基于广义极值分布的实测地震动概率统计模型

doi:10.16183/j.cnki.jsjtu.2023.558

摘要/Abstract

摘要：

为建立地震动峰值加速度的概率分布模型,收集了500个台站的 255365 条地震动记录,构成初步的峰值加速度统计样本.首先,选用广义极值分布作为地震动峰值加速度的概率模型.基于此模型,分析了常用于估算极值分布模型参数的最大似然估计法和线性矩估计法的有效性.其次,依据最大似然估计的渐近正态性,提出了确定建立广义极值分布模型时所需最小样本长度的方法;分析表明,建立地震动峰值加速度的广义极值分布模型时,数据样本长度不宜小于120.对符合样本长度要求的地震动峰值加速度数据样本进行统计分析,发现其模型参数会随着样本长度的增加而收敛于一个较小的范围.最后,建立了不同类型场地的实测地震动峰值加速度的概率统计模型和地震危险性计算公式.

关键词: 广义极值分布, 极大似然估计, 最小样本长度, 地震动概率分布, 地震危险性

Abstract:

To develop a probability distribution model of peak ground acceleration, 255365 ground motion recordings are collected from 500 stations to create initial statistical samples of peak ground acceleration. First, the generalized extreme value distribution is employed as the probability model for peak ground acceleration. The effectiveness of the maximum likelihood estimation method and the linear moment estimation method, commonly used for estimating parameters of the extreme value distribution model, is assessed using the proposed generalized extreme value distribution model. Then, a method is proposed to determine the minimum required sample length when establishing a generalized extreme value distribution model based on the asymptotic normality of the maximum likelihood estimation. The analysis indicates that the data sample size should not be less than 120 when constructing the generalized extreme value distribution model for peak ground acceleration in seismic events. Statistical analysis is conducted on seismic peak ground acceleration data samples which meet the sample size requirement. It is observed that the model parameters converge to a relatively narrow range as the sample size increases. Ultimately, probability statistical models for measured peak ground acceleration and seismic hazard calculation formulas for different types of sites are established.

Key words: generalized extreme value distribution, maximum likelihood estimation, minimum sample length, earthquake action probability distribution, seismic hazard

中图分类号:

TU312

冯鹏飞, 周敉, 李志烜, 朱国强. 基于广义极值分布的实测地震动概率统计模型[J]. 上海交通大学学报, 2025, 59(8): 1133-1144.

FENG Pengfei, ZHOU Mi, LI Zhixuan, ZHU Guoqiang. Probability Statistical Model for Measured Ground Motion Based on Generalized Extreme Value Distribution[J]. Journal of Shanghai Jiao Tong University, 2025, 59(8): 1133-1144.

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场地	k	σ	μ
I	0.891	1.974	2.863
II	0.842	2.069	3.124
III	0.848	2.179	3.325
IV	0.825	2.120	3.027