Inverse Theory And Applications In Geophysics

Author : Michael S. Zhdanov
Publisher : Elsevier
Page : 730 pages
File Size : 44,6 Mb
Release : 2015-07-15
Category : Science
ISBN : 9780444627124

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Inverse Theory and Applications in Geophysics by Michael S. Zhdanov Pdf

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.

Author : Mathias Richter
Publisher : Birkhäuser
Page : 248 pages
File Size : 43,7 Mb
Release : 2016-11-24
Category : Mathematics
ISBN : 9783319483849

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Inverse Problems by Mathias Richter Pdf

The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.

Author : William Menke
Publisher : Academic Press
Page : 272 pages
File Size : 49,9 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141284

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Geophysical Data Analysis: Discrete Inverse Theory by William Menke Pdf

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.

Author : Michael S Zhdanov
Publisher : Elsevier
Page : 635 pages
File Size : 53,5 Mb
Release : 2002-04-24
Category : Science
ISBN : 9780080532509

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Geophysical Inverse Theory and Regularization Problems by Michael S Zhdanov Pdf

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.

Author : Mathias Richter
Publisher : Springer Nature
Page : 281 pages
File Size : 54,5 Mb
Release : 2021-01-05
Category : Mathematics
ISBN : 9783030593179

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Inverse Problems by Mathias Richter Pdf

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.

Author : Max A. Meju
Publisher : SEG Books
Page : 305 pages
File Size : 46,7 Mb
Release : 1994
Category : Geophysics
ISBN : 9781560802570

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Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice by Max A. Meju Pdf

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.

Author : V. Dimri
Publisher : Elsevier
Page : 249 pages
File Size : 45,6 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483291376

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Deconvolution and Inverse Theory by V. Dimri Pdf

This is the first study to present simultaneously both deconvolution and inversion, two powerful tools of data analysis. Featured within this volume are various geophysical convolution models and a treatment of deconvolution for a time-varying signal. The single channel time-varying deconvolution is shown equivalent to the multichannel time-invariant deconvolution, thus a formalism and associated algorithms can handle both. Inverse theory as well as various inversion schemes are presented on the basis of a relationship between a small perturbation to the model and its effects on the observation. The information theory inversion scheme is discussed, and several types of norm of minimization presented. Additionally, concepts and results of inverse theory are applied to design a new deconvolution operator for estimating magnetization and density distribution, and the constraint of the Backus-Gilbert formalism of inverse theory is used to design a new prediction error filter for maximum entropy spectral estimates. Maximum likelihood, another high resolution method is also presented. This volume can be utilised as a graduate-level text for courses in Geophysics. Some chapters will be of use for graduate courses in Applied Mathematics, Applied Statistics, and Oceanography.

Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Elsevier
Page : 404 pages
File Size : 44,8 Mb
Release : 2018-10-16
Category : Science
ISBN : 9780128134238

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Parameter Estimation and Inverse Problems by Richard C. Aster,Brian Borchers,Clifford H. Thurber Pdf

Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner

Author : Mrinal K. Sen,Paul L. Stoffa
Publisher : Cambridge University Press
Page : 303 pages
File Size : 53,6 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9781107011908

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Global Optimization Methods in Geophysical Inversion by Mrinal K. Sen,Paul L. Stoffa Pdf

An up-to-date overview of global optimization methods used to formulate and interpret geophysical observations, for researchers, graduate students and professionals.

Author : Yanghua Wang
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 46,6 Mb
Release : 2016-09-15
Category : Science
ISBN : 9781119258049

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Seismic Inversion by Yanghua Wang Pdf

Seismic inversion aims to reconstruct a quantitative model of the Earth subsurface, by solving an inverse problem based on seismic measurements. There are at least three fundamental issues to be solved simultaneously: non-linearity, non-uniqueness, and instability. This book covers the basic theory and techniques used in seismic inversion, corresponding to these three issues, emphasising the physical interpretation of theoretical concepts and practical solutions. This book is written for master and doctoral students who need to understand the mathematical tools and the engineering aspects of the inverse problem needed to obtain geophysically meaningful solutions. Building on the basic theory of linear inverse problems, the methodologies of seismic inversion are explained in detail, including ray-impedance inversion and waveform tomography etc. The application methodologies are categorised into convolutional and wave-equation based groups. This systematic presentation simplifies the subject and enables an in-depth understanding of seismic inversion. This book also provides a practical guide to reservoir geophysicists who are attempting quantitative reservoir characterisation based on seismic data. Philosophically, the seismic inverse problem allows for a range of possible solutions, but the techniques described herein enable geophysicists to exclude models that cannot satisfy the available data. This book summarises the author’s extensive experience in both industry and academia and includes innovative techniques not previously published.

Author : Max A. Meju
Publisher : Unknown
Page : 316 pages
File Size : 53,8 Mb
Release : 1994
Category : Geophysics
ISBN : STANFORD:36105111318064

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Geophysical Data Analysis by Max A. Meju Pdf

Author : Gottfried Anger
Publisher : Wiley-VCH
Page : 336 pages
File Size : 53,6 Mb
Release : 1993-09
Category : Mathematics
ISBN : UOM:39015032213194

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Inverse Problems by Gottfried Anger Pdf

Most mathematical problems in science, technology, and medicine are inverse problems. Studying such problems is the only way of completely analyzing experimental results. Inverse problems may be considered among the pressing problems of current mathematical research.

Author : David Gubbins
Publisher : Cambridge University Press
Page : 128 pages
File Size : 49,9 Mb
Release : 2004-03-18
Category : Science
ISBN : 9781316582930

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Time Series Analysis and Inverse Theory for Geophysicists by David Gubbins Pdf

This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data. These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets. Solutions to the exercises are available on a website at http://publishing.cambridge.org/resources/0521819652

Author : William Menke
Publisher : Elsevier
Page : 289 pages
File Size : 54,8 Mb
Release : 1989-10-04
Category : Science
ISBN : 9780080507323

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Geophysical Data Analysis by William Menke Pdf

Please use extracts from reviews of first edition Key Features * Updated and thoroughly revised edition * additional material on geophysical/acoustic tomography * Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies

Author : Heinz W. Engl,Alfred Karl Louis,William Rundell
Publisher : Society for Industrial and Applied Mathematics (SIAM)
Page : 318 pages
File Size : 51,6 Mb
Release : 1997
Category : Geophysics
ISBN : UCSD:31822026085126

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Inverse Problems in Geophysical Applications by Heinz W. Engl,Alfred Karl Louis,William Rundell Pdf

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.