Effective Frequency Range Of Coherency Function Of Earthquake Ground Motion

Spatial variation of ground motion refers to the difference of amplitude and phase of ground motion at different locations on the surface when an earthquake occurs,which is usually expressed by coherency functions.These coherency function models are mainly obtained by statistical analysis of strong earthquake records.When fitting the parameters of the coherency function model,there are great differences in the selected frequency range,and the different frequency range has a great impact on the statistical results.Therefore,it is important to determine the effective frequency range for the rationality of the fitting results of the coherency function model.In this paper,two methods for determining the effective frequency range of coherency function are proposed.The main contents and results are as follows:First,from the point of view of power spectrum-energy,a method to determine the effective frequency range of coherency function model based on the energy ratio(i.e.the ratio of power spectrum to total power spectrum in a certain frequency range)is proposed.The horizontal component acceleration records of the 5th and 45 th earthquakes of SMART-1 array are selected and their power spectra are calculated.The energy contained in different frequency bands is analyzed and compared.The results show that the frequency corresponding to the energy ratio of 95-99% can be used as the maximum frequency for parameter fitting.When SMART-1 array records are used to fit the parameters of the coherency function model,the maximum frequency of 10 Hz is suitable.Second,from the point of view of Autoregressive Model-SNR,a method of calculating power spectrum from autoregressive model is proposed,and then the effective frequency range of coherency function model is determined according to SNR.The "signal-to-noise ratio" 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.When SNR = 0,the corresponding frequency is the maximum frequency of the effective frequency range,and the frequency component larger than the maximum frequency is regarded as the random component of seismic wave,so 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 5th and 45 th SMART-1 seismic records under different station spaces.Then the range of effective frequency band is determined according to the SNR.Combining with the attenuation trend of the coherency function curve,it shows that this method is feasible and the maximum frequency can be 10 Hz.Thirdly,Because the strong ground motion is affected by the source,propagation path and site conditions,and also has regional differences,the effective frequency band range obtained by different array records may be different.Therefore,it is suggested that the frequency band range of the model should be explained when the parameters of the coherence function model are given.Under the same array,the influence of station spacing on the selection of effective frequency band should be considered.When high frequency is emphasized under large spacing,the coherence may become unreliable.