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Inverse Theory And Applications In Geophysics

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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.

Deconvolution and Inverse Theory

Deconvolution and Inverse Theory Book
Author : V. Dimri
Publisher : Elsevier
Release : 2013-10-22
ISBN : 1483291375
Language : En, Es, Fr & De

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Book Description :

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.

Inverse Problems

Inverse Problems Book
Author : Mathias Richter
Publisher : Springer Nature
Release : 2020
ISBN : 3030593177
Language : En, Es, Fr & De

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Book Description :

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.

Seismic Inversion

Seismic Inversion Book
Author : Yanghua Wang
Publisher : John Wiley & Sons
Release : 2016-09-15
ISBN : 1119258049
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.

Parameter Estimation and Inverse Problems

Parameter Estimation and Inverse Problems Book
Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Elsevier
Release : 2018-10-16
ISBN : 0128134232
Language : En, Es, Fr & De

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Book Description :

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

Integrated Imaging of the Earth

Integrated Imaging of the Earth Book
Author : Max Moorkamp,Peter G. Leli?vre,Amir Khan,Niklas Linde
Publisher : John Wiley & Sons
Release : 2016-05-02
ISBN : 1118929055
Language : En, Es, Fr & De

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Book Description :

Reliable and detailed information about the Earth’s subsurface is of crucial importance throughout the geosciences. Quantitative integration of all available geophysical and geological data helps to make Earth models more robust and reliable. The aim of this book is to summarize and synthesize the growing literature on combining various types of geophysical and other geoscientific data. The approaches that have been developed to date encompass joint inversion, cooperative inversion, and statistical post-inversion analysis methods, each with different benefits and assumptions. Starting with the foundations of inverse theory, this book systematically describes the mathematical and theoretical aspects of how to best integrate different geophysical datasets with geological prior understanding and other complimentary data. This foundational basis is followed by chapters that demonstrate the diverse range of applications for which integrated methods have been used to date. These range from imaging the hydrogeological properties of the near-surface to natural resource exploration and probing the composition of the lithosphere and the deep Earth. Each chapter is written by leading experts in the field, which makes this book the definitive reference on integrated imaging of the Earth. Highlights of this volume include: Complete coverage of the theoretical foundations of integrated imaging approaches from inverse theory to different coupling methods and quantitative evaluation of the resulting models Comprehensive overview of current applications of integrated imaging including hydrological investigations, natural resource exploration, and imaging the deep Earth Detailed case studies of integrated approaches providing valuable guidance for both experienced users and researchers new to joint inversion. This volume will be a valuable resource for graduate students, academics, industry practitioners, and researchers who are interested in using or developing integrated imaging approaches.

Geophysical Data Analysis

Geophysical Data Analysis Book
Author : William Menke
Publisher : Academic Press
Release : 2018-04-10
ISBN : 0128135565
Language : En, Es, Fr & De

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Book Description :

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

Theory and Practice of Geophysical Data Inversion

Theory and Practice of Geophysical Data Inversion Book
Author : Andreas Vogel
Publisher : Vieweg+Teubner Verlag
Release : 1992-01-01
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The contributions to this volume cover a wide spectrum of recent developments in geophysical data inversion, including basic mathematics and general theory, numerical methods, as well as computer implementation of algorithms. Most of the papers are motivated by problems arising from geophysical research and applications both on a global scale and with respect to local geophysical surveys, underlining the increasing importance of geophysical exploration methods in various fields, such as structural geology, prospecting for mineral and energy resources, hydro geology, geotechnology, environmental protection and archaeology. The first section of the book deals with basic mathematics and general theory underlying geophysical data inversion. Papers presented here are concerned with stabilization algorithms to solve ill-posed inverse problems, sensitivity of kernel function estimations to random data errors and reduction of errors in inverse modelling of response functions by linear constraints, numerical procedures for approximating the solution to boundary value problems, accuracy and stability of inverse ill-posed problems constituted by problems of moments, and fast Fourier transforms for solving potential field problems. The second section contains papers on gravity and magnetics, dealing with the solvability of the inverse gravimetric problem for sources represented by point masses and other elementary, solution of the inverse problem in cases of nonuniformly distributed data as obtained by palaeomagnetic studies, satellite observations, and surface projections of buried archaeological targets by inverse filtering of geomagnetic data.

