Dimri Deconvolution and Inverse Theory

Application to Geophysical Problems
1. Auflage 2013
ISBN: 978-1-4832-9137-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 29, 249 Seiten, Web PDF

Reihe: Methods in Geochemistry and Geophysics

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.

Autoren/Hrsg.

Dimri, V.

Inhaltsverzeichnis

1;Front Cover;1
2;Deconvolution and Inverse Theory: Application to Geophysical Problems;4
3;Copyright Page;5
4;Table of Contents;16
5;Dedication;6
6;Foreword;8
7;Preface;10
8;Chapter 1. Convolution;20
8.1;1.1. Introduction;20
8.2;1.2. Convolution in geophysics;21
8.3;1.3. Fourier theory;25
8.4;1.4. Geophysical convolution model;34
9;Chapter 2. Deconvolution;42
9.1;2.1. Introduction;42
9.2;2.2. Predictive deconvolution;42
9.3;2.3. Time-varying deconvolution;45
9.4;2.4. Homomorphic deconvolution;61
9.5;2.5. Minimum entropy deconvolution;63
10;Chapter 3. Inverse theory;68
10.1;3.1. Introduction;68
10.2;3.2. Linearized inversion;70
10.3;3.3. Nonlinear inversion;86
10.4;3.4. Types of norms;90
11;Chapter 4. Inversion and deconvolution;100
11.1;4.1. Introduction;100
11.2;4.2. Deconvolution and inversion;101
11.3;4.3. Multichannel constrained Wiener filter;105
11.4;4.4. Discussion;110
12;Chapter 5. Inversion of reflection seismic data;112
12.1;5.1. Introduction;112
12.2;5.2. Seismic reflection method;112
12.3;5.3. Inversion methods;121
12.4;5.4. Migration;129
12.5;5.5. Seismic tomography;136
12.6;5.6. Ocean acoustic tomography;140
12.7;5.7. Stochastic tomography;142
13;Chapter 6. Inversion of other geophysical data;144
13.1;6.1. Introduction;144
13.2;6.2. Inversion of gravity data;144
13.3;6.3. Inversion of magnetic data;154
13.4;6.4. Inversion of resistivity data;158
13.5;6.5. Inversion of electromagnetic data;165
13.6;6.6. Joint and cooperative inversion;179
14;Chapter 7. Deconvolution of other geophysical data;180
14.1;7.1. Introduction;180
14.2;7.2. Estimation of density;181
14.3;7.3. Optimum filter for potential field data;184
14.4;7.4. Modified Wiener-Hopf equation;187
14.5;7.5. Nonstationarity of magnetic data;195
14.6;7.6. Kaiman approach;196
14.7;7.7. Deconvolution of resistivity data;201
14.8;7.8. Deconvolution of paleomagnetic data;202
15;Chapter 8. Spectral estimation;204
15.1;8.1. Introduction;204
15.2;8.2. Overview of conventional methods;205
15.3;8.3. High resolution methods;208
15.4;8.4. Multichannel and multidimensional spectra;221
16;Appendix A. Multichannel unimodular constrained filter;224
17;References;228
18;Subject Index;246