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 Inverse Problems written by Mathias Richter and published by Springer Nature. This book was released on 2021-01-05 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.
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 Inverse Problems of Electromagnetic Geophysical Fields written by and published by VSP. This book was released on 1999 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers topics including: two-dimensional problems of a magnetic exploration method involving artificial field magnetization and electric exploration by a direct current; effective algorithms of solution of direct and inverse three-dimensional problems of magnetic exploration; mathematical theory and algorithms of the solution of three-dimensional inverse problems of electric exploarion with a direct current; and explicit equations for inverse problems of electromagnetic field.
Download or read book Geophysical Data Analysis written by Max A. Meju and published by . This book was released on 1994 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Geophysical Data Inversion Methods and Applications written by Andreas Vogel and published by Springer-Verlag. This book was released on 2013-03-09 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Problems in Geophysical Applications written by Heinz W. Engl and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 1997 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume describe recent accomplishments in the area, and also give pointers for future research, thereby prompting questions that advance the science and lead to open questions about the underlying mathematics. This volume should be of interest to mathematicians who wish to know more about this application area, and to geophysicists interested in theoretical analysis.
Download or read book Geophysical Data Analysis and Inverse Theory with MATLAB and Python written by William Menke and published by Elsevier. This book was released on 2024-02-22 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical Data Analysis and Inverse Theory with MATLAB or Python, Fifth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. The book demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention given to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. A series of "crib sheets" offer step-by-step summaries of methods presented. Utilizing problems and case studies, along with MATLAB and Python computer code and summaries of methods, the book provides professional geophysicists, students, data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory. - Includes material on probability, including Bayesian influence, probability density function, and metropolis algorithm - Offers detailed discussions of the application of inverse theory to seismological, gravitational, and tectonic studies - Provides numerous examples, color figures, and end-of-chapter problems to help readers explore and further understand the presented ideas - Includes both MATLAB and Python examples and problem sets
Download or read book Geophysical Data Analysis written by William Menke and published by Academic Press. This book was released on 2018-04-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory. - Includes material on probability, including Bayesian influence, probability density function and metropolis algorithm - Offers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studies - Contains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas - Includes MATLAB examples and problem sets - Updated and refined throughout to bring the text in line with current understanding and improved examples and case studies - Expanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition
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 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 Geophysics Today written by Sergey Fomel and published by SEG Books. This book was released on 2010 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of papers which appear in the September-October 2010 Geophysics special section, written by recognised experts in various areas of exploration geophysics, plus an additional group of papers drawn from Geophysics which address areas beyond those invited articles. The result is a snapshot of the state-of-the-art in the field.
Download or read book Geophysical Data Analysis Discrete Inverse Theory written by William Menke and published by Academic Press. This book was released on 2012-06-26 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new edition maintains the accessible and succinct manner for which it is known, with the addition of: - MATLAB examples and problem sets - Advanced color graphics - Coverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervals - Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithm - Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies - Numerous examples and end-of-chapter homework problems help you explore and further understand the ideas presented - Use as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructors
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 Preprint Series written by Universitetet i Oslo. Matematisk institutt and published by . This book was released on 1972 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geophysical Inverse Theory written by Robert L. Parker and published by Princeton University Press. This book was released on 1994-06-05 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology. Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.
