Abstract: Reverse Time Migration (RTM) is a core technique for seismic imaging in complex structures. A key challenge in anisotropic RTM is constructing a pure qP-wave equation free of pseudo-shear-wave artifacts. In this study, we compare and analyze the dispersion relation derived from the new acoustic approximation with the accurate qP-wave dispersion relation developed by Li. Based on Li’s more precise dispersion relation, we derive a pure qP-wave equation for vertical transversely isotropic (VTI) media using the elliptic decomposition method. Furthermore, by introducing a self-adjoint differential operator, we establish a first-order velocity-stress wave equation for pure qP-waves in tilted transverse isotropy (TTI) media. Forward modeling based on the high-precision dispersion relation is implemented using a staggered-grid finite-difference method. Additionally, a second-order displacement equation for pure qP-waves in TTI media is derived via the wavenumber rotation approach and solved using a conventional grid finite-difference scheme. Both dispersion analysis and model tests demonstrate that the equations based on the updated dispersion relation achieve higher accuracy than those derived from the new acoustic approximation. When solved using the staggered-grid finite-difference method, the first-order velocity-stress equation effectively mitigates amplitude imbalance induced by the asymptotic approximation while maintaining favorable computational efficiency.