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Inverse Theory and Applications in Geophysics - 2nd Edition

Subject ISBN Author Publisher Number of Pages Title Year Price
Earth and Planetary Sciences 9780444626745 Michael Zhdanov Elsevier 730 Inverse Theory and Applications in Geophysics - 2nd Edition 2015 $ 299.95
Author: Michael Zhdanov
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. Its 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 worlds foremost experts, this work is widely recognized as the ultimate researchers reference on geophysical inverse theory and its practical scientific applications.
Table of Content: Dedication Preface to the Second Edition Preface Part I: Introduction to Inversion Theory Chapter 1: Forward and Inverse Problems in Science and Engineering Abstract 1.1 Formulation of Forward and Inverse Problems for Different Physical Fields 1.2 Existence and Uniqueness of the Inverse Problem Solutions 1.3 Instability of the Inverse Problem Solution Chapter 2: Ill-Posed Problems and the Methods of Their Solution Abstract 2.1 Sensitivity and Resolution of Geophysical Methods 2.2 Formulation of Well-Posed and Ill-Posed Problems 2.3 Foundations of Regularization Methods of Inverse Problem Solution 2.4 Family of Stabilizing Functionals 2.5 Definition of the Regularization Parameter Part II: Methods of the Solution of Inverse Problems Chapter 3: Linear Discrete Inverse Problems Abstract 3.1 Linear Least-Squares Inversion 3.2 Solution of the Purely Underdetermined Problem 3.3 Weighted Least-Squares Method 3.4 Applying the Principles of Probability Theory to a Linear Inverse Problem 3.5 Regularization Methods 3.6 The Backus-Gilbert Method Chapter 4: Iterative Solutions of the Linear Inverse Problem Abstract 4.1 Linear Operator Equations and Their Solution by Iterative Methods 4.2 A Generalized Minimal Residual Method 4.3 The Regularization Method in a Linear Inverse Problem Solution Chapter 5: Nonlinear Inversion Technique Abstract 5.1 Gradient-Type Methods 5.2 Regularized Gradient-Type Methods in the Solution of Nonlinear Inverse Problems 5.3 Regularized Solution of a Nonlinear Discrete Inverse Problem 5.4 Conjugate Gradient Re-Weighted Optimization Chapter 6: Multinary Inversion Abstract 6.1 Level Set Method 6.2 Multinary Inversion Chapter 7: Resolution Analysis of Regularized Geophysical Inversion Abstract 7.1 Resolution of a Linear Inverse Problem 7.2 Resolution Density 7.3 Resolution of a Nonlinear Inverse Problem 7.4 Application of the SLDM for Resolution Density Calculation Chapter 8: Monte Carlo Methods Abstract 8.1 Random Search Methods 8.2 Simulated Annealing 8.3 Genetic Algorithm Chapter 9: Generalized Joint Inversion of Multimodal Data Abstract 9.1 Joint Inversion Based on Functional Relationships Between Different Model Parameters 9.2 The Method of Cross-Gradients 9.3 Joint Inversion Based on Gramian Constraints Part III: Geopotential Field Inversion Chapter 10: Integral Representations of 2-D Gravity and Magnetic Fields Abstract 10.1 Basic Equations for Gravity and Magnetic Fields 10.2 Integral Representations of Potential Fields Based on the Theory of Functions of a Complex Variable 10.3 Gradient Methods of 2-D Gravity Field Inversion 10.4 Migration of 2-D Gravity Field 10.5 Gradient Methods of 2-D Magnetic Anomaly Inversion Chapter 11: Migration of 3-D Gravity, Gravity Tensor, and Total Magnetic Intensity Data Abstract 11.1 Gravity Gradiometry Data 11.2 Migration of 3-D Gravity and Gravity Gradiometry Data 11.3 Fast Density Imaging Based on Migration 11.4 Migration of Total Magnetic Intensity Data Chapter 12: Numerical Methods in Forward