Optimal transport distance for seismic imaging using full waveform inversion

Full waveform inversion is a high resolution seismic imaging method, which can be applied at various scales to obtain estimation of the mechanical properties of the subsurface. It is based one the minimization between observed and modeled seismic data. One well-known issue of full waveform inversion is the non-convexity of the least-squares misfit function which measures the distance between observed and modeled data which is conventionally used. This non-convexity, together with the necessity to rely on local minimization algorithms (due to the inherent size of applications) makes this inverse problem ill-posed.

One possibility to mitigate this non-convexity is to modify the misfit function. Recently, the use of optimal transport distance has attracted attention, for its convexity properties with respect to translation and dilation. In this presentation we discuss how optimal transport distances can be applied to the comparison of seismic data in the frame of full waveform inversion. The main difficulty is that optimal transport theory is developed for the comparison of probability measure, while we have to deal with signed data in this application. We discuss how we can manage this difficulty by interpreting the discrete graph of the data through optimal transport. We discuss the fundamentals of this technique (mathematical property, high performance computing implementation), before presenting applications on synthetic and field data.