Geophysical Inverse Theory

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Geophysical Inverse Theory

Robert L. Parker
Geophysical Inverse Theory Book PDF

Author : Robert L. Parker
Publisher : Princeton University Press
Page : 400 pages
File Size : 54,6 Mb
Release : 2019-12-31
Category : Science
ISBN : 9780691206837

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Geophysical Inverse Theory by Robert L. Parker Pdf

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.

Inverse Theory and Applications in Geophysics

Michael S. Zhdanov
Inverse Theory and Applications in Geophysics Book PDF

Author : Michael S. Zhdanov
Publisher : Elsevier
Page : 730 pages
File Size : 53,9 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.

Geophysical Data Analysis: Discrete Inverse Theory

William Menke
Geophysical Data Analysis Discrete Inverse Theory Book PDF

Author : William Menke
Publisher : Academic Press
Page : 273 pages
File Size : 49,8 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.

Geophysical Inverse Theory and Regularization Problems

Michael S Zhdanov
Geophysical Inverse Theory and Regularization Problems Book PDF

Author : Michael S Zhdanov
Publisher : Elsevier
Page : 635 pages
File Size : 42,7 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.

Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice

Max A. Meju
Geophysical Data Analysis Understanding Inverse Problem Theory and Practice Book PDF

Author : Max A. Meju
Publisher : SEG Books
Page : 305 pages
File Size : 55,5 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.

Global Optimization Methods in Geophysical Inversion

Mrinal K. Sen,Paul L. Stoffa
Global Optimization Methods in Geophysical Inversion Book PDF

Author : Mrinal K. Sen,Paul L. Stoffa
Publisher : Cambridge University Press
Page : 303 pages
File Size : 49,6 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.

Parameter Estimation and Inverse Problems

Richard C. Aster,Brian Borchers,Clifford H. Thurber
Parameter Estimation and Inverse Problems Book PDF

Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Elsevier
Page : 404 pages
File Size : 50,7 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

Time Series Analysis and Inverse Theory for Geophysicists

David Gubbins
Time Series Analysis and Inverse Theory for Geophysicists Book PDF

Author : David Gubbins
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,9 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

Geophysical Inversion Theory and Global Optimization Methods

Caiyun Liu,Jie Xiong
Geophysical Inversion Theory and Global Optimization Methods Book PDF

Author : Caiyun Liu,Jie Xiong
Publisher : Scientific Research Publishing, Inc. USA
Page : 200 pages
File Size : 52,5 Mb
Release : 2018-04-01
Category : Science
ISBN : 9781618965264

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Geophysical Inversion Theory and Global Optimization Methods by Caiyun Liu,Jie Xiong Pdf

Geophysical inversion is an ill-posed problem. Classical local search method for inversion is depend on initial guess and easy to be trapped in local optimum. The global optimization is a group of novel methods to deal with the problems mentioned above. The book introduces the geophysical inversion theory, including the classical solving approaches firstly. Then, it introduces several typical global inversion approaches including particle swarm optimization (PSO), differential evolution (DE), and multiobjective optimization methods, as well as some examples to inverse the geophysical data, such as gravity, MT sounding, well logging, self-potential, seismic data, using these global optimization approaches.

Deconvolution and Inverse Theory

V. Dimri
Deconvolution and Inverse Theory Book PDF

Author : V. Dimri
Publisher : Elsevier
Page : 249 pages
File Size : 54,7 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.

Potential Theory in Applied Geophysics

Kalyan Kumar Roy
Potential Theory in Applied Geophysics Book PDF

Author : Kalyan Kumar Roy
Publisher : Springer Science & Business Media
Page : 661 pages
File Size : 52,9 Mb
Release : 2007-11-15
Category : Science
ISBN : 9783540723349

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Potential Theory in Applied Geophysics by Kalyan Kumar Roy Pdf

This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.

Seismic Inversion

Gerard T. Schuster
Seismic Inversion Book PDF

Author : Gerard T. Schuster
Publisher : SEG Books
Page : 377 pages
File Size : 50,8 Mb
Release : 2017-07-01
Category : Science
ISBN : 9781560803416

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Seismic Inversion by Gerard T. Schuster Pdf

This book describes the theory and practice of inverting seismic data for the subsurface rock properties of the earth. The primary application is for inverting reflection and/or transmission data from engineering or exploration surveys, but the methods described also can be used for earthquake studies. Seismic Inversion will be of benefit to scientists and advanced students in engineering, earth sciences, and physics. It is desirable that the reader has some familiarity with certain aspects of numerical computation, such as finite-difference solutions to partial differential equations, numerical linear algebra, and the basic physics of wave propagation. For those not familiar with the terminology and methods of seismic exploration, a brief introduction is provided. To truly understand the nuances of seismic inversion, we have to actively practice what we preach (or teach). Therefore, computational labs are provided for most of the chapters, and some field data labs are given as well.

Geophysical Data Analysis

William Menke
Geophysical Data Analysis Book PDF

Author : William Menke
Publisher : Academic Press
Page : 352 pages
File Size : 52,6 Mb
Release : 2018-04-10
Category : Science
ISBN : 9780128135563

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Geophysical Data Analysis by William Menke Pdf

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

Wavefield Inversion

Armand Wirgin
Wavefield Inversion Book PDF

Author : Armand Wirgin
Publisher : Springer
Page : 312 pages
File Size : 42,7 Mb
Release : 2014-05-04
Category : Science
ISBN : 9783709124864

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Wavefield Inversion by Armand Wirgin Pdf

This book provides an up-to-date presentation of a broad range of contemporary problems in inverse scattering involving acoustic, elastic and electromagnetic waves. Descriptions will be given of traditional (but still in use and subject to on-going improvements) and more recent methods for identifying either: a) the homogenized material parameters of (spatially) unbounded or bounded heterogeneous media, or b) the detailed composition (spatial distribution of the material parameters) of unbounded or bounded heterogeneous media, or c) the location, shape, orientation and material characteristics of an object embedded in a wellcharacterized homogeneous, homogenized or heterogeneous unbounded or bounded medium, by inversion of reflected, transmitted or scattered spatiotemporal recorded waveforms resulting from the propagation of probe radiation within the medium.

An Introduction to the Mathematical Theory of Inverse Problems

Andreas Kirsch
An Introduction to the Mathematical Theory of Inverse Problems Book PDF

Author : Andreas Kirsch
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 46,9 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9781441984746

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An Introduction to the Mathematical Theory of Inverse Problems by Andreas Kirsch Pdf

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.