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.

中文翻译：

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2D和3D倾斜横向各向同性介质的有效混合域纯P波方程

在横观各向同性（TI）介质中，准确有效的纯P波外推是地震成像和反演算法的基础。对于TI介质中的纯P波方程，将有限差分（FD）方法与伪谱（PS）方法相结合是一种有效的解决方案。但是，如果混合域纯P波方程包含多个波数，则使用混合方法将涉及多个傅里叶变换，这将导致较高的计算成本。参照弱各向异性近似，我们提出了一个新的近似P波相速度表达式。然后，我们使用一种优化策略来减少相应色散关系中波数项的数量，并导出2D和3D倾斜横向各向同性（TTI）介质中的混合域纯P波方程。