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Conventional full waveform inversion (FWI) using least square distance (LSD)between the observed and predicted seismograms suffers from local minima.Recently, earth mover's distance (EMD) has been introduced to FWI to computethe misfit between two seismograms. Instead of comparisons bin by bin, EMDallows to compare signal intensities across different coordinates. This measurehas great potential to account for time and space shifts of events withinseismograms. However, there are two main challenges in application of EMD toFWI. The first one is that the compared signals need to satisfy nonnegativityand mass conservation assumptions. The second one is that the computation ofEMD between two seismograms is a computationally expensive problem. In thispaper, a strategy is used to satisfy the two assumptions via decomposition andrecombination of original seismic data. In addition, the computation of EMDbased on dynamic formulation is formulated as a convex optimization problem. Aprimal-dual hybrid gradient method with linesearch has been developed to solvethis large-scale optimization problem on GPU device. The advantages of the newmethod are that it is easy to implement and has high computational efficiency.Compared to LSD based FWI, the computation time of the proposed method willapproximately increase by 11% in our case studies. A 1D time-shift signals casestudy has indicated that EMD is more effective in capturing time shift andmakes the misfit function more convex. Two applications to synthetic data usingtransmissive and reflective recording geometries have demonstrated theeffectiveness of EMD in mitigating cycle-skipping issues. We have also appliedthe proposed method to SEG 2014 benchmark data, which has further demonstratedthat EMD can mitigate local minima and provide reliable velocity estimationswithout using low frequency information in the recorded data.

Misfit function for full waveform inversion based on Earth Mover's Distance with dynamic formulation