Method for Determining Effective Frequency Range of Coherency Based on Seismic Energy

Abstract

When using data recorded by dense instrument arrays to fit the coherency model of spatial variation of seismic ground motions, the selected frequency range may affect the fitting parameters, which also affects the synthesized time history of the ground motion field. In this study, the acceleration of the 5th and the 45th Earthquake of the SMART-1 array was selected. The Abrahamson and Loh models were used to perform the parameter fitting of the coherency for frequency ranges of 0–8, 0–16 and 0–24[Formula: see text]Hz, and the obtained results were different. The smaller the frequency range, the lower the fitted lagged coherency. The influence of frequency range on fitting parameters of Loh model is much greater than that of Abrahamson model. Based on the relative relationship of ground motion energy distribution in each frequency band represented by the power spectra, from the perspective of power spectrum energy, the energy ratio concept was introduced, i.e. the ratio of the power spectra for a specific frequency range to the total power spectra. Based on the energy ratio, a method for determining the effective frequency range of the coherency model was developed. Through the comparison and analysis of the horizontal-component acceleration of the SMART-1 array, it was found that when the frequency range was 0–5[Formula: see text]Hz, the energy ratio exceeded 95%, when the frequency range was 0–8[Formula: see text]Hz, the energy in the frequency band reached approximately 99% of the total energy. Therefore, it is recommended that when the parameters of the coherency model are fitted, the frequency corresponding to an energy ratio of 95% can be used as the effective frequency. Within this range, the contamination of high-frequency components on the fitting results is minimized.