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We consider the high-resolution seismic imaging method called full-waveforminversion (FWI). FWI is a data fitting method aimed at inverting for subsurfacemechanical parameters. Despite the large adoption of FWI by the academic andindustrial communities, and many successful results, FWI still suffers fromsevere limitations. From a mathematical standpoint, FWI is a large scalePDE-constrained optimization problem. The misfit function that is used, whichmeasures the discrepancy between observed seismic data and data calculatedthrough the solution of a wave propagation problem, is non-convex. Afterdiscretization, the size of the FWI problem requires the use of localoptimization solvers, which are prone to converge towards local minima. Thusthe success of FWI strongly depends on the choice of the initial model toensure the convergence towards the global minimum of the misfit function.  This limitation has been the motivation for a large variety of strategies.Among the different methods that have been investigated, the use of optimaltransport (OT) distances-based misfit functions has been recently promoted. Theleading idea is to benefit from the inherent convexity of OT distances withrespect to dilation and translation to render the FWI problem more convex.However, the application of OT distances in the framework of FWI is notstraightforward, as seismic data is signed, while OT has been developed for thecomparison of probability measures.  The purpose of this study is to review two methods that were developed toovercome this difficulty. Both have been successfully applied to field data inan industrial framework. Both make it possible to better exploit the seismicdata, alleviating the sensitivity to the initial model and to variousconventional workflow steps, and reducing the uncertainty attached to thesubsurface mechanical parameters inversion.

A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform