The anisotropy and attenuation features of subsurface media significantly affect seismic data processing. Ignoring anisotropy and attenuation in seismic wave propagation may result in inaccurate reflector positions, dimming amplitudes, and reduced spatial resolution in the imaging results. Therefore, accurate seismic wave modeling of anisotropy and attenuation is essential for understanding wave propagation in the earth’s interior. This paper derives three pure-viscoacoustic-wave equations from characterizing the earth’s frequency-independent Q behavior in transversely isotropic (TI) media. First, we develop three time-space domain pure-qP-wave equations in TI media based on different approximation methods, whose coefficients can be determined by different approximation methods and Thomsen’s anisotropic parameters ε, δ. Subsequently, we introduce the Kelvin-Voigt attenuation model into our derived three time-space domain pure-qP-wave equations and then obtain three pure-viscoacoustic-wave equations. To further demonstrate the effectiveness and accuracy of our methods, we provide some 2D and 3D numerical tests. The numerical results indicate that the wavefield generated by pure-qP-wave equations and pure-viscoacoustic-wave equations have accurate kinematic characteristics of qP-wave in TI media and attenuated TI media and are free of S-wave artifacts while remaining stable under Thomsen’s anisotropic parameters ε<δ, so our methods have broader applicability compared with some existing methods. At the same time, the simulation results of pure-viscoacoustic-wave equations also reflect the absorption and attenuation characteristics of qP-waves in attenuated TI media.

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