Mendel Optimal Seismic Deconvolution

An Estimation-Based Approach
1. Auflage 2013
ISBN: 978-1-4832-5819-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 268 Seiten, Web PDF

Optimal Seismic Deconvolution: An Estimation-Based Approach presents an approach to the problem of seismic deconvolution. It is meant for two different audiences: practitioners of recursive estimation theory and geophysical signal processors. The book opens with a chapter on elements of minimum-variance estimation that are essential for all later developments. Included is a derivation of the Kaiman filter and discussions of prediction and smoothing. Separate chapters follow on minimum-variance deconvolution; maximum-likelihood and maximum a posteriori estimation methods; the philosophy of maximum-likelihood deconvolution (MLD); and two detection procedures for determining the location parameters in the input sequence product model. Subsequent chapters deal with the problem of estimating the parameters of the source wavelet when everything else is assumed known a priori; estimation of statistical parameters when the source wavelet is known a priori; and a different block component method for simultaneously estimating all wavelet and statistical parameters, detecting input signal occurrence times, and deconvolving a seismic signal. The final chapter shows how to incorporate the simplest of all models-the normal incidence model-into the maximum-likelihood deconvolution procedure.

Autoren/Hrsg.

Mendel, Jerry M.

Inhaltsverzeichnis

1;Front Cover;1
2;Optimal Seismic Deconvolution: An Estimation-Based Approach;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Foreword;12
7;Preface;14
8;Chapter 1. Deconvolution;16
8.1;1.1. Introduction;16
8.2;1.2. Some Approaches to Deconvolution;22
8.3;1.3. State-Variable Models;28
8.4;1.4. Outline of Book;38
8.5;Appendix A: Introduction to State-Variable Models and Methods;41
9;Chapter 2. Minimum-Variance Estimation;57
9.1;2.1. Introduction;57
9.2;2.2. Elements of Minimum-Variance Estimation Theory;60
9.3;2.3. Optimal Prediction;64
9.4;2.4. Optimal Filtering;66
9.5;2.5. Optimal Smoothing;76
9.6;2.6. Final Remark;81
10;Chapter 3. Minimum-Variance Deconvolution;82
10.1;3.1. Introduction;82
10.2;3.2. Fixed-Interval Deconvolution;83
10.3;3.3. Fixed-Point Deconvolution;87
10.4;3.4. Simulation Results;95
10.5;3.5. Accounting for Other Effects;103
10.6;3.6. Fixed-Interval Smoother for a Product Model Input;105
11;Chapter 4. Maximum-Likelihood and Maximum a Posteriori Methods;109
11.1;4.1. Principles of Maximum-Likelihood Estimation;109
11.2;4.2. Log-Likelihood Function for Dynamical Systems;115
11.3;4.3. Principles of Maximum a Posteriori Estimation;118
11.4;Chapter 5. Maximum-Likelihood Deconvolution;122
11.4.1;5.1. Simultaneous Parameter Estimation and Deconvolution;122
11.4.2;5.2. A Model for µ(k);124
11.4.3;5.3. Formulations of Maximum-Likelihood Parameter Estimation and Deconvolution Problems;125
11.4.4;5.4. A Preview;130
11.5;Appendix A: Continuous- and Discrete-Time Models for Input µ;131
12;Chapter 6. Event Detection;135
12.1;6.1. Introduction;135
12.2;6.2. Unconditional Maximum-Likelihood Detection;138
12.3;6.3. Threshold Detector;142
12.4;6.4. Single Most Likely Replacement Detector;146
12.5;6.5 Simulation Results;152
12.6;6.6. Remarks;153
13;Chapter 7. Wavelet Estimation;154
13.1;7.1. Introduction;154
13.2;7.2. Estimation Formulation;154
13.3;7.3. Estimation Procedure;156
13.4;7.4. Determination of Model Order;163
13.5;7.5. Simulation Examples;164
13.6;7.6. Identifiability of Nonminimum-Phase Wavelets;170
13.7;Appendix A: Approximate Realization Procedure;181
13.8;Appendix B: Parseval's Relation;183
14;Chapter 8. Estimating Statistical Parameters;185
14.1;8.1. Introduction;185
14.2;8.2. Estimating Variances;186
14.3;8.3. Estimating Input Signal Density Parameter .;187
14.4;8.4. Estimating All Statistical Parameters Simultaneously;190
14.5;8.5. Application to Well-Log Processing;191
14.6;Appendix A: On the Proof of Theorem 8-2;202
15;Chapter 9. Simultaneous Parameter Estimation and Deconvolution;204
15.1;9.1. Introduction;204
15.2;9.2. Estimation Procedure;204
15.3;9.3. Simulation Results;207
15.4;9.4. Application to Real Data;212
16;Chapter 10. Model-Based Deconvolution;224
16.1;10.1. Introduction;224
16.2;10.2. Maximum-Likelihood Normal Incidence Inversion;229
16.3;10.3. Normal Incidence Geooptimal Deconvolution Algorithm;246
16.4;10.4. Simulation Results;249
17;Chapter 11. Epilog;252
17.1;11.1. Computation;252
17.2;11.2. Multichannel Deconvolution;254
17.3;11.3. Tying Well-Log and Seismic Data Together;255
17.4;11.4. Nonnormal Incidence Geooptimal Deconvolution;256
17.5;11.5. Recursive Waveshaping;257
17.6;11.6. Noncausal Impulse Responses;257
18;References;259
19;Index;266