An advanced analytical technique known as the Oblique Coordinate Wave Function Integral Method builds on Biot’s wave theory for saturated porous material, has been developed to address seismic wave scattering in irregular media. This method employs an integral representation of scattered waves, solved by using an oblique coordinate transformation within a rectangular coordinate system with wave function series expansion methods. The inverse transformation between rectangular and cylindrical coordinate systems frequently presents convergence issues, this method effectively resolves these issues. Moreover, using a Cartesian coordinate system to solve the scattered wave field, overcomes the limitations of earlier methods. Such as the large arc assumption in wave function series expansion, that often did not meet boundary conditions precisely. In addition, this method’s scattering analytical solutions are used to derive the coherence function of multi-point ground motion from the second-moment correlation function of a random process. Lastly, a sensitivity analysis of key parameters, such as canyon depth, incident frequency, and soil porosity, is performed to assess the robustness of the method.

中文翻译：

---

V形场地诱发P1波下多点地震动特性的理论研究


一种称为斜坐标波函数积分方法的先进分析技术建立在 Biot 的饱和多孔材料波动理论的基础上，用于解决不规则介质中的地震波散射问题。该方法采用散射波的积分表示，通过在直角坐标系中使用斜坐标变换和波函数级数展开方法求解。矩形坐标系和圆柱坐标系之间的逆变换经常出现收敛问题，该方法有效地解决了这些问题。此外，使用笛卡尔坐标系求解散射波场克服了早期方法的局限性。例如波函数级数展开中的大圆弧假设，这通常不能精确地满足边界条件。此外，该方法的散射解析解用于从随机过程的第二矩相关函数推导出多点地震动的相干函数。最后，对关键参数（如峡谷深度、入射频率和土壤孔隙度）进行敏感性分析，以评估该方法的稳健性。