基于AR模型的相干函数有效频段范围的确定

目前人们在进行地震动相干函数模型参数的拟合时,选取的频段范围存在很大差异,而确定有效的频段范围对相干函数模型拟合结果的合理性很重要。本文利用AR模型(Autoregressive Model,自回归模型)计算地震动的功率谱,提出了根据功率谱"信噪比(SNR)"确定相干函数有效频段范围的方法。本文的信噪比中的"噪",专指AR模型中的激励白噪声,用于衡量AR模型中某一频率地震动功率谱与激励白噪声功率谱之间的比例。定义信噪比SNR=0时对应的频率为有效频段的最高频率,大于最高频率的频率成分,被当作是地震波中的随机成分,可以不考虑地震动的相关性。采用这一方法,对SMART-1第45次地震记录的不同台站间距下的地震波进行了功率谱估计,根据信噪比确定出了有效频段范围,并计算了相应的相干函数,结果表明此方法是可行的。

Determination of effective frequency range for coherency function based on autoregressive model

At present,when fitting the parameters of coherence function model of ground motion,there are great differences in the selected frequency range.It is very important to determine the effective frequency range for the rationality of the fitting results of coherence function model.From the point of view of autoregressive model-signal-to-noise ratio(SNR),a method of obtaining power spectrum from autoregressive model,and then determining the effective frequency range of coherence function model based on signal-to-noise ratio is presented.The SNR introduced in this paper is only used to measure the ratio between the ground motion power spectrum and the excitation white noise power spectrum in the autoregressive model.It is found that when SNR=0,the corresponding frequency is the highest frequency in the effective frequency band,and the frequency component higher than the highest frequency is regarded as the random component in seismic wave and the correlation of seismic ground motion cannot be considered.This method is used to estimate the power spectrum and calculate the coherency function of S-wave in the EW and NS directions of the 45 th SMART-1 seismic records.The range of effective frequency band is determined according to the SNR,and the attenuation trend of the coherence function curve shows that this method is feasible.