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Corporate Inversion

United States. Congress. Senate. Committee on Appropriations. Subcommittee on Treasury and General Government

Published: 2003

Total Pages: 72


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This thesis develops a novel target-oriented inversion framework that uses wavefields as carriers of information to image both low-wavenumber component (a.k.a. background velocity) and high-wavenumber component (a.k.a. reflectivity) of the earth model in complex geological settings, such as subsalt regions. I address the problem of reflectivity imaging with target-oriented wavefield least-squares migration, and the problem of velocity estimation with target-oriented wavefield tomography. Reflectivity images of the subsurface are commonly produced by prestack depth migration. When the overburden is complex and the reflectors are unevenly or insufficiently illuminated, the migration operator alone is inadequate to provide an optimal image. I tackle the problem of distorted illumination in reflectivity imaging by wavefield least-squares migration. I formulate least-squares migration in the image domain and solve it in a target-oriented fashion. In the image-domain formulation, explicit computation of the Hessian operator (the resolution function that measures the illumination deficiency of the imaging system) is the most important and challenging step. I develop a novel method based on phase encoding to efficiently and accurately compute the target-oriented Hessian operator. The Hessian operator is then used to recover the reflectivity by iterative inverse filtering. I regularize the inversion with dip constraints, which naturally incorporate interpreted geological information into the inversion. Accurate imaging of the reflectivity also requires an accurate background velocity model. High-quality velocity model-building in complex geology requires wavefield-based velocity analysis to properly model band-limited wave phenomena. However, the high cost and lack of flexibility of target-oriented model-building prevent this method from being widely used in practice. I overcome the cost and flexibility issues of wavefield-based migration velocity analysis by developing target-oriented wavefield tomography. Target-oriented wavefield tomography is achieved by synthesizing a new data set specifically for velocity analysis. The new data set is generated based on an initial unfocused target image and by a novel application of generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling both zero and non-zero subsurface-offset-domain images. The new data set can be synthesized for a chosen target region with velocity inaccuracies. The reduced data size and computation domain, therefore, greatly improve the efficiency and flexibility of wavefield tomography, allowing fast and interpretation-driven interactive wavefield-based velocity analysis, where different geological scenarios or hypotheses can be tested in quasi-real time. The proposed target-oriented inversion framework successfully estimates subsalt velocities and recovers subsalt reflectivities from distorted illumination from 2-D synthetic and 3-D field data.
What we see depends on how we see. This introductory text in discrete mathematics, designed for computer science and math majors alike, illustrates how simple mathematics can be if we look at it from the right discrete perspectives. Key features include SageMath explorations, detailed solutions to exercises, exciting puzzles, and much much more!