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

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BIBLIOGRAPHY 82 Verm, R. and F. Hilterman. “Lithology color-coded seismic sections: the calibration of AVO crossplotting to rock properties.” The Leading Edge 14 (1995): 847–853. Vogel, C. R. and M. E. Oman. “Fast, robust total variation-based reconstruction of noisy, blurred images.” IEEE transactions on image processing 7 (1998): 813–824. Walden, A. T. “Making AVO section more robust.” Geophysical Prospecting 39 (1991): 915–942. Whitcombe, D.N., M. Dyce, C. J. S. McKenzie, and H. Hoeber. “Stabilizing the AVO gradient.” SEG Technical Program Expanded Abstracts 23 (2004): 232–235.
APPENDIX A Multivariate t distribution and Regularizations A.1 Multivariate t distribution The general central multivariate t distribution is given by, P (x i |µ, Ψ, ν) = Γ( ν+p 2 )|Ψ|−1/2 (πν) p/2Γ( ν 1 2 )[1 + ν (xi − µ) T Ψ−1 (xi − µ)] (ν+p) 2 , (A.1) The model x i is a p dimensional vector whose elements are in the range −∞ < xj < ∞ for j = 1, 2, 3 , ..., p which are correlated and having a p dimensional vector center, µ. The degree of correlation is represented by a p×p dimensional scale matrix, Ψ. The parameter ν is the degree of freedom. For N independent samples (x 1 , x 2 , x 3 ,.., x N ), the joint probability density distribution is the product of each density which can be written as where P (X|µ, Ψ, ν) = Po(Ψ, p, ν) N i=0 Po(Ψ, p, ν) = po = 1 [1 + 1 ν (xi − µ) T Ψ −1 (xi − µ)] (ν+p) 2 N i=0 83 Γ( ν+p 2 )|Ψ|−1/2 (πν) p/2 Γ( ν 2 ) . (A.2)
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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
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CHAPTER 2. AVO MODELING 23 ! !"# %$
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CHAPTER 2. AVO MODELING 25 can be r
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CHAPTER 3. BAYESIAN INVERSION APPRO
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CHAPTER 3. BAYESIAN INVERSION APPRO
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Page 51 and 52: 4.1 Introduction CHAPTER 4 Two-term
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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: BIBLIOGRAPHY 81 Sacchi, M.D. and T.
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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