基于谐和小波的空间变化地震动时变延迟相干函数估计

Evolutionary lagged coherency estimation of spatially variable seismic ground motion via generalized harmonic wavelets

空间变化地震动的非平稳特性会对大跨结构非线性响应产生显著影响。地震动建模多采用时变互谱或时变延迟相干函数描述空间变化地震动的非平稳特性。本研究发展了一种基于广义谐和小波的时变互谱估计方法,并将其应用于实测地震动记录的时变延迟相干函数估计中。首先,基于Spanos和Failla提出的演变功率谱估计方法,采用广义谐和小波推导了非平稳过程时变互谱的估计公式。由于具有频域非重叠特性,非平稳过程的时变互谱可由广义谐和小波系数显式给出。之后,利用广义谐和小波对台湾SMART-1台站组Event45地震实测地震动的时变延迟相干函数进行了估计。估计结果表明,在地震动强度平稳段,延迟相干函数峰值约为0. 8,且具有明显的随频率衰减现象;在地震动强度上升段和衰减段,延迟相干函数峰值约为0. 4,随频率衰减现象不明显。

Nonstationary characteristics of spatially variable seismic ground motions have significant effect on earthquake responses of nonlinear extended structures. Estimation and modeling of cross evolutionary power spectral density( EPSD)of spatially variable seismic ground motions are of interest in recent years for engineering purposes. An approach for estimating the cross EPSD of the spatially variable seismic ground motions by using the generalized harmonic wavelets( GHW) was present. The cross EPSD and the evolutionary lagged coherency of the realistic spatially variable seismic ground motions were estimated by this approach. The time-varying nonstationary characteristics of these ground motions were also analyzed. Firstly,a cross EPSD estimation formula was derived using the GHW within the framework of evolutionary spectra estimation given by Spanos and Failla. Then,the proposed estimation formula was used to estimate the cross EPSDs of the seismic ground motions recorded at the SMART-1 array during Event 45. The cross EPSDs and the evolutionary lagged coherency between the center station and the outer ring stations were obtained. During the stable stage of the ground-motion intensity,the lagged coherency is close to 0. 8 in the low frequency range and decays as frequency increasing. During the rising and decaying stages of the ground-motion intensity,the lagged coherency is fluctuant with a mean value of about 0. 4.