【摘要】 采用“契合”的思想,给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的解答．将整个求解区域分割成两部分来处理．其一为包括半圆形凸起地形在内的一个圆形区域Ⅰ,其余为区域Ⅱ．在区域Ⅰ和Ⅱ中分别构造位移解,并在两个区域的“公共边界”上实施“契合”．在区域Ⅰ中构造一个上半部边界应力为零, 而其余部分位移、应力任意的驻波解,在区域Ⅱ中构造出半圆形凹陷和浅埋圆孔的散射波,且要求它满足水平界面上应力为零的约束条件．然后再通过移动坐标,满足“公共边界”的“契合”条件和地下孔洞的边界条件,建立起求解该问题的无穷代数方程组．最后,给出了分析例题和数值结果,并对其进行了讨论．更多还原

【Abstract】 In this paper, the scatting of SH-wave by a semi-cylindrical hill above a subsurface cavity in half-space is studied based on the idea of match up, by using complex functions and multi-polar coordinates. During the solution, we divide the solution domain into two. The first one is a circle domain, including the boundary of the hill, and the second one consists of all of the rest parts. A solution is constructed in the circle domain, where satisfies the condition that stress is zero at the hill edge and arbitrary at the other part. In the second domain, including a semi-cylindrical canyon and a subsurface cavity in the half-space, the scattered wave function is constructed, which satisfies the condition of stress free at the horizontal surface. Then, by using the moving coordinate method, the two solutions are matched up on the junction interface,satisfying the boundary condition at the subsurface cavity edge.The problem can be reduced to solve a set of infinite linear algebraic equations. Finally the computational results of surface displacement are presented togetherwith a discussion.更多还原