Characterizing the kinematics of seismic waves in elastic vertical transversely isotropic (VTI) media involves four independent parameters. To reduce the complexity, the acoustic approximation for P-waves reduces the number of required parameters to three by setting the vertical S-wave velocity to zero. However, because only the SV-wave phase velocities parallel or perpendicular to the symmetry axis are indirectly set to zero, the acoustic approximation leads to coupled P-wave components and SV-wave artifacts. The new acoustic approximation suggests setting the vertical S-wave velocity as a phase angle-dependent variable so that the SV-wave phase velocity is zero at all phase angles. We find that manipulating this parameter is a valid approach for P-wave approximation but doing so inevitably leads to zero- or nonzero-valued spurious SV-wave components. Thus, we have developed a novel approach to efficiently approximate and thoroughly separate the two wave modes in VTI media. First, the exact P- and SV-wave phase velocity expressions are rewritten by introducing an auxiliary function. After confirming the insensitivity of this function, we construct a new expression for it and obtain simplified P- and SV-wave phase velocity expressions, which are three and four parameters, respectively. This approximation process leads to the same reasonable error for both wave modes. Accuracy analysis indicates that, for the P-wave, the overall accuracy performance of our approach is comparable to that of some existing three-parameter approximations. We then derive the corresponding P- and SV-wave equations in tilted transversely isotropic (TTI) media and provide two available solutions, the hybrid finite-difference/pseudospectral scheme and the low-rank approach. Numerical examples illustrate the separability and high accuracy of the proposed P- and SV-wave simulation methods in TTI media.

中文翻译：

---

横向各向同性介质中 P 波和 SV 波的解耦近似和单独外推

表征弹性垂直横向各向同性 (VTI) 介质中地震波的运动学涉及四个独立参数。为了降低复杂性，P 波的声学近似通过将垂直 S 波速度设置为零将所需参数的数量减少到三个。然而，因为只有平行或垂直于对称轴的 SV 波相速度间接设置为零，声学近似导致耦合 P 波分量和 SV 波伪影。新的声学近似建议将垂直 S 波速度设置为与相角相关的变量，以便 SV 波相速度在所有相角处都为零。我们发现操纵这个参数是 P 波近似的有效方法，但这样做不可避免地会导致零值或非零值的虚假 SV 波分量。因此，我们开发了一种新颖的方法来有效地近似和彻底分离 VTI 介质中的两种波模式。首先，通过引入辅助函数重写精确的 P 波和 SV 波相速度表达式。在确认了该函数的不敏感性后，我们对其构造了一个新的表达式，得到了简化的P波和SV波相速度表达式，分别为三参数和四参数。对于两种波模式，该近似过程导致相同的合理误差。精度分析表明，对于 P 波，我们的方法的整体精度性能与一些现有的三参数近似值相当。然后我们在倾斜的横向各向同性 (TTI) 介质中推导出相应的 P 和 SV 波方程，并提供两种可用的解决方案，混合有限差分/伪光谱方案和低秩方法。数值例子说明了所提出的 P 波和 SV 波模拟方法在 TTI 介质中的可分离性和高精度。