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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Technical Report |
| Language: | en_US |
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Massachusetts Institute of Technology. Earth Resources Laboratory
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/90470 |
| _version_ | 1826218009244467200 |
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| author | Letourneau, Pierre-David Demanet, Laurent Calandra, Henri |
| author2 | Massachusetts Institute of Technology. Earth Resources Laboratory |
| author_facet | Massachusetts Institute of Technology. Earth Resources Laboratory 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 | 2024-09-23T17:12:41Z |
| format | Technical Report |
| id | mit-1721.1/90470 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:12:41Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology. Earth Resources Laboratory |
| record_format | dspace |
| spelling | mit-1721.1/904702019-04-12T22:07:56Z Approximate inversion of the wave-equation Hessian via randomized matrix probing Letourneau, Pierre-David Demanet, Laurent Calandra, Henri Massachusetts Institute of Technology. Earth Resources Laboratory Inversion 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. National Science Foundation (U.S.); Alfred P. Sloan Foundation 2014-09-30T14:22:03Z 2014-09-30T14:22:03Z 2012 Technical Report http://hdl.handle.net/1721.1/90470 en_US Earth Resources Laboratory Industry Consortia Annual Report;2012-21 application/pdf Massachusetts Institute of Technology. Earth Resources Laboratory |
| spellingShingle | Inversion 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 |
| topic | Inversion |
| url | http://hdl.handle.net/1721.1/90470 |
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