochemistry and geophysics ; 36
Methods in geochemistry and geophysics ; 36
Contents Part I: Introduction to Inversion Theory -- Part II: Methods of the Solution of Inverse Problems -- Part III: Geopotential Field Inversion -- Part IV: Electromagnetic Inversion -- Part V: Seismic Inversion -- Appendix A. Functional spaces of geophysical models and data -- Appendix B. Operators in the spaces of models and data -- Appendix C. Functionals in the spaces of geophysical models -- Appendix D. Linear operators and functionals revisited -- Appendix E. Some formulae and rules from matrix algebra -- Appendix F. Some formulae and rules from tensor calculus
Summary 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, and represents an exhaustive treatise on inversion theory
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Functional analysis.
Geophysics -- Measurement.
Inversion (Geophysics)
Mathematical optimization.
Form Electronic book
ISBN 0080532500 (electronic book)
0444510893 (print)
9780080532509 (electronic book)
9780444510891 (print)