Efficient mixed-domain pure P-wave equations for 2D and 3D tilted transversely isotropic media

In transversely isotropic (TI) media, accurate and efficient pure P-wave extrapolation is the basis of seismic imaging and inversion algorithms. For pure P-wave equations in TI media, combining the finite-difference (FD) method with the pseudo-spectral (PS) method is an effective solution. However, if the mixed-domain pure P-wave equation contains multiple wavenumbers, using the hybrid approach will involve multiple Fourier transforms, which will result in high computational costs. Referring to the weak anisotropy approximation, we propose a new approximate P-wave phase velocity expression. We then use an optimization strategy to reduce the number of wavenumber terms in the corresponding dispersion relations and derive the mixed-domain pure P-wave equations in 2D and 3D tilted transversely isotropic (TTI) media. Through numerical experiments in 2D and 3D TTI models, we verify the feasibility and efficiency of the proposed mixed-domain P-wave equations.