Comparison Between Spectral Smoothing Method And AR Model Method In Calculating Coherence Function

When analyzing the seismic response of long structures such as dams,long-span bridges,high-speed railways,subways,and underground pipelines,the spatial variation of ground motion needs to be considered.Due to the many and complex factors that affect the spatial variation of ground motions,such as rupture of the source,scattering and attenuation during the propagation of seismic waves,and site conditions,etc.Therefore,the research on the spatial variation of ground motion is usually based on the random vibration theory,based on the observation data of strong seismic arrays,and a random analysis method using signal processing technology.Among them,the coherence function is the most commonly used method.According to the different methods of seismic data processing,there are two main methods to calculate the coherence function.One is the nonparametric method which uses the spectral window method to smooth the power spectrum and the cross power spectrum;The other is to use some commonly used spectra,such as K-T(Kanai-Tajimi)spectra,to fit the power spectrum and cross-power spectrum parameters.AR(Auto-Regressive)model parameter method and spectral smoothing nonparametric method are used to fit the coherence function,and the fitting parameters and standard deviation are obtained respectively.The difference between the two results is compared and analyzed,which provides more reference for the selection of coherent function in engineering application.The main work of the paper is as follows:1.On the basis of summarizing the research status of spatial variation of ground motion,the acceleration records of SMART-1 array are collected and selected as the calculation data of coherence function,and the baseline correction and time shift processing of the original seismic record data are carried out.2.Based on the acceleration records of the 5th and 45 th earthquakes of SMART-1array,the non-parametric method of smoothing the power spectrum and cross power spectrum by spectral window and the parametric method based on autoregressive model are used to calculate the spatial coherence coefficient of ground motion,and the coherence functions obtained by the two methods are fitted by Loh coherence function model.The fitting accuracy of the coherence functions obtained by the two methods is compared and analyzed.The results show that:(1)The fitted standard deviation based on the autoregressive 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)With the increase of the distance,the degree of the coherence coefficient based on the nonparametric method decreases with the increase of the frequency,while the coherence coefficient based on the parametric method obviously reflects the consensus that the coherence coefficient decreases with the increase of the frequency,and also decreases with the increase of the distance.Finally,the research work of this paper is summarized,and the problems to be further studied in the future are pointed out.