A short note on rank-2 relaxation for waveform inversion

• Main Authors: Cosse, Augustin M. (Contributor), Shank, Stephen (Contributor), Demanet, Laurent (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Society of Exploration Geophysicists, 2018-05-18T18:40:07Z.
• Subjects: Article
• Online Access: Get fulltext

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.)