Abstract: Viscoelastic and anisotropic characteristics of subsurface media cause phase dispersion and amplitude dissipation of seismic waves.If these undesired effects are ignored during seismic processing, distorted events and migration artifacts may appear in imaging results.The traditional pseudo-acoustic qP-wave equation for viscoacoustic TTI media can be used to simulate seismic-wave propagation in viscoacoustic anisotropic media.However, this equation produces shear wave artifacts, and its application is limited by model parameters (ε>δ).To address this issue, a pure qP-wave equation for viscoacoustic TTI media is derived by combining the pure qP-wave dispersion relation based on acoustic approximation with the constant-Q attenuation model.The newly derived wave equation contains decoupled phase dispersion and amplitude loss terms, and it is conducive to the implementation of attenuation-compensated reverse time migration.Based on the newly derived wave equation, the finite-difference low-rank decomposition strategy is proposed to realize pure qP-wave forward modeling for viscoacoustic TTI media.The numerical simulation results show that the newly derived wave equation overcomes the limitation of pseudo-acoustic qP-wave equation for viscoacoustic TTI media and can simulate seismic-wave propagation in viscoacoustic anisotropic media accurately and stably.In addition, the finite-difference low-rank decomposition strategy developed in this paper inherits the high efficiency of finite-difference solutions and has higher computational efficiency than traditional low-rank decomposition methods.