基于Copula理论的序列型地震动随机模型  

A STOCHASTIC MODEL FOR SEQUENTIAL GROUND MOTIONS BASED ON THE COPULA THEORY

作　　者：申家旭 陈隽[1] 丁国 SHEN Jia-xu;CHEN Jun;DING Guo(College of Civil Engineering,Tongji University,Shanghai 200092,China;East China Architectural Design&Research Institute,Shanghai 200002,China)

机构地区：[1]同济大学土木工程学院,上海200092 [2]华东建筑设计研究总院,上海200002

出　　处：《工程力学》2021年第1期27-39,共13页Engineering Mechanics

基　　金：国家自然科学基金重点项目(U1711264);新疆大学天山学者计划项目。

摘　　要：通过考虑序列型地震动中主震和余震间的空间相关性,将已有地震动物理随机模型推广至序列型地震动随机模型。依据序列型地震动的产生与传播机制,将其表示为包含16个随机变量的Fourier模型。考虑主震与余震的空间相关性,基于Copula理论,将模型更准确地表示为6个二维随机变量和2个一维随机变量;为描述地震动在局部场地上传播的过程,建立了序列型地震动的随机场模型;根据1038组实测序列型地震动及5组地震动台阵数据,对模型中的物理随机变量进行参数识别和统计分析,结合Copula函数,给出了各参数的概率分布。与实测地震动对比表明:该文提出的序列型地震动随机模型,能够较为真实地再现序列型地震动的空间相关性以及地震动在局部场地的行波效应。The existing ground motion physical stochastic model is extended to a stochastic model for sequential ground motions by considering the spatial correlation between the mainshock and aftershock.Considering the physical mechanism of ground motion generation and propagation,the sequential ground motions are represented by the Fourier model of 16 physical random variables.Meanwhile,considering the spatial correlation between the mainshock and aftershock,the model is more accurately represented by six two-dimensional random variables and two one-dimensional random variables based on the Copula theory.To describe the process of the ground motion propagation on local sites,a random field model of sequential ground motions is established.Based on 1038 pairs of measured sequential ground motions and five sets of ground motion array data,the probability distribution of each parameter is given by parameter identification and statistical analyses of physical random variables in the model combined with the Copula function.The comparison between the measured and the simulated ground motions shows that the proposed stochastic model for sequential ground motions can realistically reproduce both the spatial correlation of sequential ground motions and the wave traveling effect of ground motions at local sites.

关 键 词：COPULA理论 序列型地震动 空间相关性 参数统计 联合分布 

分 类 号：P315.9[天文地球—地震学]