Approximate inversion of the wave-equation Hessian via randomized matrix probing
We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a...
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| Format: | Article |
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Society of Exploration Geophysicists
2018
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| Online Access: | http://hdl.handle.net/1721.1/115543 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1826194276134944768 |
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| author | Letourneau, Pierre-David Demanet, Laurent Calandra, Henri |
| 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 Letourneau, Pierre-David Demanet, Laurent Calandra, Henri |
| author_sort | Letourneau, Pierre-David |
| collection | MIT |
| description | We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model. |
| first_indexed | 2024-09-23T09:53:34Z |
| format | Article |
| id | mit-1721.1/115543 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:53:34Z |
| publishDate | 2018 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/1155432022-09-30T17:31:45Z Approximate inversion of the wave-equation Hessian via randomized matrix probing Letourneau, Pierre-David Demanet, Laurent Calandra, Henri Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Department of Mathematics Demanet, Laurent We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model. TOTAL (Firm) Alfred P. Sloan Foundation National Science Foundation (U.S.) 2018-05-21T16:49:45Z 2018-05-21T16:49:45Z 2012 2018-05-17T18:14:45Z Article http://purl.org/eprint/type/ConferencePaper 1949-4645 http://hdl.handle.net/1721.1/115543 Letourneau, Pierre-David, Laurent Demanet, and Henri Calandra. “Approximate Inversion of the Wave-Equation Hessian via Randomized Matrix Probing.” SEG Technical Program Expanded Abstracts 2012 (September 2012). https://orcid.org/0000-0001-7052-5097 http://dx.doi.org/10.1190/SEGAM2012-1262.1 SEG Technical Program Expanded Abstracts 2012 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Society of Exploration Geophysicists MIT Web Domain |
| spellingShingle | Letourneau, Pierre-David Demanet, Laurent Calandra, Henri Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title | Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title_full | Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title_fullStr | Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title_full_unstemmed | Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title_short | Approximate inversion of the wave-equation Hessian via randomized matrix probing |
| title_sort | approximate inversion of the wave equation hessian via randomized matrix probing |
| url | http://hdl.handle.net/1721.1/115543 https://orcid.org/0000-0001-7052-5097 |
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