层状半空间中沉积谷地对入射SV波的放大作用——时域解答

Wave scattering of a depositional valley in layered half-space for incident plane SV waves:time domain solution

利用傅里叶变换方法,研究了层状半空间中沉积谷地对SV波的时域散射问题。首先,通过傅里叶变换将时域问题转换为离散的频域问题,针对有效频率成分采用间接边界元方法求解频域响应,再将所得频域结果进行傅里叶逆变换得到时域解答。通过与已有结果的对比,验证了方法的正确性。最后,以基岩上单一土层中沉积谷地在R icker波入射下的散射问题为例进行了数值计算分析,结果表明,沉积谷地和土层的存在都会造成振动持续时间的增长;层状半空间中沉积谷地和均匀半空间中沉积谷地对波的放大作用存在显著差别。文中分析了造成该差别的原因,并讨论了覆盖层厚度和刚度对散射效应的影响。

The Fourier transform method was used to study the problem of wave scattering by an depositional valley for incident plane SV waves in time domain. The problem was firstly transformed into the frequency domain, and then the calculations were performed in the frequency domain using indirect boundary element method for the effective frequency components, finally the results were transformed back into the time domain by the inverse Fourier transform. The validity of the method is confirmed by comparing the results with published ones. Numerical results are given by taking the amplification of incident Ricker wave by an depositional valley in one layer over half-space as an example. The results show that the duration of vibration is prolonged due to the existence of the soil layer and the depositional valley, and there exist distinct differences between the wave amplification by an depositional valley in one later over half-space and that in homogeneous half-space. The reasons were investigated and the effects of the depth and stiffness of the soil layer on scattering were discussed.