A short note on rank-2 relaxation for waveform inversion
Author(s)Cosse, Augustin M.; Shank, Stephen; Demanet, Laurent
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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.
DepartmentMassachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences; Massachusetts Institute of Technology. Department of Mathematics
SEG Technical Program Expanded Abstracts 2015
Society of Exploration Geophysicists
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).
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