Effects of Topographic Amplification Induced by a U‐Shaped Canyon on Seismic Waves
Effects of Topographic Amplification Induced by a U‐Shaped Canyon on Seismic Waves
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DOI：
10.1785/0120110306
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发表时间：
2012-08
影响因子：
3
通讯作者：
Yufeng Gao;Zhang Ning;Dayong Li;Han-long Liu;Yuanqiang Cai;Wu Yongxin
中科院分区：
文献类型：
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作者：
Yufeng Gao;Zhang Ning;Dayong Li;Han-long Liu;Yuanqiang Cai;Wu Yongxin
摘要本文提出了U形峡谷诱导的平面SH波二维散射和绕射的波函数级数解，以考虑U形峡谷的地形效应。波函数展开法由于能揭示波散射的物理过程，并能检验其它方法的精度，常被用来研究地形效应。通过一种新的区域分解策略，具有U形峡谷的半空间被划分为三个子区域。因此，我们定义了三个圆柱坐标系。在每个坐标系中，用分离变量法将满足Helmholtz方程的波场表示为复系数未知的Bessel函数和Hankel函数的级数。然后，三个波场都表示在同一个坐标系中使用格拉夫加法定理。通过满足辅助边界的连续性条件和峡谷底部的无牵引边界条件来求解未知系数。为了说明对称和非对称U形峡谷对地表地震动的影响，在频域中进行了参数分析。地表和地下的瞬态响应在时间域中表现出波的传播和散射现象。研究发现，在U形峡谷的底部有一个明显的放大区，峡谷的壁几乎是垂直的。
Abstract The series solution of wave functions for 2D scattering and diffraction of plane SH (shear horizontal) waves induced by a U‐shaped canyon is proposed herein to account for the topographic effect of such a canyon. The wave function expansion method has been frequently employed to study the topographic effect because it can reveal the physics of the wave scattering and can test the accuracy of other methods. Through a new domain decomposition strategy, the half‐space having a U‐shaped canyon is divided into three subregions. Hence, we defined three cylindrical coordinate systems. In each coordinate system, the wave field satisfying the Helmholtz equation was represented by means of the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then three wave fields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are solved by satisfying the continuity conditions of the auxiliary boundary and the traction‐free boundary conditions on the bottom of the canyon. To show the effects of symmetrical and nonsymmetrical U‐shaped canyons on the surface ground motion, a parametric analysis is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. It is found that a zone of amplification can obviously take place at the bottom of a U‐shaped canyon with nearly vertical walls.