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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Published: |
Society of Exploration Geophysicists
2018
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| Online Access: | http://hdl.handle.net/1721.1/115501 https://orcid.org/0000-0001-7052-5097 |
| Summary: | 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. |
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