Viscoelastic and anisotropic characteristics of subsurface media cause phase dispersion and amplitude dissipation of seis-mic 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 com-bining the pure qP-wave dispersion relation based on acoustic approximation with the constant-Q attenuation model.The newly de-rived wave equation contains decoupled phase dispersion and amplitude loss terms,and it is conducive to the implementation of at-tenuation-compensated reverse time migration.Based on the newly derived wave equation,the finite-difference low-rank decomposi-tion 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.
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