A parametrization study for surface seismic full waveform inversion in an acoustic vertical transversely isotropic medium

SUMMARY Full waveform inversion (FWI) of surface seismic data requires low-frequency and long-offset data, namely diving waves or post-critical reflections, to update the long wavelength features of the parameters. In most geological settings, short and long offsets cannot be interpreted simultaneously without accounting for anisotropy. FWI therefore may require anisotropic modelling, which leads to the question of the parametrization of the inversion, since it is not possible to retrieve all the earth models from pressure (or vertical displacement) data, even in the simple vertical transversely isotropic (VTI) case. With a change of variables in the acoustic VTI wave equations, it can be shown that, in the context of macromodel building, namely background estimation, acoustic VTI FWI mainly depends on the normal moveout (NMO) velocity and the horizontal velocity (or equivalently a combination of these two velocities). An analysis of the eigenvalue/eigenvector decomposition of the Hessian confirms the relevance of the parametrization of the VTI wave equations with the NMO and horizontal velocities. It also points out a possible ambiguity when one inverts for two parameters. This ambiguity is further illustrated in synthetic examples. The trade-off between velocity heterogeneities and anisotropy also complicates the recovery of the second anisotropic parameter η. Nevertheless, FWI successfully interprets the kinematics of the data.