A short note on rank-2 relaxation for waveform inversion
This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimen...
| Principais autores: | , , |
|---|---|
| Outros Autores: | |
| Formato: | Artigo |
| Publicado em: |
Society of Exploration Geophysicists
2018
|
| Acesso em linha: | http://hdl.handle.net/1721.1/115501 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1826198419399507968 |
|---|---|
| author | Cosse, Augustin M. Shank, Stephen Demanet, Laurent |
| 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 Cosse, Augustin M. Shank, Stephen Demanet, Laurent |
| author_sort | Cosse, Augustin M. |
| collection | MIT |
| description | This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimensional space. While this idea has mostly been a theoretical curiosity so far, the novelty of this note is the suggestion that a modified adjoint-state method enables algorithmic scalability of the relaxed formulation to standard 2D community models in geophysical imaging. Numerical experiments show that the new formulation leads to a modest increase in the basin of attraction of least-squares waveform inversion. |
| first_indexed | 2024-09-23T11:04:36Z |
| format | Article |
| id | mit-1721.1/115501 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:04:36Z |
| publishDate | 2018 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/1155012022-10-01T01:03:18Z A short note on rank-2 relaxation for waveform inversion Cosse, Augustin M. Shank, Stephen Demanet, Laurent Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Department of Mathematics Cosse, Augustin M. Shank, Stephen Demanet, Laurent This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimensional space. While this idea has mostly been a theoretical curiosity so far, the novelty of this note is the suggestion that a modified adjoint-state method enables algorithmic scalability of the relaxed formulation to standard 2D community models in geophysical imaging. Numerical experiments show that the new formulation leads to a modest increase in the basin of attraction of least-squares waveform inversion. TOTAL (Firm) Belgian National Foundation for Scientific Research MIT International Science and Technology Initiatives United States. Air Force. Office of Scientific Research United States. Office of Naval Research National Science Foundation (U.S.) 2018-05-18T18:40:07Z 2018-05-18T18:40:07Z 2015 2018-05-17T17:38:57Z Article http://purl.org/eprint/type/ConferencePaper 1949-4645 http://hdl.handle.net/1721.1/115501 Cosse, Augustin, Stephen D. Shank, and Laurent Demanet. “A Short Note on Rank-2 Relaxation for Waveform Inversion.” SEG Technical Program Expanded Abstracts 2015 (August 19, 2015). https://orcid.org/0000-0001-7052-5097 http://dx.doi.org/10.1190/SEGAM2015-5925071.1 SEG Technical Program Expanded Abstracts 2015 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 | Cosse, Augustin M. Shank, Stephen Demanet, Laurent A short note on rank-2 relaxation for waveform inversion |
| title | A short note on rank-2 relaxation for waveform inversion |
| title_full | A short note on rank-2 relaxation for waveform inversion |
| title_fullStr | A short note on rank-2 relaxation for waveform inversion |
| title_full_unstemmed | A short note on rank-2 relaxation for waveform inversion |
| title_short | A short note on rank-2 relaxation for waveform inversion |
| title_sort | short note on rank 2 relaxation for waveform inversion |
| url | http://hdl.handle.net/1721.1/115501 https://orcid.org/0000-0001-7052-5097 |
| work_keys_str_mv | AT cosseaugustinm ashortnoteonrank2relaxationforwaveforminversion AT shankstephen ashortnoteonrank2relaxationforwaveforminversion AT demanetlaurent ashortnoteonrank2relaxationforwaveforminversion AT cosseaugustinm shortnoteonrank2relaxationforwaveforminversion AT shankstephen shortnoteonrank2relaxationforwaveforminversion AT demanetlaurent shortnoteonrank2relaxationforwaveforminversion |