A separable strong-anisotropy approximation for pure qP-wave propagation in transversely isotropic media

The wave equation can be tailored to describe wave propagation in vertical-symmetry axis transversely isotropic (VTI) media. The qP- and qS-wave eikonal equations derived from the VTI wave equation indicate that in the pseudoacoustic approximation, their dispersion relations degenerate into a single one. Therefore, when using this dispersion relation for wave simulation, for instance, by means of finite-difference approximations, both events are generated. To avoid the occurrence of the pseudo-S-wave, the qP-wave dispersion relation alone needs to be approximated. This can be done with or without the pseudoacoustic approximation. A Padé expansion of the exact qP-wave dispersion relation leads to a very good approximation. Our implementation of a separable version of this equation in the mixed space-wavenumber domain permits it to be compared with a low-rank solution of the exact qP-wave dispersion relation. Our numerical experiments showed that this approximation can provide highly accurate wavefields, even in strongly anisotropic inhomogeneous media.