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Geophysical Data Analysis Discrete Inverse Theory

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Geophysical Data Analysis Discrete Inverse Theory

Geophysical Data Analysis  Discrete Inverse Theory Book
Author : William Menke
Publisher : Academic Press
Release : 2012-12-02
ISBN : 0323141285
Language : En, Es, Fr & De

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Book Description :

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 Data Analysis

Geophysical Data Analysis Book
Author : William Menke
Publisher : Elsevier
Release : 1989-10-04
ISBN : 0080507328
Language : En, Es, Fr & De

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Book Description :

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

Time Series Analysis and Inverse Theory for Geophysicists

Time Series Analysis and Inverse Theory for Geophysicists Book
Author : David Gubbins
Publisher : Cambridge University Press
Release : 2004-03-18
ISBN : 1316582930
Language : En, Es, Fr & De

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Book Description :

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 Data Analysis Understanding Inverse Problem Theory and Practice

Geophysical Data Analysis  Understanding Inverse Problem Theory and Practice Book
Author : Max A. Meju
Publisher : SEG Books
Release : 1994
ISBN : 156080257X
Language : En, Es, Fr & De

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Book Description :

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.

Inverse Problem Theory and Methods for Model Parameter Estimation

Inverse Problem Theory and Methods for Model Parameter Estimation Book
Author : Albert Tarantola
Publisher : SIAM
Release : 2005-01-01
ISBN : 9780898717921
Language : En, Es, Fr & De

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Book Description :

While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.

Inverse Theory and Applications in Geophysics

Inverse Theory and Applications in Geophysics Book
Author : Michael S. Zhdanov
Publisher : Elsevier
Release : 2015-07-15
ISBN : 044462712X
Language : En, Es, Fr & De

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Book Description :

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 Inverse Theory and Regularization Problems

Geophysical Inverse Theory and Regularization Problems Book
Author : Michael S. Zhdanov
Publisher : Elsevier
Release : 2002-04-24
ISBN : 9780080532509
Language : En, Es, Fr & De

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Book Description :

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 Inversion

Geophysical Inversion Book
Author : J. Bee Bednar
Publisher : SIAM
Release : 1992-01-01
ISBN : 9780898712735
Language : En, Es, Fr & De

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Book Description :

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.

Global Optimization Methods in Geophysical Inversion

Global Optimization Methods in Geophysical Inversion Book
Author : Mrinal K. Sen,Paul L. Stoffa
Publisher : Cambridge University Press
Release : 2013-02-21
ISBN : 1139619519
Language : En, Es, Fr & De

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Book Description :

Providing an up-to-date overview of the most popular global optimization methods used in interpreting geophysical observations, this new edition includes a detailed description of the theoretical development underlying each method and a thorough explanation of the design, implementation and limitations of algorithms. New and expanded chapters provide details of recently developed methods, such as the neighborhood algorithm, particle swarm optimization, hybrid Monte Carlo and multi-chain MCMC methods. Other chapters include new examples of applications, from uncertainty in climate modeling to whole earth studies. Several different examples of geophysical inversion, including joint inversion of disparate geophysical datasets, are provided to help readers design algorithms for their own applications. This is an authoritative and valuable text for researchers and graduate students in geophysics, inverse theory and exploration geoscience, and an important resource for professionals working in engineering and petroleum exploration.

Parameter Estimation and Inverse Problems

Parameter Estimation and Inverse Problems Book
Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Academic Press
Release : 2013
ISBN : 0123850487
Language : En, Es, Fr & De

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Book Description :

Preface -- 1. Introduction -- 2. Linear Regression -- 3. Discretizing Continuous Inverse Problems -- 4. Rank Deficiency and Ill-Conditioning -- 5. Tikhonov Regularization -- 6. Iterative Methods -- 7. Other Regularization Techniques -- 8. Fourier Techniques -- 9. Nonlinear Regression -- 10. Nonlinear Inverse Problems -- 11. Bayesian Methods -- Appendix A: Review of Linear Algebra -- Appendix B: Review of Probability and Statistics -- Appendix C: Glossary of Notation -- Bibliography -- IndexLinear Regression -- Discretizing Continuous Inverse Problems -- Rank Deficiency and Ill-Conditioning -- Tikhonov Regularization -- Iterative Methods -- Other Regularization Techniques -- Fourier Techniques -- Nonlinear Regression -- Nonlinear Inverse Problems -- Bayesian Methods.

Inverse Methods for Atmospheric Sounding

Inverse Methods for Atmospheric Sounding Book
Author : Clive D. Rodgers
Publisher : World Scientific
Release : 2000
ISBN : 981022740X
Language : En, Es, Fr & De

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Book Description :

Annotation Rodgers (U. of Oxford) provides graduate students and other researchers a background to the inverse problem and its solution, with applications relating to atmospheric measurements. He introduces the stages in the reverse order than the usual approach in order to develop the learner's intuition about the nature of the inverse problem. Annotation copyrighted by Book News, Inc., Portland, OR.

Discrete Inverse Problems

Discrete Inverse Problems Book
Author : Per Christian Hansen
Publisher : SIAM
Release : 2010
ISBN : 089871883X
Language : En, Es, Fr & De

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Book Description :

This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Geophysical Inverse Theory

Geophysical Inverse Theory Book
Author : Robert L. Parker
Publisher : Princeton University Press
Release : 2019-12-31
ISBN : 069120683X
Language : En, Es, Fr & De

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Book Description :

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.

