A recipe for practical full-waveform inversion in anisotropic media: An analytical parameter resolution study

In multiparameter full-waveform inversion (FWI) and specifically one describing the anisotropic behavior of the medium, it is essential that we have an understanding of the parameter resolution possibilities and limits. Because the imaging kernel is at the heart of the inversion engine (the model update), we drew our development and choice of parameters from what we have experienced in imaging seismic data in anisotropic media. In representing the most common (first-order influence and gravity induced) acoustic anisotropy, specifically, a transversely isotropic medium with a vertical symmetry direction (VTI), with the P-wave normal moveout velocity, anisotropy parameters delta, and eta, we obtained a perturbation radiation pattern that has limited trade-off between the parameters. Because delta is weakly resolvable from the kinematics of P-wave propagation, we can use it to play the role that density plays in improving the data fit for an imperfect physical model that ignores the elastic nature of the earth. An FWI scheme that starts from diving waves would benefit from representing the acoustic VTI model with the P-wave horizontal velocity, eta and epsilon. In this representation, the diving waves will help us first resolve the horizontal velocity and then reflections, if the nonlinearity is properly handled, could help us resolve eta, and epsilon could help improve the amplitude fit (instead of the density). The model update wavenumber for acoustic anisotropic FWI is very similar to that for the isotropic case, which is mainly dependent on the scattering angle and frequency.