Seismic wave scattering by multiple structures in layered half space is a classically multiple scattering problem in infinite domain. The computationally efficient substructure method is commonly adopted to solve this problem, because the structures can be modelled by the finite element scheme with the combination of the high-accuracy boundary condition to provide the dynamic stiffness of the truncated infinite rock or soil media. However, it is difficult to establish a high-accuracy boundary condition for multiple scattering problem in layered half space. In this paper, a combined zigzag-paraxial boundary condition is presented, and it is coupled with the seismic wave input method, as well as with the finite element scheme, to form the substructure method for solving the multiple scattering problem in layered half space. To verify the proposed substructure method, it is firstly applied to obliquely incident P-SV wave scatterings by a canyon, a cavity and an alluvial basin in homogeneous half space. The results are validated by comparing with several existing analytical and numerical methods. To demonstrate the capability of the proposed substructure method, it is finally applied to obliquely incident P-SV wave scattering by multiple tunnels in layered half space, and the effects of twin tunnels, soft soil interlayer and a V-shaped canyon on the structural response are discussed.

分层半空间中多个结构的地震波散射是无限域中的经典多重散射问题。通常采用计算有效的子结构方法来解决此问题，因为可以通过有限元方案对结构进行建模，并结合高精度边界条件来提供截断的无限岩石或土壤介质的动态刚度。然而，很难为分层半空间中的多重散射问题建立高精度的边界条件。本文提出了一种组合的之字形-近轴边界条件，并与地震波输入法以及有限元方案相结合，形成了解决分层半空间中多重散射问题的子结构方法。为了验证所提出的子结构方法，该方法首先应用于均质半空间中的峡谷，空腔和冲积盆地对斜入射的P-SV波的散射。通过与几种现有的分析和数值方法进行比较来验证结果。为了证明所提出的子结构方法的功能，最后将其应用于层状半空间中多个隧道的斜入射P-SV波散射，以及双隧道，软土夹层和V形峡谷对结构响应的影响讨论。