Pseudotime domain joint diving-reflected FWI using graph-space optimal transport

Reflection waveform inversion updates the P-wave velocity (Vp) macromodel beyond the depths sampled by diving waves, exploiting wide scattering angle wavepaths in a reflective subsurface. Joint full waveform inversion combines reflection waveform inversion and early-arrival waveform inversion, thereby constraining the shallow subsurface whilst enriching the low-wavenumber content of the deep Vp model with reflections. In depth-domain Vp inversion, ensuring consistency between reflectors positions and model kinematics comes at the cost of repeated least-square migrations, combined with carefully designed offset weighting. In order to efficiently address such co-dependency between reflective and kinematic parameters, we propose to cast joint full waveform inversion in the pseudotime domain. In this formulation, as Vp is updated, the reflectors are consistently repositioned in depth, in order to honor the zero-offset two-way-time seismic invariant and keep the short-spread reflections in phase. By combining a pseudotime approach with a graph-space optimal transport objective function, we show that it is possible to reconstruct a complex velocity macromodel from short offset 2D reflection data containing surface-related multiples and ghosts, starting from a 1D initial guess. Compared to a depth-domain inversion, the computing cost is reduced by one order of magnitude, associated with a significant saving in man-time, thanks to a simpler design of data weighting and inversion strategy.