Robust and efficient waveform-based velocity model building by optimal transport in the pseudotime domain; an ocean-bottom cable case study in the North Sea

Full-waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from noninformative initial models are the susceptibility to cycle skipping and a lack of sensitivity to low wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom cable 3D data set, a novel VP building methodology is applied that addresses those issues by jointly inverting reflections and refractions (joint full-waveform inversion [JFWI]) using a robust misfit function in the vertical traveltime domain (pseudotime). Pseudotime addresses reflectivity-velocity coupling and attenuates phase ambiguities at short offsets, whereas a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstruction is obtained prior to JFWI thanks to an asymptotic-preconditioned impedance waveform inversion (IpWI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI, starting from the JFWI-based model, injects the high wavenumbers missing in the JFWI solution, attaining apparent improvements in shallow and deep model reconstruction and imaging compared with the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.