The research of anisotropy is significant for subsurface precise imaging. With rapid development of computation capability and gradual generalization of seismic acquisition with wide azimuth, anisotropy should be taken into consideration. The reverse time migration is based on the accurate solution of two-way wave equation, therefore compared with other methods, it has many advantages, such as no dip limitation and the ability to image turning waves and multiples. Scalar wave equation could be used to calculate the wave field in isotropic media. In anisotropic media, however, P and SV waves are coupled and there is no pure scalar wave mode. Consequently, pseudo acoustic wave (qP-waves) which can represent the kinematic property of P-component in the coupled wave field are usually used for imaging in anisotropic media. In this paper, starting with the P-SV coupled dispersion relation for VTI media, we derive qP wave equation for TTI media, which can be solved using an explicit finite difference format. With the help of acoustic approximation, stable numerical solutions can be obtained for a model with vertical symmetric axis, epsilon >=delta and, if the velocity of shear waves becomes zero along the symmetric axis. However, acoustic approximation will cause the instability of wave field propagation and numerical computation as anisotropic parameters vary in the direction of symmetric axis in TTI media. To solve this problem, we proposed to regularize the finite shear wave equation by adding a regularized term to the original equation. The idea of our method is similar to designing a filter which could attenuate the high wave number components appropriately. We give out the specific form of regularized TTI qP wave equation. Then, the TTI reverse time migration (RTM) method using the regularized wave equation was discussed. In numerical implementation, the computing complexity of our regularized wave equation only increases by one wave field differential and the storage needed only increases by two more wave field. Numerical tests show that by choosing appropriate a, we can obtain stable wave field even with sharp variation of azimuth and dip of tilted axis. For numerical examples, we give out the modelling and RTM results on the Foothill TTI model and the imaging result of field data from a carbonate rock area. When prorogating time of the wavefield is much longer, the traditional finite shear wave equation shows wavefield instability. In contrast, our method can obtain wavefield without any instabilities. In areas with abrupt changes of model parameters, our method may still produce weak SV wave which are viewed as artificial noise in reverse time migration. But for real seismic data, we didn't find any of these SV wave energy in the final migration profile which may be caused by the quite weaker SV energy compared with P wave energy. The RTM imaging with high quality for field seismic data demonstrates that our method works well and can be applied to field data effectively.