Applications of Linear Inverse Theory in Modern Global Seismology

Applications of Linear Inverse Theory in Modern Global Seismology Book
Author : Lapo Boschi
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Applications of Linear Inverse Theory in Modern Global Seismology book written by Lapo Boschi, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Lithospheric Flexure

Lithospheric Flexure Book
Author : Dennis Lee Harry
Publisher : Unknown
Release : 1989
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Lithospheric Flexure book written by Dennis Lee Harry, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Acoustic and Elastic Wave Fields in Geophysics Part II

Acoustic and Elastic Wave Fields in Geophysics  Part II Book
Author : Alexander A. Kaufman,A.L. Levshin,K.L. Larner,Avital Kaufman
Publisher : Gulf Professional Publishing
Release : 2002-10-25
ISBN : 9780444506429
Language : En, Es, Fr & De

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Book Description :

This book is a continuation of 'Acoustic and Elastic Wave Fields in Geophysics, Part I' published in 2000. The second volume is dedicated to propagation of linear plane, spherical and cylindrical acoustic waves in different media. Chapter 1 is devoted to principles of geometric acoustic in plane wave approximation. The eikonal and transport equations are derived. Ray tracing and wavefront construction techniques are explained. Chapter 2 deals with dynamic properties of wave fields. The behavior of pressure and displacements amplitudes in zero approximation is analysed in two ways: using Poynting vector and solving the transport equation. This chapter contains several examples related to shadow zones and caustics. In Chapter 3 using the results of analysis of high-frequency wave kinematics and dynamics some fundamental aspects of Kirchhoff migration are described. Chapters 4 and 5 are devoted to propagation of plane waves in media with flat boundaries in the case of normal and oblique incidence. Special attention is paid to the case when an incident angle exceeds the critical angles. Formation of normal modes in the waveguide is discussed. Chapter 6 deals with a spherical wave reflection and refraction. The steepest descent method is introduced to describe the behavior of reflected, transmitted, head and evanescent waves. In Chapter 7 propagation of stationary and transient waves in a waveguide formed by a flat layer with low velocity are investigated. Normal modes and waves related to the branch points of integrands under consideration are studied. Dispersive properties of normal modes are discussed. Chapter 8 describes wave propagation inside cylinder in acoustic media. Several appendices are added to help the reader understand different aspects of mathematics used in the book.

Quantum Inversion Theory and Applications

Quantum Inversion Theory and Applications Book
Author : H.V.v. Geramb
Publisher : Springer
Release : 2018-05-29
ISBN : 3662139693
Language : En, Es, Fr & De

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Book Description :

This volume covers aspects of Schr|dinger equation inversion for the purposeof determining interaction potentials in particle, nuclear and atomic physics from experimental data. It includes reviews and reports on the latest developments in mathematics, supersymmetric quantum mechanics, inversion for fixed-l nucleon-nucleon potentials, inversion of fixed-E optical potentials and their generalizations. Also included are some topics on nonlinear differential equations relating to theSchr|dinger or other equations of particle, nuclear, atomic and molecular physics which can be solved by inverse scattering transformations. The material collected in this volume gives a clear picture of the status ofresearch in this rapidly growing field. The book addresses students and young scientists as well as researchers in theoretical physics and functional analysis.

Inverse Problems

Inverse Problems Book
Author : Gottfried Anger,Rudolf Gorenflo,Horst Jochmann,Helmut Moritz,Wigor Webers
Publisher : Wiley-VCH
Release : 1993-09
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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.

