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Inverse Theory And Applications In Geophysics

Author: Michael S. Zhdanov
Publisher: Elsevier
ISBN: 044462712X
Size: 42.23 MB
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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

Author: Michael S. Zhdanov
Publisher: Elsevier
ISBN: 9780080532509
Size: 63.56 MB
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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

Author: V. Dimri
Publisher: Elsevier
ISBN: 1483291375
Size: 44.63 MB
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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.

Geophysical Electromagnetic Theory And Methods

Author: Michael S. Zhdanov
Publisher: Elsevier
ISBN: 9780080931760
Size: 59.50 MB
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In this book the author presents the state-of-the-art electromagnetic (EM) theories and methods employed in EM geophysical exploration. The book brings together the fundamental theory of EM fields and the practical aspects of EM exploration for mineral and energy resources. This text is unique in its breadth and completeness in providing an overview of EM geophysical exploration technology. The book is divided into four parts covering the foundations of EM field theory and its applications, and emerging geophysical methods. Part I is an introduction to the field theory required for baseline understanding. Part II is an overview of all the basic elements of geophysical EM theory, from Maxwell's fundamental equations to modern methods of modeling the EM field in complex 3-D geoelectrical formations. Part III deals with the regularized solution of ill-posed inverse electromagnetic problems, the multidimensional migration and imaging of electromagnetic data, and general interpretation techniques. Part IV describes major geophysical electromagnetic methods—direct current (DC), induced polarization (IP), magnetotelluric (MT), and controlled-source electromagnetic (CSEM) methods—and covers different applications of EM methods in exploration geophysics, including minerals and HC exploration, environmental study, and crustal study. * Presents theoretical and methodological findings, as well as examples of applications of recently developed algorithms and software in solving practical problems * Describes the practical importance of electromagnetic data through enabling discussions on a construction of a closed technological cycle, processing, analysis and three-dimensional interpretation * Updates current findings in the field, especially with MT, magnetovariational and seismo-electrical methods and the practice of 3D interpretations

Acoustic And Elastic Wave Fields In Geophysics

Author: Alexander A. Kaufman
Publisher: Gulf Professional Publishing
ISBN: 9780444506429
Size: 68.89 MB
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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.

Principles Of Electromagnetic Methods In Surface Geophysics

Author: Alex A. Kaufman
Publisher: Newnes
ISBN: 0444538305
Size: 34.24 MB
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Principles of Electromagnetic Methods in Surface Geophysics contains information about the theory of electromagnetic fields in a conducting media. It describes the theoretical and physical principles of the main geophysical methods using electromagnetic fields, including frequency and transient soundings, electromagnetic profiling, and magnetotelluric soundings. Special attention is paid to models and signal processing methods used in modern exploration geophysics for groundwater, mineral and hydrocarbon exploration. Offers an integrated approach to the description of electromagnetic geophysical fields used for surface geophysical surveys Provides a clear introduction to the physical background of electromagnetic methods and their application Rounds off the treatment of the main geophysical methods: gravity, magnetic seismic, electric and electromagnetic methods

The Geoelectrical Methods In Geophysical Exploration

Author: Mikhail Semenovich Zhdanov
Publisher: Elsevier Science Limited
ISBN:
Size: 40.22 MB
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Hardbound. This volume deals with electrical methods as used in applied geophysics. There are 14 chapters. The first four chapters comprise a handbook of information needed in applied electrical geophysics. The next three chapters deal with three standard techniques: Direct Current (DC), Magnetotelluric (MT) and Controlled-Source Electromagnetic (EM) methods. Chapters 8 - 11 develop important aspects of the subject which are common to all three standard techniques. These common aspects include ambiguity and insensitivity, data acquisition, modeling and simulation, and interpretation. Chapters 12 and 13 cover experience with electrical methods in the solution of a wide variety of practical problems.

Principles Of The Magnetic Methods In Geophysics

Author: Alex A. Kaufman
Publisher: Elsevier
ISBN: 9780080931852
Size: 10.69 MB
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Magnetic methods are widely used in exploration, engineering, borehole and global geophysics, and the subjects of this book are the physical and mathematical principles of these methods regardless of the area of application. Beginning with Ampere's law, the force of interaction between currents is analyzed, and then the concept of the magnetic field is introduced and the fundamental features are discussed. Special attention is paid to measurements of relaxation processes, including topics as the spin echoes or refocusing. Also the special role of the magnetic method in the development of the plate tectonic theory is described. * covers all the physical and mathematical principles of magnetic methods regardless of the area of application. * presents thorough developments of magnetic methods.