Efficient pure qP-wave modeling and reverse time migration in tilted transversely isotropic media calculated by a finite-difference approach

Subsurface anisotropy is commonly induced by shale layers, aligned cracks and fine bedding, and has a significant impact on seismic wave propagation. Ignoring anisotropic effects during seismic migration will degrade image quality. Therefore, we derive a pure qP-wave equation with high accuracy for modeling seismic wave propagation in tilted transversely isotropic (TTI) media. However, the derived pure qP-wave equation requires a computationally expensive spectral-based method for performing numerical simulations. This is unsuitable for large-scale industrial applications, particularly three-dimension applications. For numerical efficiency, we first decompose the newly derived wave equation into some fractional differential operators and spatial derivatives. The spatial derivatives can be directly solved by conventional finite-difference (FD) approaches. Then, we employ an asymptotic approximation to find an equivalent form of fractional differential operators, obtaining scalar operators that we can discretize with the FD method. Numerical tests show that the proposed TTI pure qP-wave equation with an FD discretization can produce accurate and highly efficient wavefield simulations in TTI media. We also use the proposed TTI pure qP-wave equation with an FD discretization as a forward engine to implement TTI reverse time migration (RTM). Synthetic examples and a field data test demonstrate that the proposed TTI RTM can effectively correct the anisotropic effects, providing high-quality imaging results while maintaining good computational efficiency.