中文摘要：

为研究层状饱和场地中沉积谷地对斜入射地震波的三维散射问题，建立了求解问题的2.5维间接边界元方法。通过沿沉积谷地轴线方向的傅里叶变换将三维问题降为二维问题，进而在沉积谷地的截面内进行边界单元的离散和求解，求得沉积谷地截面内的动力响应，然后再将截面内计算结果沿沉积谷地轴线方向进行波数展开即可求得任意位置动力响应。通过与弹性情况的比较验证了方法的正确性，并以均匀饱和半空间和基岩上单一饱和土层中沉积谷地对斜入射平面SH波的三维散射为例进行了数值计算和分析。研究发现沉积谷地对SH波的三维散射与二维散射之间存在显著差异；饱和情况（透水或不透水）与干土情况沉积谷地附近地表位移的差别很大；另外层状饱和半空间中沉积谷地和均匀饱和半空间中沉积谷地对斜入射SH波的放大作用也存在显著差别。

英文摘要：

The indirect boundary element method （IBEM） is proposed to study the three-dimensional scattering problem by a two-dimensional valley embedded in a fluid-saturated, poroelastic layered half-space for obliquely incident seismic waves. The wave-number transform is applied in the axial direction of the valley to reduce the three-dimensional problem to a two-dimensional plane strain problem. Then the dynamic problem is solved in one section perpendicular to the axis of the valley, and finally the three-dimensional responses of the valley and of the layered site are obtained through the inverse wave-number expansion. The validity of the method is confirmed by comparison with the results of the corresponding dry poroelastic case, and numerical calculation and analyses are performed by taking the amplification of obliquely incident plane waves by an alluvial valley in a uniformly saturated poroelastic half space and in a single saturated poroelastic soil layer overlying on elastic bedrock as examples. The results show that the three-dimensional responses are distinctively different from the two-dimensional responses, that the surface displacement amplitudes near the valley in dry poroelastic and saturated poroelastic half-spaces are very different, and that the displacement amplitudes around the valley in a uniform saturated poroelastic half space are obviously different from those in a saturated, poroelastic layered half-space.