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Total-variation based velocity inversion with Bregmanized operator splitting algorithm
Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numer...
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Published in: | Journal of applied geophysics 2018-04, Vol.151, p.1-10 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.
•A new strategy based on the DCT transform is presented for efficient calculation of the TV proximity operator.•We present an efficient algorithm for constrained TV regularization which can be used to solve seismic imaging problems.•No matrix inversion is required in this algorithm which allows efficient solution of large-scale seismic problems.•Examples of seismic velocity model construction are presented based on the Born approximation and regularized Dix formula. |
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ISSN: | 0926-9851 1879-1859 |
DOI: | 10.1016/j.jappgeo.2018.01.028 |