ON SEISMIC DECONVOLUTION USING NEW ESTIMATION ALGORITHMS
K.P. MOHANADAS
Thesis submitted to the
Indian Institute of Technology, Delhi for the award of the degree of
DOCTOR OF PHILOSOPHY
Department of Electrical Engineering Indian Institute of Technology
New Delhi 110 016
JULY 1981
CERTIFICATE
This is to certify that the thesis entitled "On Seismic Deconvolution using New Estimation Algorithms" being submitted by K.P. Mohanadas for the award of the degree of Doctor of Philosophy to the Indian Institute of Technology, Delhi, is a
record of the bonafide research work he has done, during the period from July 1978 to July 1981 under our supervision. The results obtained in this thesis have not been submitted to any other University or Institute for the award of any degree or
diploma.
10-1"
A.K. Mahalanabis Surendra Prasad
Department of Electrical Engineering Indian Institute of Technology
New Delhi 110 016
IN LOVING MEMORY OF
My LATE MOTHER
ACKNOWLEDGEMENTS
I shall like to take this opportunity for recording my sincere appreciation of the effective guidance of my supervisors Professor A.K. Mahalanabis and Dr. Surendra Prasad who not only suggested the problems, but also helped at every stage of the work. Their keen interest in my work and constructive suggestions were a great help to me in my attempt to develop some algorithms useful for real seismic data deconvolution.
I am also thankful to the authorities of the Institute of Petroleum Exploration, Oil and Natural Gas Commission of India for providing the real data and for the computer facilities and speci- fically to Mr. V.C. Mohan, Director (Geophysics) and Mr. N.D.J. Rao, Deputy Superintending Geophysicist (Computer Services Division) for many helpful discussions on the seismic deconvolution problem.
It is with pleasure that I place on record my thanks to my colleagues Dr. M. Hanmandlu, Messrs. Sathya Sheel, R.G. Rao, G.Ray, and R. Prasad for the useful discussions and Dr. C.K. Pillai,
E. Gopinathan, R.R. Nair, and R. Sudhakar for making my life in the Institute more enjoyable. I am thankful to my wife Malathy and children Mini and Manoj for their cheerful company which has made my work easier than expected. I am grateful to my father, K.P.
Panicker and brother, Prof. K.P. Sasidharan, who have made me what I am.
The financial help received from the Ministry of Education, Government of India, and Principal, Calicut Regional Engineering College, in the form of a fellowship under the Quality Improvement Programme is duly acknowledged.
Finally, I wish to thank Sri P.M. Padmanabhan Nambiar, for making a neat job of typing the manuscript.
I:1.1., Delhi K.P. 11OHAN'ADA5
15 July, 1981
" So far as Mathematics do not tend to make men more sober and rational thinkers, wiser and better men, they arc only to be considered as an amusement, which ought not to take us off from serious business."
— Thomas Bayes
CONTENTS
Page List of Principal Symbols
List of Abbreviations
List of Figures vi
Abstract ix
CHAPTER 1
REVIEW AND SCOPE OF THE THESIS
1.1 INTRODUCTION 1
1.2 SEISMIC DATA PROCESSING 2
1.2.1 Data Acquisition 2
1.2.2 Data Processing 5
1.2.3 Requirements of Present Day 9 Seismic Data Processing
1.3 REVIEW OF THE EXISTING METHODS FOR DECONVOLUTION 10
1.3.1 Time Series Methods 12
1.3.2 State Variable Methods 19 1.3.3 Frequency Domain Methods 23 1.4 LIMITATIONS OF THE EXISTING METHODS 25 1.4.1 Predictive Deconvolution 25 1.4.2 Kalman Filter Applications 26 1.4.3 White Noise Estimation Approach 26 1.4.4 Detection and Estimation Approach 27 1.4.5 Adaptive Deconvolution Methods 28
