Robust full-waveform inversion with graph-space optimal transport; application to 3D ocean-bottom cable Valhall data

Improving full-waveform inversion robustness to cycle-skipping has been the subject of a large number of studies. From the several families of approaches developed, one of the most documented consists in modifying the least-squares distance misfit function. From all the propositions made to improve and replace the least-squares distance, only a few of them have been applied to field data. One of the methods proposed recently, the graph space optimal transport distance, presents appealing properties for field data applications. We compare it with the least-squares distance in an analysis performed on the three-dimensional ocean bottom cable data from the Valhall field. We first perform this comparison starting the inversion from the reflection traveltime tomography model used in previous studies. We then perform a second comparison from a crude, linearly varying in-depth one-dimensional velocity model. Starting from this model, least-squares-based full-waveform inversion fails to provide a meaningful estimate of the pressure-wave velocity model due to cycle skipping. We illustrate how the graph-space optimal transport-based full-waveform inversion mitigates this issue. A meaningful estimate of the pressure-wave velocity model is obtained in the zone sampled by both diving and reflected waves, down to almost two kilometers depth.