Inverse Theory and Applications in Geophysics, Second Edition

✍ Scribed by Zhdanov, Mikhail Semenovich

• Publisher: Elsevier
• Year: 2015
• Tongue: English
• Leaves: 686
• Series: Methods in geochemistry and geophysics
• Edition: Second edition
• Category: Library

✦ Synopsis

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.

• Presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology—the first to treat many kinds of inversion and imaging techniques in a unified mathematical way.
• Provides a critical link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on geophysical inversion theory.
• Features more than 300 illustrations, figures, charts and graphs to underscore key concepts.
• Reflects the latest developments in inversion theory and applications and captures the most significant changes in the field over the past decade.

✦ Table of Contents

Content:
Front Matter,Copyright,Dedication,Preface to the Second Edition,PrefaceEntitled to full textPart I: Introduction to Inversion TheoryChapter 1 - Forward and Inverse Problems in Science and Engineering, Pages 3-31
Chapter 2 - Ill-Posed Problems and the Methods of Their Solution, Pages 33-61
Chapter 3 - Linear Discrete Inverse Problems, Pages 65-97
Chapter 4 - Iterative Solutions of the Linear Inverse Problem, Pages 99-128
Chapter 5 - Nonlinear Inversion Technique, Pages 129-177
Chapter 6 - Multinary Inversion, Pages 179-193
Chapter 7 - Resolution Analysis of Regularized Geophysical Inversion, Pages 195-203
Chapter 8 - Monte Carlo Methods, Pages 205-214
Chapter 9 - Generalized Joint Inversion of Multimodal Data, Pages 215-233
Chapter 10 - Integral Representations of 2-D Gravity and Magnetic Fields, Pages 237-259
Chapter 11 - Migration of 3-D Gravity, Gravity Tensor, and Total Magnetic Intensity Data, Pages 261-281
Chapter 12 - Numerical Methods in Forward and Inverse Modeling of Geopotential Fields, Pages 283-295
Chapter 13 - Foundations of Electromagnetic Theory, Pages 299-327
Chapter 14 - Integral Representations in Electromagnetic Forward Modeling, Pages 329-384
Chapter 15 - Integral Representations in Electromagnetic Inversion, Pages 385-409
Chapter 16 - Electromagnetic Migration Imaging, Pages 411-440
Chapter 17 - Differential Methods in Electromagnetic Modeling and Inversion, Pages 441-475
Chapter 18 - Wavefield Equations, Pages 479-526
Chapter 19 - Integral Representations in Wavefield Theory, Pages 527-549
Chapter 20 - Integral Representations in Full Waveform Inversion, Pages 551-614
Appendix A - Functional Spaces of Geophysical Models and Data, Pages 615-645
Appendix B - Operators in the Spaces of Models and Data, Pages 647-655
Appendix C - Functionals in the Spaces of Geophysical Models, Pages 657-662
Appendix D - Linear Operators and Functionals Revisited, Pages 663-670
Appendix E - Some Formulae and Rules from Matrix Algebra, Pages 671-681
Appendix F - Some Formulae and Rules from Tensor Calculus, Pages 683-687
Bibliography, Pages 689-699
Index, Pages 701-704