Estimation of channelized features in geological media using sparsity constraint
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243610475-MIT.pdf
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17.15 MB
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191f45949c600d339ccc5e9569fe9f08
Author(s)
Jafarpour, Behnam
Advisor(s)
William T. Freeman and Vivek K. Goyal.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, a new approach is studied for inverse modeling of ill-posed problems with spatially continuous parameters that exhibit sparseness in an incoherent basis (e.g. a Fourier basis). The solution is constrained to be sparse in the transform domain and the dimension of the search space is effectively reduced to a low frequency subspace to improve estimation efficiency. The solution subspace is spanned by a subset of a discrete cosine transform (DCT) basis containing low-frequency elements. The methodology is related to compressive sensing, which is a recently introduced paradigm for estimation and perfect reconstruction of sparse signals from partial linear observations in an incoherent basis. The sparsity constraint is applied in the DCT domain and reconstruction of unknown DCT coefficients is carried out through incorporation of point measurements and prior knowledge in the spatial domain. The approach appears to be generally applicable for estimating spatially distributed parameters that are approximately sparse in a transformed domain such as DCT. The suitability of the proposed inversion framework is demonstrated through synthetic examples in characterization of hydrocarbon reservoirs.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
Includes bibliographical references (p. 86-89).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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