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The quadratic Wasserstein metric has shown its power in measuring thedifference between probability densities, which benefits optimization objectivefunction with better convexity and is insensitive to data noise. Nevertheless,it is always an important question to make the seismic signals suitable forcomparison using the quadratic Wasserstein metric. The squaring scaling isworth exploring since it guarantees the convexity caused by data shift.However, as mentioned in [Commun. Inf. Syst., 2019, 19:95-145], the squaringscaling may lose uniqueness and result in more local minima to the misfitfunction. In our previous work [J. Comput. Phys., 2018, 373:188-209], thequadratic Wasserstein metric with squaring scaling was successfully applied tothe earthquake location problem. But it only discussed the inverse problem withfew degrees of freedom. In this work, we will present a more in-depth study onthe combination of squaring scaling technique and the quadratic Wassersteinmetric. By discarding some inapplicable data, picking seismic phases, anddeveloping a new normalization method, we successfully invert the seismicvelocity structure based on the squaring scaling technique and the quadraticWasserstein metric. The numerical experiments suggest that this newly proposedmethod is an efficient approach to obtain more accurate inversion results.

The Quadratic Wasserstein Metric With Squaring Scaling For Seismic Velocity Inversion