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

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

ii c○ Copyright 2003, Laurent SIRGUE
Abstract The standard imaging approach in exploration seismology relies on a decomposition by spatial scales: the determination of the low wavenumbers of the velocity field is followed by the reconstruction of the high wavenumbers. In this standard approach, intermediate spatial wavenumbers are ignored, partly because they are known to have little effect on the data for standard near-normal incidence geometries. However, for models presenting a complex structure, the recovery of the high wavenumbers may be significantly improved by the determination of intermediate wavenumbers. These can potentially be recovered by local, non-linear waveform inversion of wide-angle data. However, waveform inversion schemes based on the computation of the gradient of the misfit function are limited by the non-linearity of the inverse problem, which is in turn governed by the minimum frequency in the data and the starting velocity model. It is critical to invert from the lowest to the highest frequencies of the seismic data. For very low temporal frequencies (< 7 Hz), the problem is reasonably linear so that waveform inversion may be applied using a starting model obtained from traveltime tomography. The frequency domain is particularly advantageous as the inversion from the low to the high frequencies is then very efficient. It is possible to discretise the frequencies with a much larger sampling interval than that dictated by the sampling theorem and still obtain an imaging result that does not suffer from aliasing (wrap-around) in the depth domain. The number of input frequencies can be reduced when a range of offsets is available; this creates a redundancy of information in the wavenumber coverage of the target. In order to optimise the use of this information, I define a new discretisation strategy that depends on the maximum effective offset present in the surface seismic survey. This strategy is defined by deriving an analytical prediction of the wavenumber coverage of a 1-D target, for a single frequency and for a given acquisition geometry. This analytic expression is obtained using the results of diffraction tomography, and is adapted to formulate an expression for the gradient image in waveform inversion. The main idea of the selection strategy is: iii
Page 1: Thèse de Doctorat de l’Universit
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 16 and 17: xvi LIST OF FIGURES 3.11 Imapact of
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
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Page 34 and 35: 14 CHAPTER 2. INVERSE THEORY Data M
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32 CHAPTER 2. INVERSE THEORY Misfit
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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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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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Sirgue, Laurent, 2003. Inversion de la forme d'onde dans le ...

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