基于小波变换的地震波时变功率谱估计

为进一步认识地震动的非平稳特性，基于小波变换提出一种估计时变功率谱的方法.利用小波变换的带通滤波特性，结合时变功率谱的物理意义，从能量的角度推导各频带上小波系数与时变功率谱密度函数的关系，从而通过地震动信号的小波系数估计时变功率谱.利用基于小波变换的估计时变功率谱方法，针对实测和模拟地震动信号进行时变功率谱估计，并与基于傅里叶变换估计的功率谱进行了比较验证.结果表明：该方法正确、可行，它将原有的频率-幅值的二维认识提高到频率-时间-幅值的三维认识，解决了傅里叶变换估计功率谱缺乏时间信息的问题.

Estimation of time dependent power spectral density of seismic wave based on wavelet transform

In order to further understand the nonstationary characteristic of ground motion, a new method to estimate the time dependent power spectral density （PSD） was proposed based on wavelet transform. With utilizing the band pass filtering characteristics of wavelet transform and combining the physical meaning of time dependent PSD, the relations between the wavelet coefficient and time dependent PSD on different frequency bands were deduced in terms of energy. And then the time dependent PSD was estimated through the wavelet coefficient of ground motion signals. Using the proposed method, the time dependent PSD for both measured and simulated ground motion signals was respectively estimated and compared with the PSD based on Fourier transform. The results show that the present method is feasible and correct. The method can extend the original two dimentional relation of frequency amplitude to three dimentional relation of time frequency amplitude, and avoid the lack of time information in the traditional PSD estimation based on Fourier transform.