Computational Mathematics and Scientific Computing Seminar
Optimal Transport for Seismic Inversion: Tackling the Nonlinearity
Speaker: Yunan Yang, Courant
Location: Warren Weaver Hall 1302
Date: Nov. 9, 2018, 10 a.m.
Full waveform inversion (FWI) is a seismic imaging method which is is now part of the conventional imaging workflow in the industry. It is also used for global and regional scale imaging in seismology. Its main interest compared to tomography is its high resolution power. FWI is formulated as a least-squares (L2) minimization problem. The L2 misfit function is highly non convex. Mitigating this non convexity is a longstanding difficulty. Despite important advances yielding successful applications through multi-scale approaches, obtaining robust and flexible FWI algorithms remains a challenge. We have proposed to use the Wasserstein distance as a misfit function. This distance, from the optimal transport (OT) theory, is convex with respect to shifted patterns. For FWI, the convexity with respect to time-shifts is a proxy for the convexity with respect to the subsurface velocities, making the Wasserstein distance a very attractive tool.