and Inverse Modeling of Geopotential Fields Abstract 12.1 Numerical Methods in Forward and Inverse Modeling 12.2 Regularized Inversion of Gravity and Gradiometry Data Part IV: Electromagnetic Inversion Chapter 13: Foundations of Electromagnetic Theory Abstract 13.1 Electromagnetic Field Equations 13.2 Electromagnetic Energy Flow 13.3 Uniqueness of the Solution of Electromagnetic Field Equations 13.4 Electromagnetic Green’s Tensors Chapter 14: Integral Representations in Electromagnetic Forward Modeling Abstract 14.1 IE Method 14.2 Family of Linear and Nonlinear Integral Approximations of the EM Field 14.3 Linear and Nonlinear Approximations of Higher Orders 14.4 Integral Representations in Numerical Dressing Chapter 15: Integral Representations in Electromagnetic Inversion Abstract 15.1 Linear Inversion Methods 15.2 Nonlinear Inversion 15.3 Quasi-Linear Inversion 15.4 Quasi-Analytical Inversion Chapter 16: Electromagnetic Migration Imaging Abstract 16.1 Electromagnetic Migration in the Frequency Domain 16.2 Electromagnetic Migration in the Time Domain Chapter 17: Differential Methods in Electromagnetic Modeling and Inversion Abstract 17.1 Electromagnetic Modeling as a Boundary-Value Problem 17.2 Finite Difference Approximation of the Boundary-Value Problem 17.3 Finite Element Solution of Boundary-Value Problems 17.4 Inversion Based on Differential Methods Part V: Seismic Inversion Chapter 18: Wavefield Equations Abstract 18.1 Basic Equations of Elastic Waves 18.2 Green’s Functions for Wavefield Equations 18.3 Kirchhoff Integral Formula and Its Analogs 18.4 Uniqueness of the Solution of the Wavefield Equations Chapter 19: Integral Representations in Wavefield Theory Abstract 19.1 Integral Equation Method in Acoustic Wavefield Analysis 19.2 Integral Approximations of the Acoustic Wavefield 19.3 Method of Integral Equations in Vector Wavefield Analysis 19.4 Integral Approximations of the Vector Wavefield Chapter 20: Integral Representations in Full Waveform Inversion Abstract 20.1 Linear Inversion Methods 20.2 Quasi-Linear Inversion 20.3 Nonlinear Inversion 20.4 Principles of Wavefield Migration 20.5 Full-Waveform Inversion of Elastic Field Appendix A: Functional Spaces of Geophysical Models and Data A.1 Euclidean Space A.2 Metric Space A.3 Linear Vector Spaces A.4 Hilbert Spaces A.5 Complex Euclidean and Hilbert Spaces A.6 Examples of Linear Vector Spaces A.7 Gramian Spaces and Their Properties Appendix B: Operators in the Spaces of Models and Data B.1 Operators in Functional Spaces B.2 Linear Operators B.3 Inverse Operators B.4 Some Approximation Problems in the Hilbert Spaces of Geophysical Data B.5 Gram-Schmidt Orthogonalization Process Appendix C: Functionals in the Spaces of Geophysical Models C.1 Functionals and Their Norms C.2 Riesz Representation Theorem C.3 Functional Representation of Geophysical Data and an Inverse Problem Appendix D: Linear Operators and Functionals Revisited D.1 Adjoint Operators D.2 Differentiation of Operators and Functionals D.3 Concepts from Variational Calculus Appendix E: Some Formulae and Rules from Matrix Algebra E.1 Some Formulae and Rules of Operation on Matrices E.2 Eigenvalues and Eigenvectors E.3 Spectral Decomposition of a Symmetric Matrix E.4 Singular Value Decomposition (SVD) E.5 The Spectral Lanczos Decomposition Method Appendix F: Some Formulae and Rules from Tensor Calculus F.1 Some Formulae and Rules of Operation on Tensor Functions F.2 Tensor Statements of the Gauss and Green’s Formulae F.3 Green’s Tensor and Vector Formulae for Lamé and Laplace Operators Bibliography Index

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