Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach
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Zamanian-2015-Iterative estimation.pdf
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Author(s)
Zamanian, S. Ahmad
Rodi, William L.
Kane, Jonathan A.
Fehler, Michael
Date Issued
June 2015
Journal
Geophysics
Publisher
Society of Exploration Geophysicists
Citation
Zamanian, S. Ahmad, William L. Rodi, Jonathan A. Kane, and Michael C. Fehler. “Iterative Estimation of Reflectivity and Image Texture: Least-Squares Migration with an Empirical Bayes Approach.” Geophysics 80, no. 4 (June 10, 2015): S113–S126. © 2015 Society of Exploration Geophysicists
Version
Final published version
Abstract
In many geophysical inverse problems, smoothness assumptions on the underlying geology are used to mitigate the effects of nonuniqueness, poor data coverage, and noise in the data and to improve the quality of the inferred model parameters. Within a Bayesian inference framework, a priori assumptions about the probabilistic structure of the model parameters can impose such a smoothness constraint, analogous to regularization in a deterministic inverse problem. We have considered an empirical Bayes generalization of the Kirchhoff-based least-squares migration (LSM) problem. We have developed a novel methodology for estimation of the reflectivity model and regularization parameters, using a Bayesian statistical framework that treats both of these as random variables to be inferred from the data. Hence, rather than fixing the regularization parameters prior to inverting for the image, we allow the data to dictate where to regularize. Estimating these regularization parameters gives us information about the degree of conditional correlation (or lack thereof) between neighboring image parameters, and, subsequently, incorporating this information in the final model produces more clearly visible discontinuities in the estimated image. The inference framework is verified on 2D synthetic data sets, in which the empirical Bayes imaging results significantly outperform standard LSM images. We note that although we evaluated this method within the context of seismic imaging, it is in fact a general methodology that can be applied to any linear inverse problem in which there are spatially varying correlations in the model parameter space.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology. Earth Resources Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1190/GEO2014-0364.1
