Zhdanov, Michael S.
Inverse theory and applications in geophysics - 2nd ed. - Amsterdam Elsevier c2015 - xxv, 704p.; 24cm.
Table of contents
Dedication
Preface to the Second Edition
Preface
Part I: Introduction to Inversion Theory
Chapter 1: Forward and Inverse Problems in Science and Engineering
Chapter 2: Ill-Posed Problems and the Methods of Their Solution
Part II: Methods of the Solution of Inverse Problems
Chapter 3: Linear Discrete Inverse Problems
Chapter 4: Iterative Solutions of the Linear Inverse Problem
Chapter 5: Nonlinear Inversion Technique
Chapter 6: Multinary Inversion
Chapter 7: Resolution Analysis of Regularized Geophysical Inversion
Chapter 8: Monte Carlo Methods
Chapter 9: Generalized Joint Inversion of Multimodal Data
Part III: Geopotential Field Inversion
Chapter 10: Integral Representations of 2-D Gravity and Magnetic Fields
Chapter 11: Migration of 3-D Gravity, Gravity Tensor, and Total Magnetic Intensity Data
Chapter 12: Numerical Methods in Forward and Inverse Modeling of Geopotential Fields
Part IV: Electromagnetic Inversion
Chapter 13: Foundations of Electromagnetic Theory
Chapter 14: Integral Representations in Electromagnetic Forward Modeling
Chapter 15: Integral Representations in Electromagnetic Inversion
Chapter 16: Electromagnetic Migration Imaging
Chapter 17: Differential Methods in Electromagnetic Modeling and Inversion
Part V: Seismic Inversion
Chapter 18: Wavefield Equations
Chapter 19: Integral Representations in Wavefield Theory
Chapter 20: Integral Representations in Full Waveform Inversion
Appendix A: Functional Spaces of Geophysical Models and Data
Appendix B: Operators in the Spaces of Models and Data
Appendix C: Functionals in the Spaces of Geophysical Models
Appendix D: Linear Operators and Functionals Revisited
Appendix E: Some Formulae and Rules from Matrix Algebra
Appendix F: Some Formulae and Rules from Tensor Calculus
Bibliography
Index
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.
9780444626745
Earth science
Geophysics
550.1515 ZHD/I
Inverse theory and applications in geophysics - 2nd ed. - Amsterdam Elsevier c2015 - xxv, 704p.; 24cm.
Table of contents
Dedication
Preface to the Second Edition
Preface
Part I: Introduction to Inversion Theory
Chapter 1: Forward and Inverse Problems in Science and Engineering
Chapter 2: Ill-Posed Problems and the Methods of Their Solution
Part II: Methods of the Solution of Inverse Problems
Chapter 3: Linear Discrete Inverse Problems
Chapter 4: Iterative Solutions of the Linear Inverse Problem
Chapter 5: Nonlinear Inversion Technique
Chapter 6: Multinary Inversion
Chapter 7: Resolution Analysis of Regularized Geophysical Inversion
Chapter 8: Monte Carlo Methods
Chapter 9: Generalized Joint Inversion of Multimodal Data
Part III: Geopotential Field Inversion
Chapter 10: Integral Representations of 2-D Gravity and Magnetic Fields
Chapter 11: Migration of 3-D Gravity, Gravity Tensor, and Total Magnetic Intensity Data
Chapter 12: Numerical Methods in Forward and Inverse Modeling of Geopotential Fields
Part IV: Electromagnetic Inversion
Chapter 13: Foundations of Electromagnetic Theory
Chapter 14: Integral Representations in Electromagnetic Forward Modeling
Chapter 15: Integral Representations in Electromagnetic Inversion
Chapter 16: Electromagnetic Migration Imaging
Chapter 17: Differential Methods in Electromagnetic Modeling and Inversion
Part V: Seismic Inversion
Chapter 18: Wavefield Equations
Chapter 19: Integral Representations in Wavefield Theory
Chapter 20: Integral Representations in Full Waveform Inversion
Appendix A: Functional Spaces of Geophysical Models and Data
Appendix B: Operators in the Spaces of Models and Data
Appendix C: Functionals in the Spaces of Geophysical Models
Appendix D: Linear Operators and Functionals Revisited
Appendix E: Some Formulae and Rules from Matrix Algebra
Appendix F: Some Formulae and Rules from Tensor Calculus
Bibliography
Index
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.
9780444626745
Earth science
Geophysics
550.1515 ZHD/I