Wave‐mode separation is a critical step in anisotropic elastic‐wave imaging. To avoid high computational costs and additional corrections, we apply a separation formula in the space domain that projects Cartesian components of the elastic wavefield onto the polarization vectors in the orthogonal direction. By solving the Christoffel equation, we implement the conversion from the phase velocity direction to the polarization direction. We use similarity between the seismic wave propagation and the optical flow problem to calculate the phase angle based on the Horn–Schunck algorithm. Compared with the conventional Poynting vector, the optical flow vector is more robust, particularly for complex underground structures. We demonstrate the performance of the proposed approach for two‐dimensional transversely isotropic media with three numerical examples and discuss the potential extension to three‐dimensional media.

中文翻译：

---

使用光流在二维横向各向同性介质中进行弹性波模式分离

波模分离是各向异性弹性波成像的关键步骤。为了避免高昂的计算成本和其他修正，我们在空间域中应用了一个分离公式，该公式将弹性波场的笛卡尔分量投影到正交方向的极化矢量上。通过求解Christoffel方程，我们实现了从相速度方向到极化方向的转换。我们使用地震波传播和光流问题之间的相似性，基于Horn-Schunck算法来计算相角。与传统的坡印廷矢量相比，光流矢量更健壮，尤其是对于复杂的地下结构。