Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach
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...
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| Format: | Article |
| Language: | en_US |
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Society of Exploration Geophysicists
2015
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| Online Access: | http://hdl.handle.net/1721.1/98495 https://orcid.org/0000-0002-8814-5495 |
| _version_ | 1811087692466749440 |
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| author | Zamanian, S. Ahmad Rodi, William L. Kane, Jonathan A. Fehler, Michael |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Zamanian, S. Ahmad Rodi, William L. Kane, Jonathan A. Fehler, Michael |
| author_sort | Zamanian, S. Ahmad |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:50:30Z |
| format | Article |
| id | mit-1721.1/98495 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:50:30Z |
| publishDate | 2015 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/984952022-09-28T16:31:57Z Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach Zamanian, S. Ahmad Rodi, William L. Kane, Jonathan A. Fehler, Michael Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Earth Resources Laboratory Zamanian, S. Ahmad Rodi, William L. Fehler, Michael 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 Energy Initiative (Shell International Exploration and Production B.V.) ERL Founding Member Consortium 2015-09-15T14:28:29Z 2015-09-15T14:28:29Z 2015-06 2015-01 Article http://purl.org/eprint/type/JournalArticle 0016-8033 1942-2156 http://hdl.handle.net/1721.1/98495 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 https://orcid.org/0000-0002-8814-5495 en_US http://dx.doi.org/10.1190/GEO2014-0364.1 Geophysics 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. application/pdf Society of Exploration Geophysicists Society of Exploration Geophysicists |
| spellingShingle | Zamanian, S. Ahmad Rodi, William L. Kane, Jonathan A. Fehler, Michael Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title | Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title_full | Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title_fullStr | Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title_full_unstemmed | Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title_short | Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach |
| title_sort | iterative estimation of reflectivity and image texture least squares migration with an empirical bayes approach |
| url | http://hdl.handle.net/1721.1/98495 https://orcid.org/0000-0002-8814-5495 |
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