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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.
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.
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.
Auteur
Michael S. Zhdanov is Professor of Geophysics in the Department of Geology and Geophysics at the University of Utah in Salt Lake City. Dr. Zhdanov is also Director of the Center of Electromagnetic Research at the same university. He has more than 30 years of experience in research and instruction in geophysical electromagnetic theory and he has authored more than 100 papers on the subject. He is the founding director of the Geoelectromagnetic Research Institute of the Russian Academy of Sciences and Member of the Russian Academy of Natural Science.
Échantillon de lecture
Preface
Michael S. Zhdanov, Salt Lake City, Utah
Inverse solutions are key problems in many natural sciences. They form the basis of our understanding of the world surrounding us. Whenever we try to learn something about physical laws, the internal structure of the earth or the nature of the Universe, we collect data and try to extract the required information from these data. This is the actual solution of the inverse problem. In fact the observed data are predetermined by physical laws and by the structure of the earth or Universe. The method of predicting observed data for given sources within given media is usually referred to as the forward problem solution. The method of reconstructing the sources of some physical, geophysical, or other phenomenon, as well as the parameters of the corresponding media, from the observed data is referred to as the inverse problem solution.
In geophysics, the observed data are usually physical fields generated by natural or artificial sources and propagated through the earth. Geophysicists try to use these data to reconstruct the internal structure of the earth. This is a typical inverse problem solution.
Inversion of geophysical data is complicated by the fact that geophysical data are invariably contaminated by noise and are acquired at a limited number of observation points. Moreover, mathematical models are usually complicated, and yet at the same time are also simplifications of the true geophysical phenomena. As a result, the solutions are ambiguous and error-prone. The principal questions arising in geophysical inverse problems are about the existence, uniqueness, and stability of the solution. Methods of solution can be based on linearized and nonlinear inversion techniques and include different approaches, such as least-squares, gradient-type methods (including steepest-descent and conjugate-gradient), and others.
A central point of this book is the application of so-called "regularizing" algorithms for the solution of ill-posed inverse geophysical problems. These algorithms can use a priori geological and geophysical information about the earth's subsurface to reduce the ambiguity and increase the stability of the solution.
In mathematics, we have a classical definition of the ill-posed problem: a problem is ill-posed, according to Hadamard (1902), if the solution is not unique or if it is not a continuous function of the data (i.e., if to a small perturbation of data; there corresponds an arbitrarily large perturbation of the solution). Unfortunately, from the point of view of classical theory, all geophysical inverse problems are ill-posed, because their solutions are either nonunique or unstable. However, geophysicists solve this problem and obtain geologically reasonable results in one of two ways. The first is based on intuitive estimation of the possible solutions and selection of a geologically adequate model by the interpreter. The second is based on the application of different types of regularization algorithms, which allow automatic selection of the proper solution by the computer using a priori geological and geophysical information about the earth's structure. The most consistent approach to the const…