We have developed a new approach for acoustic wave modeling in transversely isotropic media with a vertical axis of symmetry. This approach is based on using a pure acoustic wave equation derived from the basic physical laws — Hooke’s law and the equation of motion. We find that the conventional equation noted as a pure quasi-P-wave equation computes only one stress component. In our approach, there is no need to approximate the pseudodifferential operator for decomposition purposes. We make a discrete inverse Fourier transform of the desired frequency response contained in the pseudodifferential operator to build the corresponding spatial operator. We then cut off the operator with a window to reduce edge effects. As a result, the obtained spatial operator is applied locally to the wavefield through a simple convolution. Consequently, we derive an explicit numerical scheme for a pure quasi-P-wave mode. The most important advantage of our method lies in its locality, which means that our spatial operator can be applied in any selected region separately. Our approach can be combined with classical fast finite-difference methods when media are isotropic or elliptically anisotropic, therefore avoiding spurious fields and reducing the total computational time and memory. The accuracy, stability, and absence of residual S-waves of our approach were proven with several numerical examples.

中文翻译：

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VTI介质中的高效声标量波方程建模

我们已经开发出一种在垂直各向同性的横向各向同性介质中进行声波建模的新方法。这种方法基于使用纯声波方程式，该方程式是从基本物理定律（胡克定律）和运动方程式派生而来的。我们发现，记为纯准P波方程的常规方程仅计算一个应力分量。在我们的方法中，无需出于分解目的近似伪微分算子。我们对包含在伪微分算符中的所需频率响应进行离散傅立叶逆变换，以构建相应的空间算符。然后，我们用一个窗口切断运算符以减少边缘效应。结果，通过简单的卷积将获得的空间算子局部应用于波场。所以，我们推导了纯准P波模式的显式数值方案。我们方法的最重要优势在于其局部性，这意味着我们的空间算子可以单独应用于任何选定区域。当介质是各向同性或椭圆各向异性时，我们的方法可以与经典的快速有限差分方法结合使用，因此避免了杂散场并减少了总的计算时间和内存。我们的方法的准确性，稳定性和不存在残留S波，已通过几个数值示例得到了证明。当介质是各向同性或椭圆各向异性时，我们的方法可以与经典的快速有限差分方法结合使用，因此避免了杂散场并减少了总的计算时间和内存。我们的方法的准确性，稳定性和不存在残留S波的情况已通过几个数值示例得到了证明。当介质是各向同性或椭圆各向异性时，我们的方法可以与经典的快速有限差分方法结合使用，因此避免了杂散场并减少了总的计算时间和内存。我们的方法的准确性，稳定性和不存在残留S波，已通过几个数值示例得到了证明。