Based on the two-dimensional (2D) three-component first-order velocity-stress equation,the high order staggered mesh finite difference numerical simulation method was used to simulate the elastic and viscoelastic tilted transversely isotropic (TTI) media.The perfect matched layer (PML) absorption boundary condition was selected to eliminate the boundary effect.The results show that: (①)Under the condition of fixed elastic parameters of elastic TTI medium,when the polarization angle and azimuth are 60° and 45° respectively,the degree of shear wave splitting is significantly greater than the angle of 0°;② The influence of viscoelasticity on TTI medium is mainly reflected in the amplitude.If the quality factor decreases,the attenuation of the seismic wave amplitude increases,causing the waveform to become wider and distorted.If the quality factor increases,the viscoelastic medium becomes closer to elastic medium;③ For TTI medium with different polarization angle and azimuth angle in the upper and lower layers,the shear wave can multiple splits at the interface of medium.The symmetry of seismograms is affected by the polarization angle and azimuth angle of TTI medium;④ Viscoelasticity has a great influence on reflected wave,transmitted wave and converted wave in the low-velocity model.When the viscoelasticity is strong,the weaker waves may not be shown.