Lithosperic Flexure

Lithosperic Flexure Book
Author : Dennis Lee Harry
Publisher : Unknown
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Lithosperic Flexure book written by Dennis Lee Harry, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Foundations of Geophysical Electromagnetic Theory and Methods

Foundations of Geophysical Electromagnetic Theory and Methods Book
Author : Michael S. Zhdanov
Publisher : Elsevier
Release : 2017-10-27
ISBN : 0444638911
Language : En, Es, Fr & De

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Book Description :

Foundations of Geophysical Electromagnetic Theory and Methods, Second Edition, builds on the strength of the first edition to offer a systematic exposition of geophysical electromagnetic theory and methods. This new edition highlights progress made over the last decade, with a special focus on recent advances in marine and airborne electromagnetic methods. Also included are recent case histories on practical applications in tectonic studies, mineral exploration, environmental studies and off-shore hydrocarbon exploration. The book is ideal for geoscientists working in all areas of geophysics, including exploration geophysics and applied physics, as well as graduate students and researchers working in the field of electromagnetic theory and methods. Presents theoretical and methodological foundations of geophysical field theory Synthesizes fundamental theory and the most recent achievements of electromagnetic (EM) geophysical methods in the framework of a unified systematic exposition Offers a unique breadth and completeness in providing a general picture of the current state-of-the-art in EM geophysical technology Discusses practical aspects of EM exploration for mineral and energy resources

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 : 1107011906
Language : En, Es, Fr & De

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Book Description :

"Making inferences about systems in the Earth's subsurface from remotely-sensed, sparse measurements is a challenging task. Geophysical inversion aims to find models which explain geophysical observations - a model-based inversion method attempts to infer model parameters by iteratively fitting observations with theoretical predictions from trial models. Global optimization often enables the solution of non-linear models, employing a global search approach to find the absolute minimum of an objective function, so that predicted data best fits the observations. This new edition provides an up-to-date overview of the most popular global optimization methods, including a detailed description of the theoretical development underlying each method, and a thorough explanation of the design, implementation, and limitations of algorithms. A new chapter provides details of recently-developed methods, such as the neighborhood algorithm, and particle swarm optimization. An expanded chapter on uncertainty estimation includes a succinct description on how to use optimization methods for model space exploration to characterize uncertainty, and now discusses other new methods such as hybrid Monte Carlo and multi-chain MCMC methods. Other chapters include new examples ofapplications, 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. "--

The Probabilistic Formulation of the Inverse Theory with Application to Selected Seismological Problems

The Probabilistic Formulation of the Inverse Theory with Application to Selected Seismological Problems Book
Author : Wojciech Dębski
Publisher : Unknown
Release : 1997
ISBN : 9788385173632
Language : En, Es, Fr & De

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Book Description :

Download The Probabilistic Formulation of the Inverse Theory with Application to Selected Seismological Problems book written by Wojciech Dębski, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Gravity

Gravity Book
Author : Taher Zouaghi
Publisher : BoD – Books on Demand
Release : 2018-02-21
ISBN : 9535138235
Language : En, Es, Fr & De

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Book Description :

This book deals with different aspects of gravity that has proved its effectiveness throughout the world, hence their solicitation in recent years. Fundamental theories, applications, and tools have been presented, emphasizing the implementation of the gravity technique. Different research themes for diverse areas in the world are detailed here, highlighting new methods of studies that could be helpful for sophisticated and modern development over the next few years. Four main sections are presented: Gravity Interpretation Tools in Geoscience, Gravity in Geoscience Applications, Gravity in Industrial Technology, and Quantum Gravity. Theoretical and acquisition tools and adapted processing methods have been designed to take into account the initial data, and modeling results thus converge toward a better solution. This book, which makes a worthwhile contribution to the topic gravity, is specifically addressed to specialists, researchers, and industry professionals who shall find its content extremely useful for a better comprehension of the geological, spatial, and industrial aspects of gravity.

Geophysical Data Analysis

Geophysical Data Analysis Book
Author : William Menke
Publisher : Academic Press
Release : 2012
ISBN : 0123971608
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