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The Inversion Theory
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Book Synopsis Inversion Theory and Conformal Mapping by : David E. Blair
Download or read book Inversion Theory and Conformal Mapping written by David E. Blair and published by American Mathematical Soc.. This book was released on 2000-08-17 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.
Book Synopsis Inverse Theory and Applications in Geophysics by : Michael S. Zhdanov
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
Book Synopsis Geophysical Data Analysis: Discrete Inverse Theory by : William Menke
Download or read book Geophysical Data Analysis: Discrete Inverse Theory written by William Menke and published by Academic Press. This book was released on 2012-12-02 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geophysical Inverse Theory by : Robert L. Parker
Download or read book Geophysical Inverse Theory written by Robert L. Parker and published by Princeton University Press. This book was released on 2019-12-31 with total page 400 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.
Book Synopsis Inverse Problem Theory and Methods for Model Parameter Estimation by : Albert Tarantola
Download or read book Inverse Problem Theory and Methods for Model Parameter Estimation written by Albert Tarantola and published by SIAM. This book was released on 2005-01-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Seismic Inversion by : Gerard T. Schuster
Download or read book Seismic Inversion written by Gerard T. Schuster and published by SEG Books. This book was released on 2017-07-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to the Mathematical Theory of Inverse Problems by : Andreas Kirsch
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Science & Business Media. This book was released on 2011-03-24 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Seismic Inversion Methods by : Brian H. Russell
Download or read book Introduction to Seismic Inversion Methods written by Brian H. Russell and published by SEG Books. This book was released on 1988 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the current techniques used in the inversion of seismic data is provided. Inversion is defined as mapping the physical structure and properties of the subsurface of the earth using measurements made on the surface, creating a model of the earth using seismic data as input.
Book Synopsis Geophysical Inversion Theory and Global Optimization Methods by : Caiyun Liu
Download or read book Geophysical Inversion Theory and Global Optimization Methods written by Caiyun Liu and published by Scientific Research Publishing, Inc. USA. This book was released on 2018-04-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Great Mental Models, Volume 1 by : Shane Parrish
Download or read book The Great Mental Models, Volume 1 written by Shane Parrish and published by Penguin. This book was released on 2024-10-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the essential thinking tools you’ve been missing with The Great Mental Models series by Shane Parrish, New York Times bestselling author and the mind behind the acclaimed Farnam Street blog and “The Knowledge Project” podcast. This first book in the series is your guide to learning the crucial thinking tools nobody ever taught you. Time and time again, great thinkers such as Charlie Munger and Warren Buffett have credited their success to mental models–representations of how something works that can scale onto other fields. Mastering a small number of mental models enables you to rapidly grasp new information, identify patterns others miss, and avoid the common mistakes that hold people back. The Great Mental Models: Volume 1, General Thinking Concepts shows you how making a few tiny changes in the way you think can deliver big results. Drawing on examples from history, business, art, and science, this book details nine of the most versatile, all-purpose mental models you can use right away to improve your decision making and productivity. This book will teach you how to: Avoid blind spots when looking at problems. Find non-obvious solutions. Anticipate and achieve desired outcomes. Play to your strengths, avoid your weaknesses, … and more. The Great Mental Models series demystifies once elusive concepts and illuminates rich knowledge that traditional education overlooks. This series is the most comprehensive and accessible guide on using mental models to better understand our world, solve problems, and gain an advantage.
Download or read book Seismic Inversion written by Yanghua Wang and published by John Wiley & Sons. This book was released on 2016-09-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Seismic Imaging and Inversion: Volume 1 by : Robert H. Stolt
Download or read book Seismic Imaging and Inversion: Volume 1 written by Robert H. Stolt and published by Cambridge University Press. This book was released on 2012-02-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the use of inverse scattering theory in seismic imaging for seismic processing practitioners and theoretical geophysicists.
Book Synopsis Parameter Estimation and Inverse Problems by : Richard C. Aster
Download or read book Parameter Estimation and Inverse Problems written by Richard C. Aster and published by Elsevier. This book was released on 2018-10-16 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Inverse Methods for Atmospheric Sounding by : Clive D. Rodgers
Download or read book Inverse Methods for Atmospheric Sounding written by Clive D. Rodgers and published by World Scientific. This book was released on 2000 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Inversion Factor by : Linda Bernardi
Download or read book The Inversion Factor written by Linda Bernardi and published by MIT Press. This book was released on 2018-09-11 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why companies need to move away from a “product first” orientation to pursuing innovation based on customer need. In the past, companies found success with a product-first orientation; they made a thing that did a thing. The Inversion Factor explains why the companies of today and tomorrow will have to abandon the product-first orientation. Rather than asking “How do the products we make meet customer needs?” companies should ask “How can technology help us reimagine and fill a need?” Zipcar, for example, instead of developing another vehicle for moving people from point A to point B, reimagined how people interacted with vehicles. Zipcar inverted the traditional car company mission. The authors explain how the introduction of “smart” objects connected by the Internet of Things signals fundamental changes for business. The IoT, where real and digital coexist, is powering new ways to meet human needs. Companies that know this include giants like Amazon, Airbnb, Uber, Google, Tesla, and Apple, as well as less famous companies like Tile, Visenti, and Augury. The Inversion Factor offers a roadmap for businesses that want to follow in their footsteps. The authors chart the evolution of three IoTs—the Internet of Things (devices connected to the Internet), the Intelligence of Things (devices that host software applications), and the Innovation of Things (devices that become experiences). Finally, they offer a blueprint for businesses making the transition to inversion and interviews with leaders of major companies and game-changing startups.
Book Synopsis Gravity Inversion and Integration by : Lars E. Sjöberg
Download or read book Gravity Inversion and Integration written by Lars E. Sjöberg and published by Springer. This book was released on 2017-04-19 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains theory and applications of gravity both for physical geodesy and geophysics. It identifies classical and modern topics for studying the Earth. Worked-out examples illustrate basic but important concepts of the Earth’s gravity field. In addition, coverage details the Geodetic Reference System 1980, a versatile tool in most applications of gravity data. The authors first introduce the necessary mathematics. They then review classic physical geodesy, including its integral formulas, height systems and their determinations. The next chapter presents modern physical geodesy starting with the original concepts of M.S. Molodensky. A major part of this chapter is a variety of modifying Stokes’ formula for geoid computation by combining terrestrial gravity data and an Earth Gravitational Model. Coverage continues with a discussion that compares today’s methods for modifying Stokes’ formulas for geoid and quasigeoid determination, a description of several modern tools in physical geodesy, and a review of methods for gravity inversion as well as analyses for temporal changes of the gravity field. This book aims to broaden the view of scientists and students in geodesy and geophysics. With a focus on theory, it provides basic and some in-depth knowledge about the field from a geodesist’s perspective. /div
Book Synopsis Sexual Inversion by : Havelock Ellis
Download or read book Sexual Inversion written by Havelock Ellis and published by . This book was released on 1901 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
