Full waveform inversion with unbalanced optimal transport distance
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Full waveform inversion (FWI) is an important and popular technique in subsurface earth property estimation. However, using the least-squares norm in the misfit function often leads to cycle-skipping artifacts, increased nonlinearity of the optimization problem and local minima. Several methods that apply optimal transport distances to mitigate this problem have been proposed recently. The optimal transport distance is to compare two positive signals 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 is used to compute the distance and its gradient efficiently. Two strategies of normalization methods which transform the seismic signals into non-negative functions are compared. Numerical examples in one and two dimension are solved to demonstrate the efficiency and effectiveness of the new method.
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