Modeling and RTM for arbitrary-order pure acoustic wave equation in VTI media using normalized pseudo-analytical method

The conventional pseudo-acoustic wave equations（PWEs） in vertical transversely isotropic（VTI）media may generate SV-wave artifacts and propagation instabilities when anisotropy parameters cannot satisfy the pseudo-acoustic assumption. One solution to these issues is to use pure acoustic anisotropic wave equations, which can produce stable and pure P-wave responses without any SVwave pollutions. The commonly used pure acoustic wave equations（PAWEs） in VTI media are mainly derived from the decoupled P-SV dispersion relation based on first-order Taylor-series expansion（TE）, thus they will suffer from accuracy loss in strongly anisotropic media. In this paper, we adopt arbitrary-order TE to expand the square root term in Alkhalifah＇s accurate acoustic VTI dispersion relation and solve the corresponding PAWE using the normalized pseudoanalytical method（NPAM） based on optimized pseudodifferential operator. Our analysis of phase velocity errors indicates that the accuracy of our new expression is perfectly acceptable for majority anisotropy parameters. The effectiveness of our proposed scheme also can be demonstrated by several numerical examples and reverse-time migration（RTM） result.