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 ζ, 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 shearwave 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 ζ. 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 ζ while ρ will map into ϵ. For large errors, vs adversely affects the recovery of ζ and might leak into vh while ρ will preferentially leak into ϵ, then ζ and, in smaller proportions, into vh.