为从理论上揭示二维土层放大效应、地形效应及其相对重要性,构造了含有风化层的半圆形河谷的数学物理模型,利用波函数展开法在弹性动力学的理论框架内提出了风化半圆形河谷对平面SH波散射和衍射的解析级数解。计算并对比了风化与未风化河谷的地表位移反应,通过系统分析地面运动的放大形态与幅值,发现二维土层放大效应通常在风化土层范围内占据绝对优势,而地形效应控制着风化土层范围以外的地面运动放大,并且土层放大值通常大于地形放大值。 In order to theoretically reveal the magnifying effect, the topographic effect and its relative importance of two-dimensional soil layers, a mathematical and physical model of a semicircular valley with weathering layers is constructed. Based on the theoretical framework of elastic dynamics, a wave function expansion method is proposed Analytic series solutions to scattering and diffraction of plane SH waves in weathered semi - circular river. The surface displacement responses of the weathered and unweathered valleys are calculated and compared. By analyzing the amplifying patterns and amplitudes of the ground motions systematically, it is found that the amplifying effect of two-dimensional soil usually occupies the absolute dominant position within the weathered soil layer, while the topographic effect controls the weathering The ground motion outside the soil layer is magnified, and the soil layer magnification is usually larger than the landform magnification.