平面SH波作用下部分充填圆弧形沉积谷的二维土层和地形放大效应

场地效应通常包含土层放大效应和地形放大效应，为了揭示二者的相对贡献，本文构造了平面SH波作用下部分充填沉积谷的解析模型，借助于区域分解策略，在波函数展开法的框架下，提出了超定方程组解法，得到了部分充填圆弧形沉积谷对平面SH波散射的波函数级数解，而且级数解的收敛测试表明了超定方程组解法的必要性.通过与文献结果进行对比，验证了本文方法的正确性.通过调整解析模型中两个子区域内的材料参数，计算了沉积谷引起的场地放大效应和相应的空河谷引起的地形放大效应.对二维土层与地形效应进行对比分析，结果显示，在沉积谷内二维土层放大效应通常强于地形放大效应，而地形放大效应决定了沉积谷外的地面运动放大形态.针对最大地面运动，进行了沉积谷和相应空河谷的参数分析，进一步描述了二维土层放大效应，研究结果表明二维土层放大效应引起的最大地面运动通常远远大于地形放大效应引起的最大地面运动，并且二维土层效应通常随着土层与基岩的阻抗比的增大而增大，但不是一维土层放大效应与二维地形放大效应的简单线性叠加. 

Two-dimensional soil and topographic amplification effects of a partially filled circular-arc alluvial valley under plane SH waves

Site amplification consists of two-dimensional (2D) soil layer amplification effects and topographic amplification effects. The objective of this study is to investigate the relative contribution of soil amplification and topographic amplification. To that end, the wavefunction series solution for the scattering of plane SH waves by a partially filled circular-arc alluvial valley is proposed. The wavefunction series solution is obtained by a novel method of over-determined system of equations in the framework of the wavefunction expansion technique with the aid of a region-matching strategy. The convergence tests are conducted to reveal the necessity of the proposed over-determined system of equations method. The validity of the proposed solution is verified by comparison with previous results. By adjusting the material parameters of the two sub-regions in the analytical model, both of the surface motions of the alluvial valley and the empty canyon are calculated. The site amplification patterns of the alluvial valley are compared with the topographic amplification patterns of the empty canyon with the same geometry, the results show that the soil amplification effects are usually larger than the topographic amplification effects within the alluvial valley, while the topographic effects dominate the amplification pattern of ground motions outside the alluvial valley. Afterwards, a parametric study in terms of the maximum surface motion is carried out to determine the relative importance of soil and topographic contributions in a more comprehensive manner and to further characterize the 2D soil layer amplification effects. It is evident that the maximum soil layer amplification generally far outweighs the maximum topographic amplification. The 2D soil amplification increases with the impedance contrast between the soil layer and the underlying bedrock but is not a simple linear superposition of 1D soil amplification and 2D topographic amplification.