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Total variation and adjoint state methods for seismic wavefield imaging Open Access


Other title
migration,inversion, total variation, edge-preserving, adjoint state, Born approximation
Type of item
Degree grantor
University of Alberta
Author or creator
Anagaw, Amsalu Y.
Supervisor and department
Sacchi, Mauricio (Geophysics)
Examining committee member and department
Kavanaugh, Jeffrey (Earth and Atmospheric Sciences)
Dumberry, Mathieu (Geophysics)
Boninsegni, Massimo (Physics)
Department of Physics

Date accepted
Graduation date
Master of Science
Degree level
Many geophysical inverse problems are ill-posed and have to be regularized. The most often used solution methods for solving ill-posed problems are based on the use of quadratic regularization that results in smooth solutions. Solutions of this type are not to be suitable when the model parameter is piecewise continuous blocky and edges are desired in the regularized solution. To avoid the smoothing of edges, which are very important attributes of an image, an edge-preserving regularization (non-quadratic regularization) term has to be employed. Total Variation (TV) regularization is one of the most effective regularization techniques for allowing sharp edges and the existence of discontinuities in the solutions. The edge-preserving regularization based on the TV method for small-scale geophysical inverse problems to the problem of estimating the acoustic velocity perturbation from a multi-source-receiver geophysical experiment is studied. The acoustic velocity perturbation is assumed to be piecewise continuous and blocky. The problem is based on linearization acoustic modeling using the framework of the single-scattering Born approximation from a known constant background medium. To solve this non-linear and ill-posed problem, an iterative scheme based on the conjugate gradient method is employed. The TV regularization method provides us with the opportunity to recover more useful information of velocity profiles from the measured seismic data. Though it requires more effort in implementing the TV term to control the smoothing and regularization parameter, the algorithm possesses the strong ability of marking the discontinuities and ensures their preservation from over-smoothing.
License granted by Amsalu Anagaw ( on 2009-09-30T17:35:18Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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File title: Total variation and adjoint state methods for seismic wavefield imaging, MS. c. Thesis
File author: Amsalu Y. Anagaw
Page count: 86
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