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High-resolution reflectivity inversion
THANG NGUYEN,
JOHN CASTAGNA
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Department of Earth and Atmospheric Sciences, The University of Houston, 4800 Cathoun Rd., Houston, TX 77204, U.S.A.,
JSE 2010, 19(4), 303–320;
Submitted: 9 April 2010 | Accepted: 26 June 2010 | Published: 1 October 2010
© 2010 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Assuming the convolutional model and a known wavelet, reflectivity inversion is an ill-posed problem. Existing methods mostly regularize the problem using mathematical criterion, such as minimization of the reflectivity vector norm. We propose reflectivity inversion using atomic decomposition, in which the atoms can be basic geological structures or derived from well logs. This is equivalent to replacing mathematical criterion by geological ones. Numerical results show that atomic decomposition is robust to noise. When applied to multi-dimensional data in a trace by trace basis, atomic decomposition shows lateral instability. The solutions are non-unique. Atomic decomposition results are probable solutions, which can be laterally regularized by re-projection.
Keywords
reflectivity
inversion
matching pursuit
regularization
geological pattern
sparse spike inversion
basis pursuit
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