Analysis of Scattered Waves on Ground with Irregular Topography Using the Direct Boundary Element Method and Neumann Series Expansion
Analysis of Scattered Waves on Ground with Irregular Topography Using the Direct Boundary Element Method and Neumann Series Expansion
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DOI：
10.1785/0120060178
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发表时间：
2007-08
影响因子：
3
通讯作者：
H. Mogi;H. Kawakami
中科院分区：
文献类型：
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作者：
H. Mogi;H. Kawakami
众所周知，具有不规则地形表面的地面会引起复杂的地震反应。复杂的地震反应主要是由散射和波转换引起的。然而，散射主要发生的表面的具体位置及其影响的程度尚不清楚。本文从散射波的贡献出发，研究了不规则地表引起的复杂地震反应的激发过程。首先，基于直接边界元法和边界元矩阵的Neumann级数展开，给出了二维SH波场中散射波贡献的计算公式。在推导过程中指出，一阶散射波贡献的数学表达式是由波函数和倾斜因子组成的，与惠更斯-菲涅耳原理得到的结果相似。接下来，对在中心具有正弦形表面并且在两端具有平坦部分的地面进行数值分析。结果表明，复杂的响应波形是由散射波的到达引起的。最后，基于数学表达式，对参考点处一阶散射波的贡献进行了详细的分析，得出以下结论：（1）一阶散射波在时域中的极性主要由倾斜因子决定，而倾斜因子仅取决于参考点与散射波源点之间的几何关系。(2)在谷底，由于离散射波源的距离很近，在其附近表面产生的散射波占主导地位。这些散射波几乎与入射波同时到达，并且由于它们的负极性，总是减小入射波的振幅。(3)相反，在山顶，在附近的表面产生的散射波具有正极性，它们总是增强振幅响应。
It is well known that ground with irregular topographic surfaces causes complicated seismic responses. The complex seismic response is mainly caused by scattering and wave conversions. However, the specific locations of the surface where the scattering mainly occurs and the extent of their effects are not yet clear. In this study, we investigated the excitation process of complicated seismic responses induced by irregular ground surfaces in terms of the contribution of scattered waves. First, the formulation of scattered-wave contribution in a two-dimensional SH -wave field based on the direct boundary element method and the Neumann series expansion of the bem matrix was shown. In the formulation process, it was pointed out that the mathematical expression of the first-order scattered-wave contribution has a form consisting of a wave function and an inclination factor, which was similar to that obtained by the Huygens–Fresnel principle. Next, numerical analyses were conducted for a ground that had a sinusoidal-shaped surface at the center and flat parts at both ends. A comparison of the results showed that the complicated waveforms of the responses were caused by the arrivals of the scattered waves. Finally, the contributions of the first-order scattered waves at the reference points were closely examined based on the mathematical expression; the following conclusions were drawn: (1) The polarity of the first-order scattered waves in the time domain is attributed to the inclination factor, which depends only on the geometrical relationship between the reference point and the source point from which the scattered waves emanate. (2) At the bottom of a valley, the scattered waves generated at its nearby surface are dominant because of the short distance from the source of the scattered waves. These scattered waves appear nearly at the same time of arrival as the incident wave and always reduce the amplitude of the incident wave because of their negative polarity. (3) On the contrary, at the peak of a hill, the scattered waves generated at the nearby surface have positive polarity, and they always enhance the amplitude response.