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

Abstract

Improving full-waveform inversion to make it more robust 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 defining the discrepancy between observed and calculated data. 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. This study compares it with the least-squares distance in an analysis performed on the three-dimensional ocean bottom cable data from the Valhall field. This data has already been at the heart of several full-waveform inversion studies, making it a good candidate to evaluate the properties of this new misfit function. 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. To our knowledge, this is the first application of a graph space optimal transport-based full-waveform inversion to three-dimensional field data.

Robust and efficient waveform-based velocity-model building by optimal transport in the pseudotime domain: Methodology

“…Though no offset windowing has been necessary in those datasets, a multi-scale approach was adopted to further minimize the risk of cycle-skipping. This is consistent with the real data application of GSOT-FWI shown in Górszczyk et al (2021) and Pladys et al (2022), who also show that GSOT does not altogether eliminate the need for data selection and weighting. The extra cost of GSOT with respect to L 2 norm in these 2D examples has been in the order of 20%.…”

“…Cycle skipping is likely to occur at intermediate-to-long offsets in least-squares V p waveform inversion when the traveltime prediction error is larger than half a dominant period. Among different misfit function alternatives to L 2 , the graph-space optimal transport (GSOT) distance has shown interesting properties to mitigate cycle skipping for conventional FWI applications (Górszczyk et al, 2021;Pladys et al, 2022). The conceptual core of GSOT is the re-mapping of each seismic trace as a two-dimensional discrete distribution of K unit-weight points (point cloud) in a time-amplitude space (graph space).…”

A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform

“…However, KR FWI shows a much better matching than least-squares FWI, which is an indication that KR FWI has converged to a better minimum thanks its enhanced convexity. The results presented here are extracted from a recently published study [64].…”

Robust localized adaptive waveform inversion: A new regularization for Gabor deconvolution

“…Thus, compared to direct projecting all information contained in observed data onto gradient, it could be more suitable if the gradient is constructed by only accounting for the events in the predicted data and gently including more information in observed data, especially when facing the cycle-skipping issue. This is the philosophy behind the layer-stripping strategy, which is effective to mitigate the cycle-skipping issue and widely used in practice (Wang and Rao, 2009;Pladys et al, 2022). The zero-type regularization naturally follows this principle.…”