Comment on 'Geophysical inversion and optimal transport' by M. Sambridge, A. Jackson and A. P. Valentine

A similarity measure between waveforms developed by Sambridge et al. realized an effective use of optimal transport as well as computational efficiency through the marginalization of a 2-D probability distribution obtained from a seismogram. We demonstrate that information loss due to marginalization could lead to significant non-uniqueness in the resulting measure and propose the use of the sliced Wasserstein distance as a potential solution. This formulation may enhance the robustness of the method developed by Sambridge et al. by maintaining its computational efficiency.