Combining diving and reflected waves for velocity model building by waveform inversion

Full Waveform Inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, subcritical reflections and short-spread reflections. Most of the successful applications of FWI have been driven by the information carried out by diving waves and subcritical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches have been recently revisited to retrieve this long-wavelength content from short-spread reflections only using some prior knowledge of the reflectivity. The present study presents a unified formalism, which aims to update the low wavenumbers of the velocity model by joint inversion of the diving waves and the full reflected wavefield. The method relies on an explicit scale separation between a smooth velocity macromodel and reflectivity, which is assumed to be known, and an explicit data separation between the short-spread reflections and the wide-angle arrivals (i.e., diving waves and subcritical reflections). Applications on simple layered models and a synthetic Valhall model show how the low-wavenumber content of the subsurface is emphasized at all depths by keeping only the transmission wavepaths generated by full wavefields in the gradient of FWI.