Seminar in Numerical Analysis: Ludovic Métivier (Université Grenoble Alpes)
Full waveform inversion (FWI) is a powerful high resolution seismic imaging method, used in the academy for global and regional scale imaging, and in the oil & gas industry for exploration purposes. It can be understood as a PDE constrained optimization problem: the misfit between recorded seismic data and synthetic seismic data computed as the solution of a wave propagation problem is reduced over a space of parameters controlling the wave propagation. One of the main limitation of FWI is its dependency on the accuracy of the initial guess of the solution. This limitation is due to the non-convexity of the standard least-squares misfit function used to measure the discrepancy between recorded and synthetic data, and the use of local optimization techniques to reduce this misfit. In recent studies, we have studied the interest for using a misfit function based on an optimal transport distance to mitigate this issue. The convexity of this distance with respect to shifted patterns is the main reason why we are interested in this distance, as it can be seen as a proxy for the convexity with respect to the wave velocities we want to reconstruct. In this talk, we will give an overview of this work, starting by introducing basic concepts on optimal transport, before detailing the difficulties for using the optimal transport distance in the framework of FWI, and reviewing the solutions we have proposed.
Veranstaltung übernehmen als iCal