参数和非参数方法计算相干函数的比较

Comparison of parametric and non-parametric methods for calculating coherence function

地震动空间相干函数计算主要两类方法,一是采用谱窗方法对功率谱和互功率谱进行平滑的非参数方法,另一类是采用K-T(Kainai-Tajimi)谱拟合功率谱和互功率谱的参数方法。本文选取了SMART-1台阵第5次和第45次地震的水平分量加速度记录,采用AR(Auto-Regressive)自回归模型的参数方法,计算了不同台站间距的相干系数,并选用Loh相干函数模型,对两种方法的相干系数进行拟合,分别得到了拟合参数和标准差。结果表明:(1)基于AR自回归模型方法得到的拟合标准差小于非参数法;(2)非参数法和参数法的相干系数有明显差别;(3)随着间距的增大,基于非参数法的相干系数随着频率增大而变小的程度放缓,而基于参数法的相干系数明显反映出相干系数符合随着频率增大而变小,同时也随距离的增大而减小的共识。

There are two main methods for calculating the spatial coherence function of ground motion.One is the non-parametric method when smoothing the power spectrum and the cross power spectrum by using the spectral window method,and the other is the parameter method using the K-T(Kainai-Tajimi)spectrum to fit the power spectrum and cross power spectrum.In this paper,the horizontal component acceleration records of the No.5 and No.45 earthquakes of SMART-1 array are selected,based on the parameter method of the AR(Auto-Regressive)model,the coherence coefficients of different station spacings are calculated,and Loh coherency function model is selected to fit the coherence coefficients of the two methods,and the fitting parameters and standard deviation are obtained respectively.The results show that:(1)The fitting Root Mean Squared Error based on the auto-regressive model method is smaller than the non-parametric method;(2)There is a significant difference in the coherence coefficient between the non-parametric method and the parametric method;(3)As the distance increases,the coherence coefficient based on the non-parametric method decreases slowly with increasing frequency,and the coherence coefficient based on the parametric method obviously reflects that the coherence coefficient decreases with frequency.At the same time,the consensus decreases as the distance increases.