Full waveform inversion with unbalanced optimal transport distance

Da Li, Michael P. Lamoureux, Wenyuan Liao

Full waveform inversion (FWI) has become a major seismic imaging technique. However, using the least-squares norm in the misfit functional possibly leads to cycle-skipping issue and increases the nonlinearity of the optimization problem. Several works of applying optimal transport distances to mitigate this problem have been proposed recently. The optimal transport distance is to compare two positive measures with equal mass. To overcome the mass equality limit, we introduce an unbalanced optimal transport (UOT) distance with Kullback–Leibler divergence to balance the mass difference. An entropy regularization and a scaling algorithm have been used to compute the distance and its gradient efficiently. Two strategies of normalization methods which transform the seismic signals into non-negative functions have been compared. Numerical examples in one and two dimension have been provided.