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

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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，本文采用多维自回归（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。

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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

Abstract：The power spectrum need to be artificially smoothed when traditional periodic diagram method is used to compute the ground motion coherence function, in addition, only two recordings could be considered. Considering these limitations, the multi-dimensional auto-regressed (AR) model was introduced in this paper to calculate coherence function instead of periodic diagram method and evaluate its applicability at many occasions. Firstly, this study took China Taiwan SMART-1 array data as an example to compare the coherence function results using AR model and periodic diagram method respectively. Then the difference among results of multidimensional AR model was discussed considering the reconstruction performance of time-histories, power spectrum and coherence function. Finally, the spatial multi-point ground motion simulation was adopted to evaluate the performance of coherence function obtained by different dimensions AR models through comparing the simulated and target ground motion. It was found that accurate reconstruction of strong ground motion records can be achieved in different dimensions AR models. However influence of the transfer function matrix would further affect the calculation results of 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 of 3-dimensional AR model is closer to the target ground motion in terms of time history and power spectrum than 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 using the multidimensional AR model are not better than the traditional periodic diagram method.

Key words： spatial coherency function autoregressive model power spectrum periodogram method China Taiwan SMART-1 stations multi-point ground motion simulation;

收稿日期: 2020-06-22 出版日期: 2022-01-28

引用本文:

温攀1,2，冀昆1,2，温瑞智1,2，任叶飞1,2. 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[J]. 振动与冲击, 2022, 41(2): 140-150.
WEN Pan1,2，JI Kun1,2，WEN Ruizhi1,2，REN Yefei1,2. Applicability of the computation method for spatial coherence functions based on the multidimensional autoregressive (AR) model. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(2): 140-150.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I2/140

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