Efficient reverse time migration method in TTI media based on a pure pseudo-acoustic wave equation

In general, velocity anisotropy in shale media has been widely observed in lab and field work, which means that disregarding this characteristic can lead to inaccurate imaging locations when data are imaged with reverse time migration (RTM). Wavefields simulated with the conventional coupled pseudo-acoustic wave equation may introduce shear wave noise and this equation is only valid in transversely isotropic media (TI, [Formula: see text]). Certain decoupled qP-wave equations require the use of the pseudo-spectral method, which makes them computationally inefficient. To address these issues, we propose a new pure qP acoustic wave equation based on the acoustic assumption, which can be solved more efficiently using the finite difference method. This equation can also be used in the forward modeling process of RTM in tilted transverse isotropic (TTI) media. First, we perform a Taylor expansion of the root term in the pure qP-wave dispersion relation. This leads to an anisotropic dispersion relation that is decomposed into an elliptical anisotropic background factor and a circular correction factor. Second, we obtain the pure qP-wave equation in TTI media without a pseudo-differential operator. The new equation can be efficiently solved using finite difference methods and can be applied to RTM in TTI media with strong anisotropy. The proposed method shows greater tolerance to numerical errors and is better suited for strong anisotropy, as compared to previously published methods. Numerical examples show the high kinematic and phase accuracy of the proposed pure qP-wave equation along with its stability in TTI media characterized by ([Formula: see text]). By utilizing a sag model and an overthrust TTI model, we demonstrate the efficiency and accuracy of the proposed TTI RTM.