Modeling of High Accuracy Pure Acoustic Wave Equations in Transversely Isotropic Media Using Optimized Pseudo-Analytical Method

The previous pure acoustic anisotropic wave equations (PAAWEs) mainly derived from the decoupled elastic wavefield and had complicated spatial pseudo differential operator (SPDO). It can directly apply some spectral methods to these equations or employ series expansions to approximate the SPDO and then solve the approximate pure P-wave equations. Considering the spectral methods need fairly large computational load and low-order series expansions have accuracy loss in some cases, here, we present the corresponding solutions to these issues. The square root term in Alkhalifah’s accurate dispersion relation in transversely isotropic (TI) media is expanded by arbitrary-order expansions and the corresponding PAAWEs are efficiently solved by the normalized pseudo-analytical method (NPAM) based on optimized pseudo-differential operator (OPO). Our analyses of phase velocity errors indicate that the accuracy of new expressions is perfectly acceptable for majority anisotropic parameters. The effectiveness of the proposed method also can be verified by several numerical examples and reverse time migration (RTM) profile.