Wide-angle seismic refraction profiles are commonly undertaken to image crust and uppermost mantle structure. Seismic waveform data like those above (black phases in panels above) encode variations in subsurface velocity and density but are typically band limited. As a consequence, traditional inversion approaches are highly susceptible to cycle-skipping, a manifestation of nonlinearity in the inverse problem.
Górszczyk et al.  employ a new inverse formulation based on optimal transport theory to mitigate this nonlinearity and apply it to observations from the Nankai Trough in Japan. They demonstrate successful solution recovery (blue phases are predicted data from solution in lower panel) even when the initial model is far from the solution (red/blue phases are predicted data from initial model).
Citation: Górszczyk, A., Brossier, R., & Métivier, L. . Graph-space optimal transport concept for time-domain full-waveform inversion of ocean-bottom seismometer data: Nankai Trough velocity structure reconstructed from a 1D model. Journal of Geophysical Research: Solid Earth, 126, e2020JB021504. https://doi.org/10.1029/2020JB021504
—Michael Bostock, Editor, JGR: Solid Earth