Comment on 'Geophysical inversion and optimal transport' by M. Sambridge, A. Jackson and A. P. Valentine. Issue 2 (5th January 2023) - Okazaki, Tomohisa; Ueda, Naonori
SUMMARY: 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.