Download or read book The Magnetotelluric Inverse Problem written by Ashley E. Medin and published by . This book was released on 2008 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear inverse problem of electromagnetic induction to recover electrical conductivity is examined. As this is an ill-posed problem based on inaccurate data, there is a strong need to find the reliable features of the models of electrical conductivity. By using optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data, we attempt to make conclusions about Earth structure under assumptions of one-dimensional and two-dimensional structure. The forward modeling equations are constraints in an optimization problem solving for the fields and the conductivity simultaneously. The computational framework easily allows additional inequality constraints to be imposed. Under the one-dimensional assumption, we develop the optimization approach for use on the magnetotelluric inverse problem. After verifying its accuracy, we use our method to obtain bounds on Earth's average conductivity that all conductivity profiles must obey. There is no regularization required to solve the problem. With the emplacement of additional inequality constraints, we further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models. We take the lessons from the 1-D inverse problem and apply them to the 2-D inverse problem. The difficulty of the 2-D inverse problem requires that we first examine our ability to solve the forward problem, where the conductivity structure is known and the fields are unknown. Our forward problem is designed such that we are able to directly transfer it into the optimization approach used for the inversion. With the successful 2-D forward problem as the constraints, a one-dimensional 2-D inverse problem is stepped into a fully 2-D inverse problem for testing purposes. The computational machinery is incrementally modified to meet the challenge of the realistic two-dimensional magnetotelluric inverse problem. We then use two shallow-Earth data sets from different conductivity regimes and invert them for bounded and regularized structure.
Download or read book An Inverse Problem of Mathematical Physics with Application to the Magnetotelluric Method of Geophysical Exploration written by James N. Towle and published by . This book was released on 1972 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Magnetotelluric Method written by Alan D. Chave and published by Cambridge University Press. This book was released on 2012-04-26 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The magnetotelluric method is a technique for imaging the electrical conductivity and structure of the Earth, from the near surface down to the 410 km transition zone and beyond. This book forms the first comprehensive overview of magnetotellurics, from the salient physics and its mathematical representation to practical implementation in the field, data processing, modeling and geological interpretation. Electromagnetic induction in 1-D, 2-D and 3-D media is explored, building from first principles, and with thorough coverage of the practical techniques of time series processing, distortion, numerical modeling and inversion. The fundamental principles are illustrated with a series of case histories describing geological applications. Technical issues, instrumentation and field practices are described for both land and marine surveys. This book provides a rigorous introduction to magnetotellurics for academic researchers and advanced students, and will be of interest to industrial practitioners and geoscientists wanting to incorporate rock conductivity into their interpretations.
Download or read book Inversion of Magnetotelluric Data for a One dimensional Conductivity written by Kenneth Patrick Whittall and published by . This book was released on 1992 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Problems of Mathematical Physics written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2012-05-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Download or read book Geophysical Data Analysis Understanding Inverse Problem Theory and Practice written by Max A. Meju and published by SEG Books. This book was released on 1994 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication is designed to provide a practical understanding of methods of parameter estimation and uncertainty analysis. The practical problems covered range from simple processing of time- and space-series data to inversion of potential field, seismic, electrical, and electromagnetic data. The various formulations are reconciled with field data in the numerous examples provided in the book; well-documented computer programmes are also given to show how easy it is to implement inversion algorithms.
Download or read book Geophysical Inverse Theory and Regularization Problems written by Michael S. Zhdanov and published by Elsevier. This book was released on 2002-04-24 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Magnetotellurics in the Context of the Theory of Ill posed Problems written by Mark Naumovich Berdichevskiĭ and published by SEG Books. This book was released on 2002 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume serves as an introduction to modern magnetotellurics originating with the pioneering work of Tikhonov and Cagniard. It presents a comprehensive summary of theoretical and methodological aspects of magnetotellurics. It provides a bridge between textbooks on electrical prospecting and numerous papers on magnetotelluric methods scattered among various geophysical journals and collections. The book has been written in the terms of the theory of ill-posed problems and contains a special chapter encouraging readers to master the elements of this theory that defines the philosophy of the physical experiment. The book thus offers the connected and consistent account of the principles of magnetotellurics from that single viewpoint. The book also brings together developments from many sources and involves some little-known results developed in Russia in Tikhonov's magnetotellurics school. Of particular interest are concluding chapters of the book that demonstrate the potential of magnetotellurics in oil and gas surveys, including discovery of the Urengoy gas field in Western Siberia, one of the largest gas fields in the world. This potential also is revealed in studies of the earth's crust and upper mantle.
Download or read book Inverse Problems and Large Scale Computations written by Larisa Beilina and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of two international workshops, namely the Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, held jointly in Sunne, Sweden from May 1-6 2012. The subject of the inverse problems workshop was to present new analytical developments and new numerical methods for solutions of inverse problems. The objective of the large-scale modeling workshop was to identify large-scale problems arising in various fields of science and technology and covering all possible applications, with a particular focus on urgent problems in theoretical and applied electromagnetics. The workshops brought together scholars, professionals, mathematicians, and programmers and specialists working in large-scale modeling problems. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.
Download or read book Inverse Problems in Physical Diagnostics written by Konstantin P. Gaikovich and published by Nova Publishers. This book was released on 2004 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike direct problems related to the solution of differential equations, inverse problems are typically expressed by integral equations. These equations relate media parameters to parameters of a measured signal, or input parameters to output ones in various measurement systems. The solution of integral equations is, with few exceptions, an ill-posed problem, and additional a priori information about the exact solution should be used to solve such problems. The specific character of the a priori information determines various regularisation methods that are in use here to obtain an approximate solution: Tikhonov's method, statistical regularisation method, methods based on the use of additional equations or restrictions or of models with limited number of unknown parameters. The main point of this book is the study of convergence properties of each method and the wide application of numerical modelling that gives the accuracy of the solution in a chosen metric. It is an unaccustomed procedure for physicists, but, because there is no proportionality between data and solution errors in ill-posed problems, such approach is inevitable.
