Optimal transport for seismic inversion: tackling the nonlinearity.听
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Full waveform inversion (FWI) is a seismic imaging method which is now part of the conventional imaging workflow in the industry. It is also used for global and regional scale imaging in seismology. Its primary 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 nonconvex. Mitigating this nonconvexity 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.