Optimal Seismic Deconvolution

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.

Foreword

Preface

1. Deconvolution

1.1. Introduction

1.2. Some Approaches to Deconvolution

1.3. State-Variable Models

1.4. Outline of Book

Appendix A. Introduction to State-Variable Models and Methods

2. Minimum-Variance Estimation

2.1. Introduction

2.2. Elements of Minimum-Variance Estimation Theory

2.3. Optimal Prediction

2.4. Optimal Filtering

2.5. Optimal Smoothing

2.6. Final Remark

3. Minimum-Variance Deconvolution

3.1. Introduction

3.2. Fixed-Interval Deconvolution

3.3. Fixed-Point Deconvolution

3.4. Simulation Results

3.5. Accounting for Other Effects

3.6. Fixed-Interval Smoother for a Product Model Input

4. Maximum-Likelihood and Maximum a Posteriori Methods

4.1. Principles of Maximum-Likelihood Estimation

4.2. Log-Likelihood Function for Dynamical Systems

4.3. Principles of Maximum a Posteriori Estimation

5. Maximum-Likelihood Deconvolution

5.1. Simultaneous Parameter Estimation and Deconvolution

5.2. A Model for μ(k)

5.3. Formulations of Maximum-Likelihood Parameter Estimation and Deconvolution Problems

5.4. A Preview

Appendix A. Continuous- and Discrete-Time Models for Input μ

6. Event Detection

6.1. Introduction

6.2. Unconditional Maximum-Likelihood Detection

6.3. Threshold Detector

6.4. Single Most Likely Replacement Detector

6.5. Simulation Results

6.6. Remarks

7. Wavelet Estimation

7.1. Introduction

7.2. Estimation Formulation

7.3. Estimation Procedure

7.4. Determination of Model Order

7.5. Simulation Examples

7.6. Identifiability of Nonminimum-Phase Wavelets

Appendix A. Approximate Realization Procedure

Appendix B. Parseval's Relation

8. Estimating Statistical Parameters

8.1. Introduction

8.2. Estimating Variances

8.3. Estimating Input Signal Density Parameter λ

8.4. Estimating All Statistical Parameters Simultaneously

8.5. Application to Well-Log Processing

Appendix A. On the Proof of Theorem 8-2

9. Simultaneous Parameter Estimation and Deconvolution

9.1. Introduction

9.2. Estimation Procedure

9.3. Simulation Results

9.4. Application to Real Data

10. Model-Based Deconvolution

10.1. Introduction

10.2. Maximum-Likelihood Normal Incidence Inversion

10.3. Normal Incidence Geooptimal Deconvolution Algorithm

10.4. Simulation Results

11. Epilog

11.1. Computation

11.2. Multichannel Deconvolution

11.3. Tying Well-Log and Seismic Data Together

11.4. Nonnormal Incidence Geooptimal Deconvolution

11.5. Recursive Waveshaping

11.6. Noncausal Impulse Responses

References

Index