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

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CHAPTER 4. TWO-TERM AVO INVERSION 54 Time (s) a) Time (s) a) b) 0.2 0.2 0.4 0.6 −0.2 0 0.2 0.4 0.6 −0.2 0 0.2 Figure 4.13: (a) P-wave impedance (RMSErα = 0.007), and (b) S-wave impedance (RMSErα = 0.0108) retrieved from data with S/N=4 using Bivariate Cauchy as a priori. 0.2 0.4 0.6 100 Offset (m) 1100 2100 b) 0.2 0.4 0.6 100 Offset (m) 1100 2100 c) 0.2 0.4 0.6 100 Offset (m) 1100 2100 Figure 4.14: (a) The input data (S/N=4), (b) the predicted data, and (c) the difference between the input and the predicted data using Bivariate Cauchy as a priori. 0.04 0.02 0 -0.02 -0.04
5.1 Introduction CHAPTER 5 Three-term AVO Inversion Three-term AVO inversion uses three-term approximations on Zoeppritz equation as a for- ward model. It is the most favored inversion method for two main basic reasons. First, the three-term approximations like Aki and Richards’s are considered as the best approximation to the exact reflection coefficient (Rpp). In addition, the three term approximation allows to retrieve one more model parameter i.e direct density information which is useful parameter to characterize physical property of rocks (subsurface geology). Including the third term provides information which can be used to separate gas sands from wet sands, tight sands, and shales or to study gas saturation (Kabir et al., 2006; Sun et al., 2005; Li, 2005). However, as pointed out in the introduction part of chapter 4, using three-term approximations as inversion model is more ill-conditioned than a two-term approximation. This suggests that more attention should be given to stabilizing the inversion although both cases need regularization in order to make the solution more stable. Following a similar pro- cedure given in the previous chapter, the three term AVO regularizations are constructed via Bayesian approach. This chapter is mainly to address a new way of regularizing the three-term AVO inversion using Trivariate Cauchy probability distribution in comparison with other two possible regularization methods. This is demonstrated by both synthetic and real data examples. 55
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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
Page 15 and 16: CHAPTER 1. INTRODUCTION 3 ! !!!!!!!
Page 17 and 18: CHAPTER 1. INTRODUCTION 5 1.4.1 Rel
Page 19 and 20: CHAPTER 1. INTRODUCTION 7 three-ter
Page 21 and 22: 2.1 Introduction CHAPTER 2 AVO Mode
Page 23 and 24: CHAPTER 2. AVO MODELING 11 (S-wave
Page 25 and 26: CHAPTER 2. AVO MODELING 13 At this
Page 27 and 28: CHAPTER 2. AVO MODELING 15 The resu
Page 29 and 30: CHAPTER 2. AVO MODELING 17 2.3.3 Sh
Page 31 and 32: CHAPTER 2. AVO MODELING 19 Assuming
Page 33 and 34: 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 65: CHAPTER 4. TWO-TERM AVO INVERSION 5
Page 69 and 70: 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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