Simulation of pure qP-wave in vertical transversely isotropic media

Acoustic wave equations are widely employed in wavefield extrapolation and inversion due to their simplicity compared to the elastic wave equations. In anisotropic media, qP- and qSV-waves are coupled. Multiple acoustic approximations in the vertical transversely isotropic (VTI) media have been proposed during the last decades. A classic way is to set the vertical S-wave velocity zero. As such, the S-wave artefacts still exist, whose amplitude increases with anisotropy. Setting S-wave velocity zero in all propagating directions tackles the issue. However, the higher-order spatial derivatives in the pure qP-wave equation make it hard to solve in the space domain. The spatial derivatives in the denominator of the pure qP-wave equation make the solution by the spatial-domain finite-difference unstable.  In this study, we employed the time-domain pseudospectral method to solve both the classic acoustic wave equation and the pure qP-wave equation in VTI media. Hybrid absorbing boundary conditions are used. Both equations are applied to reverse time migration (RTM) for the anisotropic Marmousi model. The new qP-wave equation outperformed the classic qP-wave equation regarding the computational time. Further work can be extended to waveform inversion with the pure qP-wave equation.