A short note on rank-2 relaxation for waveform inversion
Name
note-r2as.pdf
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386.15 KB
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Adobe PDF
Checksum (MD5)
daa7634e866de0039389219a06891c26
Author(s)
Cosse, Augustin M.
Shank, Stephen
Demanet, Laurent
Date Issued
2015
Journal
SEG Technical Program Expanded Abstracts 2015
Publisher
Society of Exploration Geophysicists
Citation
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).
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1190/SEGAM2015-5925071.1
