Convexity of the quadratic Wasserstein metric as a misfit function for full waveform inversion

摘要

We analyze the properties of Wasserstein metric, a new misfit function for full waveform inversion (FWI) and prove such properties as convexity in different aspects. Considering the observed data and predicted data as two density functions, the quadratic Wasserstein metric corresponds to the optimal cost of rearranging one function into the other with a cost function that is quadratic in distance. In other words, we match the observed data and the predicted data by the optimal map which takes the information geometry of the data sets into consideration. The inversion follows the normal scheme of FWI as a PDE-constrained optimization. The velocity model can be updated using a gradient- based optimization with the new adjoint source.