Geophysical Inverse Theory And Regularization Problems

Geophysical Inverse Theory And Regularization Problems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Geophysical Inverse Theory And Regularization Problems book. This book definitely worth reading, it is an incredibly well-written.

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 : 48,5 Mb
Release : 2002-04-24
Category : Science
ISBN : 9780080532509

Get Book

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.

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 : 51,7 Mb
Release : 2015-07-15
Category : Science
ISBN : 9780444627124

Get Book

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.

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Springer Nature
Page : 281 pages
File Size : 44,5 Mb
Release : 2021-01-05
Category : Mathematics
ISBN : 9783030593179

Get Book

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.

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 : 55,9 Mb
Release : 2018-10-16
Category : Science
ISBN : 9780128134238

Get Book

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

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 : 53,5 Mb
Release : 2018-04-01
Category : Science
ISBN : 9781618965264

Get Book

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.

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 : 52,9 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9781441984746

Get Book

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.

Geophysical Inversion

J. Bee Bednar
Geophysical Inversion Book PDF

Author : J. Bee Bednar
Publisher : SIAM
Page : 472 pages
File Size : 48,9 Mb
Release : 1992-01-01
Category : Science
ISBN : 0898712734

Get Book

Geophysical Inversion by J. Bee Bednar Pdf

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.

Geophysical Inverse Theory

Robert L. Parker
Geophysical Inverse Theory Book PDF

Author : Robert L. Parker
Publisher : Princeton University Press
Page : 400 pages
File Size : 53,7 Mb
Release : 2019-12-31
Category : Science
ISBN : 9780691206837

Get Book

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.

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 : Academic Press
Page : 377 pages
File Size : 41,8 Mb
Release : 2013
Category : Computers
ISBN : 9780123850485

Get Book

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

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.

Handbook of Mathematical Methods in Imaging

Otmar Scherzer
Handbook of Mathematical Methods in Imaging Book PDF

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 50,7 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

Get Book

Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Computational Methods for Inverse Problems

Curtis R. Vogel
Computational Methods for Inverse Problems Book PDF

Author : Curtis R. Vogel
Publisher : SIAM
Page : 183 pages
File Size : 44,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780898717570

Get Book

Computational Methods for Inverse Problems by Curtis R. Vogel Pdf

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

Introduction to Geostatistics

P. K. Kitanidis
Introduction to Geostatistics Book PDF

Author : P. K. Kitanidis
Publisher : Cambridge University Press
Page : 276 pages
File Size : 47,7 Mb
Release : 1997-05-13
Category : Science
ISBN : 0521587476

Get Book

Introduction to Geostatistics by P. K. Kitanidis Pdf

Engineers and applied geophysicists routinely encounter interpolation and estimation problems when analysing data from field observations. Introduction to Geostatistics presents practical techniques for the estimation of spatial functions from sparse data. The author's unique approach is a synthesis of classic and geostatistical methods with a focus on the most practical linear minimum-variance estimation methods, and includes suggestions on how to test and extend the applicability of such methods. The author includes many useful methods (often not covered in other geostatistics books) such as estimating variogram parameters, evaluating the need for a variable mean, parameter estimation and model testing in complex cases (e.g. anisotropy, variable mean, and multiple variables), and using information from deterministic mathematical models. Well illustrated with exercises and worked examples taken from hydrogeology, Introduction to Geostatistics assumes no background in statistics and is suitable for graduate-level courses in earth sciences, hydrology, and environmental engineering, and also for self-study.

Inverse Problems: Tikhonov Theory And Algorithms

Ito Kazufumi,Jin Bangti
Inverse Problems Tikhonov Theory And Algorithms Book PDF

Author : Ito Kazufumi,Jin Bangti
Publisher : World Scientific
Page : 332 pages
File Size : 49,9 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9789814596213

Get Book

Inverse Problems: Tikhonov Theory And Algorithms by Ito Kazufumi,Jin Bangti Pdf

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

Discrete Inverse Problems

Per Christian Hansen
Discrete Inverse Problems Book PDF

Author : Per Christian Hansen
Publisher : SIAM
Page : 220 pages
File Size : 54,8 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898718836

Get Book

Discrete Inverse Problems by Per Christian Hansen Pdf

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.

Inverse Problems

Gottfried Anger
Inverse Problems Book PDF

Author : Gottfried Anger
Publisher : Wiley-VCH
Page : 336 pages
File Size : 52,9 Mb
Release : 1993-09
Category : Mathematics
ISBN : UOM:39015032213194

Get Book

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.