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

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CHAPTER 3. BAYESIAN INVERSION APPROACH AND ALGORITHMS 30 !" #" !% $ &'# ! # ! # $" !# & # % $ !% !# & ! " # % & !% !# & # % $ !% !# & ! " # % & $ &'"( &'" &'&( &'# &'"( &'" &'&( ! # ! # !% !# & # % $ !% !# & ! " # % & % $ !% !# & ! " # % & Figure 3.2: The peak of the (a) the Bivariate Cauchy Probability distribution (ν = 1), and the Bivariate t distributions for (b) ν = 2, c) ν = 5, and d) ν = 10. %" !% !# & # $ $ &'# &'"( &'" &'&( &'# &'"( &'" &'&(
CHAPTER 3. BAYESIAN INVERSION APPROACH AND ALGORITHMS 31 !" !% $ &'&" #" ! # ! # !# & # % $ !% !# & ! " # % & % $ !% !# & ! " # % & &'&&) &'&&( &'&&% &'&&# $" %" !% $ &'&" !% !# & # &'&&) &'&&( &'&&% &'&&# ! # ! # !% !# & # % $ !% !# & ! " # % & % $ !% !# & ! " # % & Figure 3.3: The tail of a) the Bivariate Cauchy distribution (ν = 1), and the Bivariate t distributions for b) ν = 2, c) ν = 5, and d) ν = 10. !# & # $ $ &'&" &'&&) &'&&( &'&&% &'&&# &'&" &'&&) &'&&( &'&&% &'&&#
Page 1 and 2: University of Alberta Regularizatio
Page 3 and 4: Abstract Amplitude Variation with O
Page 5 and 6: Contents 1 Introduction 1 1.1 Forwa
Page 7 and 8: 5 Three-term AVO Inversion 55 5.1 I
Page 9 and 10: List of Figures 1.1 A simple diagra
Page 11 and 12: 5.3 (a) P-wave reflectivity (RMSEA
Page 13 and 14: 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 41: 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 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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