Download or read book Geophysical Inversion written by J. Bee Bednar and published by SIAM. This book was released on 1992-01-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers on geophysical inversion contains research and survey articles on where the field has been and where it's going, and what is practical and what is not. Topics covered include seismic tomography, migration and inverse scattering.
Download or read book Models and Methods of Magnetotellurics written by Mark N. Berdichevsky and published by Springer Science & Business Media. This book was released on 2010-07-15 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetotellurics is finding increasing applications for imaging electrically conductive structures below the Earth`s surface - in both industrial and academic research projects. In this book the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretations of magnetotelluric and magnetovariational soundings. The interpretation is conducted in an interactive way.
Download or read book Geophysical Data Analysis Discrete Inverse Theory written by William Menke and published by Academic Press. This book was released on 2012-12-02 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical Data Analysis: Discrete Inverse Theory is an introductory text focusing on discrete inverse theory that is concerned with parameters that either are truly discrete or can be adequately approximated as discrete. Organized into 12 chapters, the book's opening chapters provide a general background of inverse problems and their corresponding solution, as well as some of the basic concepts from probability theory that are applied throughout the text. Chapters 3-7 discuss the solution of the canonical inverse problem, that is, the linear problem with Gaussian statistics, and discussions on problems that are non-Gaussian and nonlinear are covered in Chapters 8 and 9. Chapters 10-12 present examples of the use of inverse theory and a discussion on the numerical algorithms that must be employed to solve inverse problems on a computer. This book is of value to graduate students and many college seniors in the applied sciences.
Download or read book Inverse Theory and Applications in Geophysics written by Michael S. Zhdanov and published by Elsevier. This book was released on 2015-07-15 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Carleman Estimates for Coefficient Inverse Problems and Numerical Applications written by Michael V. Klibanov and published by Walter de Gruyter. This book was released on 2012-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.
Download or read book Electrical Properties of the Earth s Mantle written by CAMPBELL and published by Birkhäuser. This book was released on 2013-03-08 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table 1 Earth conductivity profiles Figure File Name Apx. Depth Remarks References 1. Global Models 1939-69 LAPR39 0--1250 global Sq, Dst LAHIRI and PRICE, 1939; PRICE, 1973 RIKI50 0--1400 misc. data sources RIKITAKE. 1950; 1966 MCD057 0--2900 LAPR39 + secular change McDoNALD, 1957 CANT60 100--600 see ECKHARDT et a!. , 1963 CANTWELL, 1960 YUKU65 380--1900 ring current YUKUTAKE, 1965 BANK69 0--1700 ring current BANKS, 1969; 1972 2. Global Models 1970--74 BFRS70 100--700 Sq, Dst 27-d variations BERDICHEVSKY et a!. , 1970; 1973 PRKR70 0--3200 rework BANKS, 1969, data PARKER, 1970 SCJA72 0--1000 pulsations, bays, Sq, Dst SCHMUCKER and JANKOWSKI, 1972 BANK72 230--1250 model summary BANKS, 1972 JADY74 0--2951 Sq, 27-d, annual variations JADY, 1974 FAR074 300--1500 with BFRS70 FAINBERG and ROTANOVA, 1974 SCHM74 0--1000 see HAAK, 1980 SCHMUCKER, 1974 DMRB77 0--1450 all available data DMITRIEV et al. , 1977 Global Models 1974-1983 3. PRKN74 60-430 Sq PARKINSON, 1974 DUCM80 0--2900 annual means DUCRUIX et a!. , 1980 ISIK80 320--2020 Sq, Dst, annual, solar cycle ISIKARA, 1980 ACMC81 0--2875 secular impulse ACACHE et a!. , 1980 ROKI82 350--1200 various methods ROKITYANSKY. 1982 JAPA83 0--1200 Dst JADY and PATERSON, 1983 4. Pacific Models LAUN74 0--500 near Calif. ; see DRURY, 1978 LAUNAY, 1975 LARSEN, 1975 LAHA75 0--800 Hawaii 7-1350 FILL80 NE Pacific FILLOUX, 1980 LAW and GREENHOUSE, LWGR81 0--200 Juan de Fuca 1981 0--250 Juan de Fuca OLDENBURG et a!. , 1984 OLJA84 OLCA84 0-250 near Calif. OLDENBURG et al. , 1984 OLNC84 0--250 N. cent. Pacific OLDENBURG et ai.
Download or read book Electromagnetic Sounding of the Earth s Interior written by Viacheslav V. Spichak and published by Elsevier. This book was released on 2011-09-22 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given in the First Russian School-Seminar on electromagnetic soundings of the Earth held in Moscow on 15th November, 2003, this book acquaints scientists and technologists with the latest achievements in theory, techniques and practical applications of the methods of electromagnetic sounding. This three part text covers the methods considered for Earth electromagnetic sounding on a global, regional, and local scale; modern methods for solving forward and inverse problems of geoelectrics, particularily contemporary approaches to the EM data modeling and interpretation in the class of three-dimensional models; and the results of regional EM on-land and sea soundings*Presents theoretical and methodological findings, as well as examples of applications of recently developed algorithms and software in solving practical problems *Describes the practical importance of electromagnetic data through enabling discussions on a construction of a closed technological cycle, processing, analysis and three-dimensional interpretation*Updates current findings in the field, especially with MT, magnetovariational and seismo-electriccal methods and the practice of 3D interpretaions
