Full-waveform inversion in an anisotropic elastic Earth - Can we isolate the role of density and shear wave velocity?

Five parameters are needed to describe VTI anisotropy in 2-D elastic media. With conventional streamer data, an optimal parameterization for full-waveform inversion (FWI) consists in using the horizontal velocity vh, the anellipicity parameter η, and the parameter that relates the horizontal-to-vertical velocity, ε. This parameterization, derived with a pseudo-acoustic formulation of the wave equation, minimizes crosstalks. We extend this analysis to the elastic case and wonder what are the effects of density and shear-wave velocity on the inversion results if ignored. Using radiation patterns derived in the elastic case and a modified version of the Marmousi II model, we see that PP-waves are mostly helping to recover vh and ε, while PS-waves are mostly helping to recover η. For all scattering angles and wave modes, ε and ρ are strongly coupled. Keeping ρ and vs unchanged during the inversion is a valid strategy if their background models are good enough. For small vs and ρ errors, the vs perturbation will map into η while ρ will map into ε. For large errors, vs adversely affects the recovery of η and might leak into vh while ρ will preferentially leak into ε, then η and, in smaller proportions, into vh.