Information Based Inversion and Processing with Applications

Information Based Inversion and Processing with Applications Book
Author : T.J. Ulrych,M.D. Sacchi
Publisher : Elsevier
Release : 2005-12-16
ISBN : 9780080461342
Language : En, Es, Fr & De

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Book Description :

Information-Based Inversion and Processing with Applications examines different classical and modern aspects of geophysical data processing and inversion with emphasis on the processing of seismic records in applied seismology. Chapter 1 introduces basic concepts including: probability theory (expectation operator and ensemble statistics), elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection to seismic data analysis problems. Chapter 3 introduces concepts of Information theory and contains a synopsis of those topics that are used throughout the book. Examples are entropy, conditional entropy, Burg's maximum entropy spectral estimator, and mutual information. Chapter 4 provides a description of inverse problems first from a deterministic point of view, then from a probabilistic one. Chapter 5 deals with methods to improve the signal-to-noise ratio of seismic records. Concepts from previous chapters are put in practice for designing prediction error filters for noise attenuation and high-resolution Radon operators. Chapter 6 deals with the topic of deconvolution and the inversion of acoustic impedance. The first part discusses band-limited extrapolation assuming a known wavelet and considers the issue of wavelet estimation. The second part deals with sparse deconvolution using various 'entropy' type norms. Finally, Chapter 7 introduces recent topics of interest to the authors. The emphasis of this book is on applied seismology but researchers in the area of global seismology, and geophysical signal processing and inversion will find material that is relevant to the ubiquitous problem of estimating complex models from a limited number of noisy observations. Non-conventional approaches to data processing and inversion are presented Important problems in the area of seismic resolution enhancement are discussed Contains research material that could inspire graduate students and their supervisors to undertake new research directions in applied seismology and geophysical signal processing

Seismic Inversion

Seismic Inversion Book
Author : Yanghua Wang
Publisher : John Wiley & Sons
Release : 2016-12-14
ISBN : 1119258022
Language : En, Es, Fr & De

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Book Description :

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.

Computational Methods in Geophysical Electromagnetics

Computational Methods in Geophysical Electromagnetics Book
Author : Eldad Haber
Publisher : SIAM
Release : 2014-12-11
ISBN : 1611973791
Language : En, Es, Fr & De

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Book Description :

This monograph provides a framework for students and practitioners who are working on the solution of electromagnetic imaging in geophysics. Bridging the gap between theory and practical applied material (for example, inverse and forward problems), it provides a simple explanation of finite volume discretization, basic concepts in solving inverse problems through optimization, a summary of applied electromagnetics methods, and MATLAB??code for efficient computation.

Geophysical Data Analysis Discrete Inverse Theory

Geophysical Data Analysis  Discrete Inverse Theory Book
Author : William Menke
Publisher : Academic Press
Release : 2012-06-21
ISBN : 0123971608
Language : En, Es, Fr & De

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Book Description :

"The treatment of inverse theory in this book is divided into four parts. Chapters 1 and 2 provide a general background, explaining what inverse problems are and what constitutes their solution as well as reviewing some of the basic concepts from linear algebra and probability theory that will be applied throughout the text. Chapters 3-7 discuss the solution of the canonical inverse problem: the linear problem with Gaussian statistics. This is the best understood of all inverse problems; and it is here that the fundamental notions of uncertainty, uniqueness, and resolution can be most clearly developed. Chapters 8-11 extend the discussion to problems that are non-Gaussian, nonlinear and continuous. Chapters 12-13 provide examples of the use of inverse theory and a discussion of the steps that must be taken to solve inverse problems on a computer"--

Environmental Data Analysis with MatLab

Environmental Data Analysis with MatLab Book
Author : William Menke,Joshua Menke
Publisher : Elsevier
Release : 2011-09-02
ISBN : 0123918863
Language : En, Es, Fr & De

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Book Description :

"Environmental Data Analysis with MatLab" is for students and researchers working to analyze real data sets in the environmental sciences. One only has to consider the global warming debate to realize how critically important it is to be able to derive clear conclusions from often-noisy data drawn from a broad range of sources. This book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge with carefully chosen, realistic scenarios. MatLab, a commercial data processing environment, is used in these scenarios; significant content is devoted to teaching how it can be effectively used in an environmental data analysis setting. The book, though written in a self-contained way, is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial. It is well written and outlines a clear learning path for researchers and students. It uses real world environmental examples and case studies. It has MatLab software for application in a readily-available software environment. Homework problems help user follow up upon case studies with homework that expands them.

Geophysical Signal Analysis

Geophysical Signal Analysis Book
Author : Enders A. Robinson,Sven Treitel
Publisher : SEG Books
Release : 2000
ISBN : 1560801042
Language : En, Es, Fr & De

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Book Description :

Addresses the construction, analysis, and interpretation of mathematical and statistical models. The practical use of the concepts and techniques developed is illustrated by numerous applications. The chosen examples will interest many readers, including those engaged in digital signal analysis in disciplines other than geophysics.

Computational Methods for Inverse Problems

Computational Methods for Inverse Problems Book
Author : Curtis R. Vogel
Publisher : SIAM
Release : 2002
ISBN : 0898717574
Language : En, Es, Fr & De

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Book Description :

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.