Regularization of the AVO inverse problem by means of a ...

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CHAPTER 5. THREE-TERM AVO INVERSION 74 Time (s) a) 0.8 1.0 1.3 CDP number 10 30 50 0.03 0.01 0 -0.01 -0.03 b) 0.8 1.0 1.3 CDP number 10 30 50 0.03 0.01 0 -0.01 -0.03 c) 0.8 1.0 1.3 CDP number 10 30 50 Figure 5.16: (a) Stacked section of the real data , (b) data generated using the inverted reflectivities (Figure 5.14) and then stacked, and (c) data generated using the inverted reflectivities (Figure 5.15) and then stacked. 0.03 0.01 0 -0.01 -0.03
CHAPTER 5. THREE-TERM AVO INVERSION 75 5.5 Summary In this chapter, the Bayes’ theorem was used to formulate the inversion using three possible prior distributions which could be used to regularize AVO inversion. Each regularization method was investigated with synthetic and real data examples. The synthetic data inversion via Univariate Cauchy prior does a good job in the two-term inversion but the result is unstable when this prior is used for the three-term inversion. This implies that the two-term is more stable than three-term. In other words, the regularization with correlation infor- mation is very important to stabilize the inverse problem. This was demonstrated by the Multivariate Gaussian and Trivariate Cauchy regularizations although the result in Multi- variate Gaussian prior has no sparsity in the solution. The Trivariate Cauchy regularization has two advantages combined (introducing correlation and also its role for sparsity). In nutshell, it plays a good role in stabilizing the inversion and increase the resolution of the inverted parameters. This makes it promising for better prediction of subsurface physical parameters by avoiding discrepancy which usually arises for decision making.
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University of Alberta Regularizatio
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Abstract Amplitude Variation with O
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Contents 1 Introduction 1 1.1 Forwa
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5 Three-term AVO Inversion 55 5.1 I
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List of Figures 1.1 A simple diagra
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5.3 (a) P-wave reflectivity (RMSEA
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CHAPTER 1 Introduction The reflecti
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CHAPTER 1. INTRODUCTION 3 ! !!!!!!!
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CHAPTER 1. INTRODUCTION 5 1.4.1 Rel
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CHAPTER 1. INTRODUCTION 7 three-ter
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2.1 Introduction CHAPTER 2 AVO Mode
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CHAPTER 2. AVO MODELING 11 (S-wave
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CHAPTER 2. AVO MODELING 13 At this
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CHAPTER 2. AVO MODELING 15 The resu
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CHAPTER 2. AVO MODELING 17 2.3.3 Sh
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CHAPTER 2. AVO MODELING 19 Assuming
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CHAPTER 2. AVO MODELING 21 Reflecti
Page 35 and 36: CHAPTER 2. AVO MODELING 23 ! !"# %$
Page 37 and 38: CHAPTER 2. AVO MODELING 25 can be r
Page 39 and 40: CHAPTER 3. BAYESIAN INVERSION APPRO
Page 51 and 52: 4.1 Introduction CHAPTER 4 Two-term
Page 53 and 54: CHAPTER 4. TWO-TERM AVO INVERSION 4
Page 67 and 68: 5.1 Introduction CHAPTER 5 Three-te
Page 69 and 70: CHAPTER 5. THREE-TERM AVO INVERSION
Page 85: CHAPTER 5. THREE-TERM AVO INVERSION
Page 89 and 90: CHAPTER 6. CONCLUSIONS 77 two terms
Page 91 and 92: Bibliography Aki, K. and P. G. Rich
Page 93 and 94: BIBLIOGRAPHY 81 Sacchi, M.D. and T.
Page 95 and 96: APPENDIX A Multivariate t distribut
Page 97 and 98: APPENDIX A. MULTIVARIATE T DISTRIBU
Page 99 and 100: APPENDIX B EM Algorithm B.1 EM-Algo
Page 101: APPENDIX C Calculation of root mean
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