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

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

8 CHAPTER 1. INTRODUCTION techniques and depends strongly on the accuracy of the macro-model. 1.6 Non-linear inversion of wide-angle data Mora (1988) recognised that the inversion of transmission data may allow the recovery of some of the low wavenumbers of the velocity model. Non-linear waveform inversion may therefore be utilised for the recovery of both the low and the high wavenumbers as in Mora’s (1989) expression inversion = migration + tomography. The standard concept of imaging that decomposes the model of subsurface into the very low and the very high wavenumbers may be redefined: waveform inversion may be used to describe the velocity model over a continuous range of wavenumbers so that the “hole” of wavenumber information present in classical methods no longer exists. The determination of the intermediate wavenumbers is particularly important for the recovery of the high wavenumbers. This was shown by Versteeg (1993) who demonstrated that prestack depth migration in the Marmousi model may be significantly improved when spatial wavelengths up to 200 m are present in the macro-model. In order to exploit the information contained in transmission data such as diving and refracted waves, waveform inversion has been applied on wide-angle (large offset) seismic data (Mora, 1988, 1989; Sun and McMechan, 1992; Pratt et al., 1996; Shipp and Singh, 2002). The introduction of large offset data in the misfit function however contributes to an increase of the non-linearity of the inverse problem. Since the traveltime error is the result of integration of slowness errors over the ray path, errors contained in the starting velocity model are expected to have a greater effect on the large offset data which correspond to the longest ray paths. Convergence into a local minimum will yield a wrong update of the low and intermediate wavenumbers of the velocity model and thus will have a dramatic effect on the reconstruction of the high wavenumbers. Therefore, local minima must be very carefully avoided during the recovery of the low and intermediate wavenumbers to insure an accurate reconstruction of the high wavenumbers. The linearity of the waveform inverse problem also varies with temporal frequency of the data as low frequencies are more linear than high frequencies. The inversion of the lowest frequencies in the data thus appears to be desirable in order to increase the chance of conver-
1.7. AIM OF THE THESIS 9 gence into the global minimum (Bunks et al., 1995). The typical seismic data bandwidth is nevertheless limited by acquisition practice. Another important aspect of the waveform inversion is the determination of the starting model where the initial descent direction of the misfit function is computed. The starting model must be obtained using the standard methods discussed previously for the determination of the macro-model (stacking velocity analysis, traveltime inversion...). The requirements on the starting model are often very vague as it is considered that it must be in the neighbourhood of the global minimum. This begs the important question of the compatibility between the waveform inversion of the lowest frequencies available in the data and the limitations of classical methods in terms of accuracy of the macro-model. It is primarily this question that I seek to investigate in this thesis. 1.7 Aim of the thesis The objective of this thesis is to apply local, non-linear waveform inversion methods on wideangle seismic data for the recovery of a continuous range of wavenumbers of a complex velocity model. Two velocity models will be used to investigate this question: the 2D Marmousi model and a 1-D velocity model representing the sub-basalt imaging problem. The 2D Marmousi numerical experiment explores the application of waveform inversion using a realistic starting velocity model that was obtained from a standard method such as traveltime tomography. The 1D sub-basalt experiment analyses the requirements of the starting model that ensure the success of waveform inversion. The method of waveform inversion in the frequency domain will be used (Pratt and Worthington, 1990), as it presents significant advantages in term of computational efficiency. This work will examine the potential for applying waveform inversion in the frequency domain. The difficulties caused by the non-linearity of the waveform inverse problem will also be investigated, particularly with respect to the minimum frequency available in the data. This thesis also seeks to propose a methodology to incorporate a range of preconditioning tools in the inversion process (Tarantola, 1987; Mora, 1987), that may improve the linearity of the inverse problem.
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,
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Page 16 and 17: xvi LIST OF FIGURES 3.11 Imapact of
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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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136 CHAPTER 5. WAVEFORM INVERSION A
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156 CHAPTER 6. CONCLUSIONS The wave
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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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