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.
I. Introduction to Inversion Theory.
- Forward and inverse problems in geophysics. 1.1 Formulation of forward and inverse problems for different geophysical fields. 1.2 Existence and uniqueness of the inverse problem solutions. 1.3 Instability of the inverse problem solution.
- Ill-posed problems and the methods of their solution. 2.1 Sensitivity and resolution of geophysical methods. 2.2 Formulation of well-posed and ill-posed problems. 2.3 Foundations of regularization methods of inverse problem solution. 2.4 Family of stabilizing functionals. 2.5 Definition of the regularization parameter. II. Methods of the Solution of Inverse Problems.
- Linear discrete inverse problems. 3.1 Linear least-squares inversion. 3.2 Solution of the purely under determined problem. 3.3 Weighted least-squares method. 3.4 Applying the principles of probability theory to a linear inverse problem. 3.5 Regularization methods. 3.6 The Backus-Gilbert method.
- Iterative solutions of the linear inverse problem. 4.1 Linear operator equations and their solution by iterative methods. 4.2 A generalized minimal residual method. 4.3 The regularization method in a linear inverse problem solution.
- Nonlinear inversion technique. 5.1 Gradient-type methods. 5.2 Regularized gradient-type methods in the solution of nonlinear inverse problems. 5.3 Regularized solution of a nonlinear discrete inverse problem. 5.4 Conjugate gradient re-weighted optimization.III. Geopotential Field Inversion.
- Integral representations in forward modeling of gravity and magnetic fields. 6.1 Basic equations for g
- No. of pages:
- © Elsevier Science 2002
- 24th April 2002
- Elsevier Science
- eBook ISBN:
- Hardcover ISBN:
Michael S. Zhdanov is Professor of Geophysics and Director of the Consortium for Electromagnetic Modeling and Inversion (CEMI) at the University of Utah in Salt Lake City. Dr. Zhdanov has authored more than 100 journal articles and 18 books on Geophysical Inverse Theory and related topics over the past 40 years.
Department of Geology and Geophysics, University of Utah, Salt Lake City, USA
@from:M. Lewandowski @qu:...will be very beneficial for graduate students in global geophysics and geophysical prospection, as well as utilized by professionals dealing with mathematical geophysics. @source:Pure and Applied Geophysics