New insights on the graph space optimal transport distance for full waveform inversion
Résumé
Non-convexity issues in full waveform inversion is a topic still deserving significant research efforts. One direction relies on modifying the function measuring the distance between observed and synthetic data on which is based the full waveform inversion process. Recently, optimal transport distances have been considered to play this role. As optimal transport theory has been developed for the comparison of positive functions, adaptation needs to be brought to apply it to the comparison of seismic data which are oscillatory. Among different propositions, the graph space optimal transport distance consists in considering each seismic trace as a point cloud in a time/amplitude two-dimensional space. The method has shown interesting properties in application both to synthetic and three-dimensional field data. In this abstract, we present new insights on this misfit function. We first provide a theoretical comparison with the dynamic time-warping approach. We propose a novel formulation of the graph space optimal transport problem making its application more flexible. We demonstrate the simple form of the second-order derivatives of the corresponding misfit function, making it possible to use standard preconditioning method such as pseudo-Hessian which is illustrated on a synthetic experiment with the Marmousi model.
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