Joint FWI for imaging deep structures: A graph-space OT approach
Résumé
Joint full waveform inversion (JFWI) aims at building a velocity macromodel of the subsurface by combining early arrivals and reflection waveform inversions. JFWI requires an explicit separation between early-arrivals and reflections, which is accomplished by applying time-windows to the data in practice. The JFWI approach is formulated as a workflow in which one repeatedly alternates two steps: the velocity macromodel is reconstructed assuming a known perturbation model, then the perturbation model is updated using the previously retrieved velocity as the background model. The perturbation model is used as an input to build the low-wavenumber sensitivity kernel along the two-way reflection paths. JFWI followed by FWI can further enrich the high-wavenumber contents of the subsurface model. However, JFWI, as FWI, suffers from cycleskipping issues because one attempts to fit the data using the $\ell^2$ misfit function. Optimal transport (OT) distances have been recently proposed to mitigate the non-convexity of the $\ell^2$ misfit function in seismic imaging. Nevertheless, OT is initially designed to compare probability distributions, which is not the case for the original seismic data due to the oscillatory and signed natures. To overcome this difficulty, one possibility is to compare the discrete graph of data through OT. In this study, we assess the graph-space OT based JFWI approach for the inversion of 2D streamer synthetic data with a limited offset range (6 km) for the Marmousi model. Starting form a 1D linear model, GSOT-JFWI is less prone to cycle skipping than in the $\ell^2$-JFWI case, and consequently provides a sufficient initial velocity macromodel for subsequent FWI.
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