基于轮廓似然估计的广义极值分布在地震中长期预测中的应用

赵宜宾 张艳芳 王福昌 任晴晴

赵宜宾,张艳芳,王福昌,任晴晴. 2022. 基于轮廓似然估计的广义极值分布在地震中长期预测中的应用. 地震学报,44(6):1−11 doi: 10.11939/jass.20210067
引用本文: 赵宜宾,张艳芳,王福昌,任晴晴. 2022. 基于轮廓似然估计的广义极值分布在地震中长期预测中的应用. 地震学报,44(6):1−11 doi: 10.11939/jass.20210067
Zhao Y B,Zhang Y F,Wang F C,Ren Q Q. 2022. Application of generalized extreme value distribution based on profile likelihood estimation in long term earthquake prediction. Acta Seismologica Sinica,44(6):1−11 doi: 10.11939/jass.20210067
Citation: Zhao Y B,Zhang Y F,Wang F C,Ren Q Q. 2022. Application of generalized extreme value distribution based on profile likelihood estimation in long term earthquake prediction. Acta Seismologica Sinica44(6):1−11 doi: 10.11939/jass.20210067

基于轮廓似然估计的广义极值分布在地震中长期预测中的应用

doi: 10.11939/jass.20210067
基金项目: 河北省高等学校科学技术研究项目(Z2020224)、中央高校基本科研业务费项目(Z2020224)和河北省高等教育教学改革与实践项目(2020GJJG351)共同资助
详细信息
    作者简介:

    赵宜宾,本科,教授,主要从事系统建模与仿真、灾害损失预测与评估等方面的研究,e-mail:zhaoyibin5326@126.com

    通讯作者:

    张艳芳,硕士,副教授,主要研究方向为系统优化与决策,统计分析建模等,e-mail:zyf_o@126.com

  • 中图分类号: P315.75

Application of generalized extreme value distribution based on profile likelihood estimation in long term earthquake prediction

  • 摘要: 为描述强震预测的不确定性,在地震预报极值分析模型的参数估计中,引入轮廓似然估计法。对广义极值分布中形状参数和地震重现水平的轮廓似然估计原理及数值算法进行了详细地阐述,并利用构建的广义极值分布模型对东昆仑山地震带进行了地震危险性分析。关于形状参数和重现水平的点估计,以及10年以内的重现水平置信区间的估计,轮廓似然估计法与极大似然估计法效果基本相同,但在中长期地震重现水平置信区间的预测中,轮廓似然估计法得到的关于置信水平不对称的置信区间,在强震水平下对预测震级的不确定性表达更准确,预测结果更加有效。

     

  • 图  1  东昆仑地震带的地震分布规律

    (a) 地震空间分布;(b) M-t

    Figure  1.  Distribution law of earthquake in East Kunlun seismic zone

    (a) Spatial distribution of earthquakes;(b) Magnitude-time diagram

    图  2  形状参数与轮廓似然对数之间的关系

    Figure  2.  Relationship between shape parameters and profile likelihood logarithmic

    图  3  GEV分布模型适应性检验图

    (a)密度曲线与直方图;(b)P-P 检验

    Figure  3.  Adaptability test of GEV distribution model

    (a) Density curves and histograms;(b) P-P test

    图  4  重现水平及置信区间的轮廓似然估计

    (a) 20年重现期;(b) 50年重现期;(c) 100年重现期;(d) 500年重现期

    Figure  4.  The reappearance level and confidence interval the profile likelihood estimation

    (a) 20-year return period;(b) 50-year return period;(c)100-year return period;(d) 500-year return period

    图  5  重现水平的轮廓似然估计与极大似然估计对比

    Figure  5.  Comparation of the reproduction level between profile likelihood estimation and maximum likelihood estimation

    表  1  轮廓似然估计与极大似然估计GEV的分布结果对比

    Table  1.   Comparation of the Profile likelihood estimation and maximum likelihood estimation of GEV distribution

    模型分析项目轮廓似然估计极大似然估计
    参数估计(−0.204 0,0.847 5,4.834 5)(−0.204 4,0.847 8,4.834 8)
    形状参数置信区间 [ −0.259 0,−0.134 0 ] [ −0.268 8,−0.140 1 ]
    震级理论上限8.989 18.981 9
    地震带最大震级均值5.178 95.179 0
    下载: 导出CSV

    表  2  极大似然估计与轮廓似然估计的重现水平对比

    Table  2.   Comparation of the recurrence level between profile likelihood estimation and maximum likelihood estimation

    重现期
    /年
    极大似然估计
    重现水平/MS
    极大似然估计95%
    置信区间
    轮廓似然估计
    重现水平/MS
    轮廓似然估计95%
    置信区间
    轮廓估计重现水平
    两侧区间长度比
    15.13 [ 4.97,5.29 ] 5.13 [ 4.98,5.29 ] 1.07
    56.36 [ 6.15,6.57 ] 6.36 [ 6.17,6.59 ] 1.21
    106.72 [ 6.48,6.96 ] 6.72 [ 6.51,7.00 ] 1.33
    207.03 [ 6.75,7.30 ] 7.03 [ 6.79,7.37 ] 1.42
    507.36 [ 7.03,7.69 ] 7.36 [ 7.10,7.80 ] 1.69
    1007.58 [ 7.20,7.95 ] 7.58 [ 7.29,8.10 ] 1.79
    5007.97 [ 7.48,8.46 ] 7.97 [ 7.63,8.68 ] 2.09
    下载: 导出CSV
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  • 收稿日期:  2021-05-10
  • 修回日期:  2021-12-02
  • 网络出版日期:  2022-10-18

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