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Full waveform inversion (FWI) is an important and popular technique insubsurface earth property estimation. However, using the least-squares norm inthe misfit function often leads to the local minimum solution of theoptimization problem, and this phenomenon can be explained with thecycle-skipping artifact. Several methods that apply optimal transport distancesto mitigate the cycle-skipping artifact have been proposed recently. Theoptimal transport distance is designed to compare two probability measures. Toovercome the mass equality limit, we introduce an unbalanced optimal transport(UOT) distance with KullbackLeibler divergence to balance the mass difference.Also, a mixed L1/Wasserstein distance is constructed that can preserve theconvex properties with respect to shift, dilation, and amplitude changeoperation. An entropy regularization approach and scaling algorithms are usedto compute the distance and the gradient efficiently. Two strategies ofnormalization methods that transform the seismic signals into non-negativefunctions are provided. Numerical examples are provided to demonstrate theefficiency and effectiveness of the new method.

Application of an unbalanced optimal transport distance and a mixed L1/Wasserstein distance to full waveform inversion