Sirgue, Laurent, 2003. Inversion de la forme d'onde dans le ...

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$Fayek & Kyser 2000 uraninite fractionations.pdf - Queen's University$

xvi LIST OF FIGURES 3.11 Imapact of noise on the reconstruction of the 1-D target. . . . . . . . . . . . . 75 3.12 Marmousi wide angle synthetic data. . . . . . . . . . . . . . . . . . . . . . . . 77 3.13 Example of the finite difference solver of the eikonal. . . . . . . . . . . . . . . 78 3.14 Evolution of the traveltime misfit function with respect to smoothness of the true Marmousi model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.15 First arrival traveltime inversion. . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.16 Waveform inversion in Marmousi. . . . . . . . . . . . . . . . . . . . . . . . . 82 3.17 Waveform inversion results in the Marmousi model at progressively higher frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.18 Velocity profiles at three locations in the Marmousi model. . . . . . . . . . . . 84 3.19 Data residuals in the Marmousi model. . . . . . . . . . . . . . . . . . . . . . . 86 4.1 SVD at 3 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2 SVD at 5 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.3 SVD at 10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.4 1-D velocity model with a constant vertical velocity gradient. . . . . . . . . . . 100 4.5 SVD at 3 Hz in the model with a vertical velocity gradient. . . . . . . . . . . . 101 4.6 SVD at 5 Hz in the model with a vertical velocity gradient.. . . . . . . . . . . . 102 4.7 SVD at 10 Hz in the model with a vertical velocity gradient.. . . . . . . . . . . 103 4.8 SVD at 3 Hz in model with velocity gradient. Slowness parameterisation. . . . 105 4.9 SVD at 5 Hz in model with velocity gradient. Slowness parameterisation. . . . 106 4.10 SVD at 10 Hz in model with velocity gradient. Slowness parameterisation. . . . 107 4.11 Illustration of the cycle skipping problem. . . . . . . . . . . . . . . . . . . . . 109 4.12 Misfit function of the linearization of the 3D homogeneous Green’s function . . 111 4.13 The 1-D Marmousi velocity model. . . . . . . . . . . . . . . . . . . . . . . . 112 4.14 Non-linearity and wavenumbers. . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.15 Non-linearity and offset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.16 2-D low-pass wavenumber filter of the gradient vector. . . . . . . . . . . . . . 116 4.17 1-D inversion with gradient preconditioning by wavenumber filtering. . . . . . 117 4.18 Finite difference modelling with different value of τ. . . . . . . . . . . . . . . 120 4.19 Misfit function of the far offset at 7 Hz and time damping. . . . . . . . . . . . 121 4.20 1-D velocity model containing a shallow and deep heterogeneity. . . . . . . . . 123 4.21 Preconditioning of the data residuals using an f-k filter. . . . . . . . . . . . . . 123
LIST OF FIGURES xvii 4.22 Standard waveform inversion at 7 Hz in the 1-D Marmousi model. . . . . . . . 126 4.23 1-D waveform inversion at 7 Hz with preconditioning of the data residuals and gradient vector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.24 2D extended Marmousi model. . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.25 Standard waveform inversion at 7 Hz. . . . . . . . . . . . . . . . . . . . . . . 129 4.26 Preconditioned Inversion at 7 Hz starting from the extended “FAST” model. . . 130 4.27 Velocity profiles at 3 locations in the model. . . . . . . . . . . . . . . . . . . . 131 4.28 Shot gathers at 3 locations in the true model. . . . . . . . . . . . . . . . . . . . 132 4.29 Inversion at 7 Hz starting from an improved macro model. . . . . . . . . . . . 133 5.1 Converted waves in sub-basalt imaging. . . . . . . . . . . . . . . . . . . . . . 137 5.2 The sub-basalt synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.3 Inversion starting from an accurate macro-model. . . . . . . . . . . . . . . . . 142 5.4 Evolution of the misfit function as the entire model is decreasingly smoothed. . 