中文摘要：

利用Green函数、复变函数及多极坐标法研究了浅埋裂纹附近的半圆形凸起地形对SH波的散射问题。首先求解出适合本问题的Green函数，即含有半圆形凸起的弹性半空间内任意一点承受时间谐和的出平面线源荷载作用时位移场的解答。然后，从半圆形凸起地形对SH波的散射问题出发，利用本问题的Green函数在基体内构造裂纹。最后给出了浅埋裂纹附近的半圆形凸起地形对SH波散射的位移场。通过算例讨论了裂纹对地表位移幅值的影响，结果表明裂纹在一定情况下具有减震作用。

英文摘要：

Scattering of SH wave by a semi-cylindrical hill above a subsurface crack is studied by the Green function, the complex function and the multi-polar coordinates. Firstly, a suitable Green function is constructed, which is the fundamental solution of the displacement field for an elastic half space with a semi-cylindrical hill under an out-plane harmonic line source loading at an arbitrary point in matrix. Secondly, based on the problem of scattering of SH wave by a semi-cylindrical hill, the Green function is employed to construct a subsurface crack. Finally, the displacement field of semi-cylindrical hill above a subsurface crack under SH wave is given. The calculating results of the hill motion are plotted to show the influence of crack on the surface displacement, which demonstrates that the presence of the crack has obvious earthquake damping function under certain conditions.