多维自回归(AR)模型计算地震动空间相干函数的适用性研究  

Applicability of the computation method for spatial coherence functions based on the multidimensional autoregressive(AR)model

作　　者：温攀 冀昆[1,2] 温瑞智[1,2] 任叶飞[1,2] WEN Pan;JI Kun;WEN Ruizhi;REN Yefei(Institute of Engineering Mechanics,China Earthquake Administration,Harbin 150080,China;Key Laboratory of Earthquake Engineering and Engineering Vibration,China Earthquake Administration,Harbin 150080,China)

机构地区：[1]中国地震局工程力学研究所,哈尔滨150080 [2]中国地震局地震工程与工程振动重点实验室,哈尔滨150080

出　　处：《振动与冲击》2022年第2期140-150,共11页Journal of Vibration and Shock

基　　金：黑龙江省自然科学基金联合引导项目(LH2020E022);黑龙江省自然科学基金优秀青年项目(YQ2019E036);国家自然科学基金广东省联合基金项目(U1901602);国家自然科学基金(51908518);中国地震局工程力学研究所所长基金(2019B09)。

摘　　要：传统周期图法求解地震动相干函数时需要进行功率谱的人为加窗平滑,且仅能考虑记录两两之间的空间相关性。针对以上缺陷,该研究采用多维自回归(autoregressive,AR)模型代替周期图法进行相干函数计算,并从多个方面对其合理性加以评估和验证。首先以中国台湾SMART-1台阵数据为算例,对比AR模型以及周期图法计算相干函数的结果,从记录的重构效果、功率谱和相干函数等多个角度讨论了不同维度下AR模型的计算结果差异。最后通过采取对已知台站记录进行空间多点地震动模拟,与目标地震动对比,探讨不同维度下AR模型求解地震动空间相干函数的合理性。结果表明:不同维度下的AR模型均可实现对强震动加速度记录的精确重构,但是维度的不同会导致传递矩阵的差异,进一步影响功率谱及相干函数的计算结果;对于彼此间距较小的内环台站记录,不同维度AR模型下所求的功率谱和相干函数差异较明显。基于三维AR模型所求相干函数得到的模拟地震动与目标地震动在时程和功率谱上均较周期图法更为接近。随着记录台站间距的增大,彼此相关性减弱,AR模型维度对相干函数和结果的影响减弱,此类工况采用多维AR模型计算相关函数得到的空间地震动效果并未优于传统周期图法。The power spectrum needs to be artificially smoothed when the traditional periodic diagram method is used to compute the ground motion coherence function,in addition,only two recordings can be considered.Considering these limitations,a multidimensional auto regression(AR)model was introduced to calculate the coherence function instead of the periodic diagram method and its applicability in many occasions was evaluated.Firstly,the China Taiwan SMART-1 array data was taken as an example to compare the resulted coherence function using the AR model and periodic diagram method respectively.Then the difference among results of some multidimensional AR models was discussed from the aspects of the reconstruction performances of time-histories,power spectrum and coherence function.Finally,the spatial multi-point ground motion simulation was adopted to evaluate the performance of coherence functions obtained by different dimensions of AR models through comparing the simulated and target ground motion.It is found that the accurate reconstruction of strong ground motion records can be achieved by using different dimensions of AR models.However the influence of the transfer function matrix will further affect the calculation results of the power spectrum and coherence function.For the case of stations with small distance,the power spectrum calculation results are significantly influenced by different dimensions.The simulated ground motion based on the coherence function by using the 3-dimensional AR model is closer to the target ground motion in terms of the time history and power spectrum than the periodic diagram method.The influence decreases with the increase of the spacing between the recording stations,which is resulted by the decreasing of correlation relationship between them.In this occasion,the spatial ground motions simulated by using the multidimensional AR model are not better than the traditional periodic diagram method.

关 键 词：相干函数 自回归模型 功率谱 周期图法 中国台湾SMART-1台阵 多点地震动模拟 

分 类 号：P315.9[天文地球—地震学]