1.5 SCOPE OF THE THESIS 28
Page CHAPTER 2
REAL SEISMIC DATA DECONVOLUTION USING KALMAN PREDICTOR MODEL
2.1 INTRODUCTION 33
2.2 PROBLEM FORMULATION 35
2.3 THE IDENTIFICATION ALGORITHM 37
2.4 RESULTS OF IDENTIFICATION ALGORITHM 42 2.4.1 Identification Results — 42
Simulated Data
2.4.2 Identification Results — Real Data 46 2.5 RESULTS OF PREDICTIVE DECONVOLUTION 49 2.5.1 Results of Predictive Deconvolution — 49
Simulated Data
2.5.2 Results of Predictive Deconvolution — 54 Real Data
2.6 COMPARATIVE STUDY OF THE KALMAN PREDICTOR 56 AND AR PREDICTOR BASED ALGORITHMS
2.7 CONCLUDING REMARKS 66
CHAPTER 3
WHITE NOISE ESTIMATORS FOR REAL SEISMIC DATA
3.1 INTRODUCTION 67
3.2 PROBLEM FORMULATION 68
3.3 MODEL IDENTIFICATION 70
3.4 WHITE NOISE ESTIMATION ALGORITHM 76 3.5 RESULTS OF REAL DATA PROCESSING 78
3.6 CONCLUDING REMARKS 88
Page
CHAPTER 4
nAP DETECTION AND DECISION DIRECTED ESTIMATION OF REFLECTION COEFFICIENTS
4.1 INTRODUCTION 89
4.2 PROBLEM FORMULATION 90
4.3 ESTIMATION OF REFLECTION LOCATIONS 93 4.4 ESTIMATION OF REFLECTION AMPLITUDES 99
4.5 EXPERIMENTAL RESULTS 100
4.6 COMPARISON OF ML AND MAP DETECTORS 103
4.7 CONCLUDING REMARKS 113
CHAPTER 5
KALMAN IDENTIFIERS FOR ADAPTIVE DECONVOLUTION
5.1 INTRODUCTION 114
5.2 ALGORITHMS FOR ADAPTIVE DECONVOLUTION 116 5.2.1 Adaptive Deconvolution via CKA 117 5.2.2 FKA for Adaptive Deconvolution 119 5.2.3 Improved Deconvolution via FKA 122 5.3 COMPARATIVE STUDY OF THE ALGORITHMS BASED ON 124
SIMULATED DATA
5.3.1 Rate of Parameter Convergence and 125 'Sensitivity to Initial Parameters
5.3.2 Deconvolution Results via CKA, FKA and 129 Smoothing
5.3.3 Computational Requirements 133 5.4 RESULTS OF REAL DATA PROCESSING 134
5.5 CONCLUDING REMARKS 143
Page
CHAPTER 6
ADAPTIVE LATTICE ALGORITHMS FOR DECONVOLUTION OF NONSTATIONARY DATA
6.1 INTRODUCTION 144
6.2 ADAPTIVE LATTICE STRUCTURES 146
6.2.1 Review of Adaptive Gradient Lattice 147
6.2.2 Least Squares Lattice 152
6.2.3 Improved Deconvolution Using Lattice 156 Filter
6.3 COMPARATIVE STUDY OF THE ALGORITHMS BASED ON 156 SIMULATED DATA
6:3.1 Rate of M.S. Convergence and 157 Sensitivity to Algorithm Parameters
6.3.2 Predictive Deconvolution Results ; 161 Simulated Data
6.3.3 Computational Requirements 166 6.4 RESULTS OF REAL DATA PROCESSING 169
6.5 CONCLUDING REMARKS 179
CHAPTER 7
DECONVOLUTION OF SEISMIC DATA USING ARMA PREDICTORS
7.1 INTRODUCTION 180
7.2 PROBLEM FORMULATION 182
7.3 ARMA ORDER DETERMINATION 184
7.4 DECONVOLUTION WITH ARMA MODELS 187 7.4.1 Box and Jenkin's Approach to 188
ARMA Modelling
7.4.2 Recursive ARMA Algorithm 189
Page
7.5 RESULTS OF EXPERIMENTS ON SIMULATED DATA 191 7.5.1 Deconvolution Results on 191
Simulated Data
7.5.2 Results of ARMA Deconvolution on 194 Real Data
7.6 CONCLUDING REMARKS 202
CHAPTER 8
COMPARATIVE STUDY OF ALGORITHMS FOR REAL DATA PROCESSING
8.1 INTRODUCTION 203
8.2 CRITERIA FOR COMPARISON 203
8.3 RESULTS OF THE COMPARAT/VE STUDY 205 8.3.1 Non—adaptive Algorithms 205
8.3.2 Adaptive Algorithms 209
8.4 CONCLUDING REMARKS 213
CHAPTER 9
CONCLUDING REMARKS AND SUGGESTIOftS fOR FURTHER WORK
9.1 INTRODUCTION 214
9.2 SUMMARY OF RESULTS 214
9.3 SUGGESTIONS FOR FURTHER WORK 218 9.3.1 Extension of the work of Chapter 219 9.3.2 Future Work on MAP Algorithm of Chapter 4 219 9.3.3 Fast Filtering Algorithms based on 220
ARMA Model
9.3.4 Vector Data Processing 221
9.3.5 Multidimensional Processing 221
Page
REFERENCES 223
BIBLIOGRAPHY 229
APPENDIX A 230
APPENDIX B 238
