瑞利面波单点谱比曲线的理论计算与分析  

Study on spectral ratio of horizontal to vertical spectral ratio for Rayleigh waves

作　　者：杨天春[1,2] 王齐仁[1,2] 廖建平[1] 

机构地区：[1]湖南科技大学土木工程学院,湘潭411201 [2]湖南科技大学页岩气资源利用湖南省重点实验室,湘潭411201

出　　处：《应用力学学报》2015年第4期630-635,707,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(41274126);湖南省自然科学基金(12JJ6035)

摘　　要：对瑞利面波的研究过去主要注重其速度频散信息,而对其位移特征研究相对较少一些。本文主要研究水平层状介质模型的瑞利波单点谱比曲线计算,同时对曲线特征进行分析。采用水平层状介质模型,应用传递矩阵方法推导地表瑞利面波的质点位移表达式。对于工程中常见的3种典型层状介质模型,利用频散方程和波数加权平均的方法求各模型的瑞利波频散曲线以及合并化的速度频散曲线,再进一步利用地表质点位移计算公式和位移权值法分别计算各模式的H/V谱比曲线以及所有模式的合并化H/V谱比曲线。由此可见,本文在研究H/V谱比曲线时考虑了瑞利波多模式同时存在的问题。由模拟计算结果可知:对于规则地层模型和含硬夹层的地层模型而言,合并化的H/V谱比曲线与基阶模式H/V谱比曲线基本吻合;而对含有软夹层的复杂地层模型来说,基阶模式H/V谱比曲线与合并化的H/V谱比曲线之间存在十分明显的差异。由此说明在某些情况下基阶模式H/V谱比曲线不能代表整个地层的响应。Researches on Rayleigh waves are mainly interested in the velocity dispersion in the past, and very little attention has been paid on the displacement characteristics of Rayleigh waves. Calculation of horizontal to vertical spectral ratio for Rayleigh waves is studied in horizontally stratified medium in this paper, and characteristics of HVSR(Horizontal to Vertical Spectral Ratio) curves are discussed. Expressions of surface displacement of Rayleigh waves are derived by the transfer matrix method for a horizontally stratified medium model. Taking three kind of typical horizontal stratum models in civil engineering as examples, and combining with the dispersion equation and the weighted wave number method, we obtain dispersion curves and the incorporative dispersion curves for given models. Then, HVSR curves of different modes and the incorporative HVSR curve can be obtained by using the expression of surface displacement and the weighted displacement method. Thus, the problem of multi-modes for Rayleigh waves has been considered. The simulation results show that the incorporative HVSR curve is consistent with the HVSR curve of the first mode for the regular model and the model with a hard interlayer. However, there are significant differences between the HVSR curve of the first mode and the incorporative HVSR curve for stratum with a soft under-layer. According to the results, it can be concluded that in some cases the HVSR spectral ration curve of the first mode cannot represent the response of the model.

关 键 词：瑞利波 H/V谱比法 频散 传递矩阵法 

分 类 号：P631.414[天文地球—地质矿产勘探]