局部不规则地形及复杂介质对SH波的散射与地震动

多年来，地形地貌一直是影响地震动特征的主要因素之一。本项目旨在研究不规则地形及复杂介质条件对SH波的散射与地震动问题。对于复杂的凸起地形，无法直接通过分离变量法推导出问题的解析解。本项目提出一种新颖的区域划分方式，将山体模型进行多次“分区”，得到多个子区域，以便利用波函数展开法进行求解。而对于形状特殊的子区域，本项目拟给出有效的波场表达式构造方法。以上方法可用于研究包括非对称等多种复杂不规则凸起地形对地震波响应。针对复杂地质条件，基于复变函数法进行保角变换，推导出合适的介质非均匀变化函数，并结合局部地形研究非均匀介质条件下局部地形对SH波传播的影响。

Over the years, topography has been considered as one of the main factors affecting the characteristics of ground motion. This project aims to study the scattering of SH waves by complex geological conditions and irregular surfaces. For complex convex topography, the analytical solution of the problem cannot be deduced directly by the method of separating variables. In this project, a novel regional division method is proposed. The hill model is divided into multiple sub-regions, so as to solve the problem by using the wave function expansion method. For subregions with special shapes, this project intends to provide an effective method for constructing wave field expressions. The above methods can be used to study the responses of various complex and irregular convex terrains including asymmetry terrain, to seismic waves. For complex geological conditions, the conformal transformation is carried out based on the complex variable function method, and an appropriate inhomogeneous variation function of the medium is derived. Combined with local topography, the effect of local topography on SH wave propagation in inhomogeneous media is studied.