143 5.5 Evolution of the misfit function as the sediment and top basalt interface are decreasingly smoothed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.6 Illustration of the idealised layer stripping strategy . . . . . . . . . . . . . . . . 145 5.7 Evolution of the misfit function as the sediment layer is decreasingly smoothed. 146 5.8 Evolution of the misfit function as the basalt layer is decreasingly smoothed. . 147 5.9 Evolution of the misfit function as the sub-basalt layer is decreasingly smoothed. 147 5.10 Adequate velocity models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.11 Waveform inversion at 7 Hz when for a wrong and adequate starting models. . . 150 5.12 Wavefield in the sediments in time in the true model and inversion results with the bad starting model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Page 1 and 2: Thèse de Doctorat de l’Universit
Page 3 and 4: Abstract The standard imaging appro
Page 5 and 6: Résumé de thèse L’approche sta
Page 7 and 8: vii l’inversion de la forme d’o
Page 9: Ackowledgments First and foremost,
Page 12 and 13: xii CONTENTS 3 A strategy for selec
Page 14 and 15: xiv CONTENTS 6 Conclusions 155 6.1
Page 18 and 19: xviii LIST OF FIGURES
Page 20 and 21: xx LIST OF TABLES
Page 22 and 23: 2 CHAPTER 1. INTRODUCTION is made t
Page 24 and 25: 4 CHAPTER 1. INTRODUCTION the data
Page 26 and 27: 6 CHAPTER 1. INTRODUCTION quantify
Page 28 and 29: 8 CHAPTER 1. INTRODUCTION technique
Page 30 and 31: 10 CHAPTER 1. INTRODUCTION 1.8 Summ
Page 32 and 33: 12 CHAPTER 1. INTRODUCTION
Page 34 and 35: 14 CHAPTER 2. INVERSE THEORY Data M
Page 36 and 37: 16 CHAPTER 2. INVERSE THEORY Unknow
Page 38 and 39: 18 CHAPTER 2. INVERSE THEORY where
Page 40 and 41: 20 CHAPTER 2. INVERSE THEORY Where
Page 42 and 43: 22 CHAPTER 2. INVERSE THEORY The mi
Page 44 and 45: ‰ 24 CHAPTER 2. INVERSE THEORY St
Page 46 and 47: œS œ *ž œ7Ÿ• ›&œ žu¡[¢
Page 48 and 49: 28 CHAPTER 2. INVERSE THEORY Adding
Page 50 and 51: 30 CHAPTER 2. INVERSE THEORY a) b)
Page 52 and 53: 32 CHAPTER 2. INVERSE THEORY Misfit
Page 54 and 55: 34 CHAPTER 2. INVERSE THEORY Gauss-
Page 56 and 57: O P 36 CHAPTER 2. INVERSE THEORY St
Page 58 and 59: 38 CHAPTER 2. INVERSE THEORY a) YZ
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Page 62 and 63: € 42 CHAPTER 2. INVERSE THEORY 10
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46 CHAPTER 2. INVERSE THEORY For a
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48 CHAPTER 2. INVERSE THEORY The gr
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50 CHAPTER 2. INVERSE THEORY using
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52 CHAPTER 2. INVERSE THEORY
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54 CHAPTER 3. STRATEGY FOR SELECTIN
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ë ¸ · 0 0.1 0.2 0.3 0.4 0.5 0.6
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„ 64 CHAPTER 3. STRATEGY FOR SELE
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a) Depth (Km) Depth (Km) 0 0.5 1.0
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92 CHAPTER 4. STARTING FROM REALIST
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a) b) Depth (km) 0 0.5 1.0 1.5 2.0
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100 CHAPTER 4. STARTING FROM REALIS
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a) b) Depth (km) 0 0.5 1.0 1.5 2.0
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136 CHAPTER 5. WAVEFORM INVERSION A
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156 CHAPTER 6. CONCLUSIONS The wave
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158 CHAPTER 6. CONCLUSIONS 6.3 Wave
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160 CHAPTER 6. CONCLUSIONS
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162 APPENDIX A. IMAGE STRETCH AND N
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164 BIBLIOGRAPHY Bleistein, N., 198
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166 BIBLIOGRAPHY Forgues, E., Scala
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168 BIBLIOGRAPHY Lafond, C., Kaculi
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170 BIBLIOGRAPHY Pratt, R. G., and
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172 BIBLIOGRAPHY Tarantola, A., 198
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