文档介绍：摘要
随着研究的不断深入,人们发现地震波存在着极强的非平稳性,以往用于平稳
信号分析的万能之剑——傅立叶变换,在此失去了光芒。于是,一个新的研究思路
孕育而生——时频联合分析,随之诞生的是一系列时频联合分析的方法。
本文主要就两种方法做了介绍:离散谐小波变换和 S 变换,推导出了它们各自
的定义表达式和能量时变谱表达式,并通过实际地震波算例做简单的验证和分析;
收集并归类了多条实际地震波,通过编程分析各类地震波的时频特性,研究发现:
硬场地上地震波的能量在频域范围内比较分散,具有较大的中心频率和较宽的频带,
而在时域范围内比较集中;建立了地震波时变谱均匀调制非平稳随机模型,利用谱
强度因子建立了地震波单位能量时变谱和实际时变谱之间的关系。
本文还就地震波时频特征与结构地震响应之间的关系,进行了简单的分析。为
了便于研究,将三条自然波和一条人工波调整为相同的类别,分析在同类地震波的
输入下结构地震响应的差异。分析发现了地震波的时频特征谱和特征子波,前者与
地震波的弹性加速度反应谱有很好的相关性,可以建立它们之间的相互转换关系;
后者影响着非线性结构的地震位移反应,使得同类地震波输入下的结构位移反应有
很大的离散性,可以利用正弦函数来模拟特征子波。

关键词:结构地震响应时频分析谐小波变换时变谱
时频特征谱特征子波

基金项目:国家自然科学基金资助项目(50778079);湖北省自然科学基金资助项目(2006ABA067)
I
Abstract
With the gradual research in depth, it was discovered that seismic wave is a kind of
strongly non-stationary stochastic signal. Fourier transform, the omnipotent sword of
analyzing and processing stationary signal in the past, failed to deal with this kind of
signal. Time-frequency joint analysis has arisen, followed with the birth of a series of
time-frequency analysis joint methods.
In this paper, the author mainly introduced two methods: discrete harmonic wavelet
transform and S transform, deduced their respective expression of definition and
time-varying spectrum, and validated the expression. By program analysis to earthquake
datum which was collected and classified, time-frequency characteristic of every sort was
obtained and some conclusions were as following: the energy of seismic wave on hard site
scatters and has larger central frequency and wider frequency band in frequency-domain,
while it relatively concentrates in time-domain. The average time-varying spectrum of
seismic wave is simulated by uniform non-stationary stochastic model. The relation
between specific energy’s time-varying spectrum and actual earthquake’s are created
based on spectral intensity factor.
The author also analyzed the relationship between time-frequency characteristic