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Article(id=1228653710990049928, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.11.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1679241600000, receivedDateStr=2023-03-20, revisedDate=1685980800000, revisedDateStr=2023-06-06, acceptedDate=null, acceptedDateStr=null, onlineDate=1770863471982, onlineDateStr=2026-02-12, pubDate=1732723200000, pubDateStr=2024-11-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770863471982, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770863471982, creator=13701087609, updateTime=1770863471982, updator=13701087609, issue=Issue{id=1228653708687377017, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='11', pageStart='1803', pageEnd='1992', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770863471433, creator=13701087609, updateTime=1770863902026, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228655514792427773, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228655514792427774, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1875, endPage=1883, ext={EN=ArticleExt(id=1228653711220736650, articleId=1228653710990049928, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Attenuation relationship of peak ground acceleration near the fault of the Wenchuan earthquake, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In this paper，the strong earthquake records of 13 soil stations within 41 km from the fault of the 2008 Wenchuan 8.0 magnitude earthquake are selected. These records are combined with the strong earthquake records of 29 calculation points obtained by using the stochastic finite fault method simulation. Moreover，nonlinear least squares fitting is performed by using three near-fault ground motion attenuation models and the fifth-generation ground motion parameter zoning map attenuation model to obtain the peak ground motion acceleration of the Wenchuan earthquake near-fault. The attenuation relationships are obtained and analyzed by considering ±1 times standard deviation and correlation coefficients for reliability. The results show that there are some differences in the attenuation relations obtained by different attenuation models. The peak acceleration obtained by the Shao Guangbiao model is low. The prediction results of Wang Guoquan model has a large deviation for other magnitude earthquakes because the magnitude term is not considered. Besides，the peak acceleration of the fifth-generation ground motion parameter zoning map attenuation model is low.

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本文选取2008年汶川8.0级特大地震断层距41 km内13个土层台站的强震记录，结合以随机有限断层法模拟得到的29个计算点的强震记录，采用三种近断层地震动衰减模型和第五代地震动参数区划图衰减模型进行了非线性最小二乘法拟合，得到了汶川地震近断层地震动峰值加速度衰减关系，并通过±1倍标准差和相关性系数进行可靠性分析。结果表明，采用不同衰减模型得到的衰减关系有一定的差异：邵广彪模型得到的峰值加速度偏低；王国权模型因没有考虑震级项，其预测结果针对其他震级的地震会产生较大偏差；第五代地震动参数区划图衰减模型得到的峰值加速度偏低。

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李平（1981—），男，博士，教授。 E-mail： 。

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李平（1981—），男，博士，教授。 E-mail： 。

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李平（1981—），男，博士，教授。 E-mail： 。

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caption=本文模型PGA预测曲线与观测值的对比, figureFileSmall=i3e9CvaFGet1ZtSwYFWgqQ==, figureFileBig=zx3YTa1qlsOlYhzeVzTK5g==, tableContent=null), ArticleFig(id=1228653724764143725, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=EN, label=Tab.1, caption=

Information of stations within 41 km of the Wenchuan earthquake near faults

, figureFileSmall=null, figureFileBig=null, tableContent=
序号台站代码台站名称断层距/km场地条件
151MZQ绵竹清平3.1土层
251SFB什邡八角7.8土层
351WCW汶川卧龙6.0土层
451JYH江油含增18.8土层
551LXT理县桃平23.0土层
651LXM理县木卡26.0土层
751JYD江油地震台26.4土层
851PWM平武木座27.7土层
951AXT安县塔水28.1土层
1051JYC江油重华30.5土层
1151DXY大邑银屏31.2土层
1251QLY邛崃油榨31.2土层
1351DYB德阳白马37.0土层
1451PXZ郫县走石山21.0基岩
1551MXD茂县地办24.0基岩
), ArticleFig(id=1228653724839641199, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=CN, label=表1, caption=

汶川地震近断层41 km内的台站信息表

, figureFileSmall=null, figureFileBig=null, tableContent=
序号台站代码台站名称断层距/km场地条件
151MZQ绵竹清平3.1土层
251SFB什邡八角7.8土层
351WCW汶川卧龙6.0土层
451JYH江油含增18.8土层
551LXT理县桃平23.0土层
651LXM理县木卡26.0土层
751JYD江油地震台26.4土层
851PWM平武木座27.7土层
951AXT安县塔水28.1土层
1051JYC江油重华30.5土层
1151DXY大邑银屏31.2土层
1251QLY邛崃油榨31.2土层
1351DYB德阳白马37.0土层
1451PXZ郫县走石山21.0基岩
1551MXD茂县地办24.0基岩
), ArticleFig(id=1228653724961276020, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=EN, label=Tab.2, caption=

Parameters used for simulating the Wenchuan ground motion site by stochastic finite fault method

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值出处
矩震级7.9文献[8]
断层走向/[倾角/(°)]229/33文献[18]
沿走向×倾向的断层尺寸/km2280×40文献[8]
子断层尺寸/km25×5文献[8]
子断层个数(走向×倾向)56×8计算取值
地壳剪切波速/()3.4文献[10]
破裂传播速度/()3.4×0.8文献[10]
地壳平均密度/()2.7文献[10]
应力降/MPa120文献[19]
Kappa0.03文献[10]
品质因子Q(f)=303f 0.39文献[10]
窗函数Saragoni-Hart文献[8]
几何扩散方程1/R, R≤70 km文献[8]
1/R0, 70 km<R<130 km
1/R0.5, R≥130 km
), ArticleFig(id=1228653725040967800, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=CN, label=表2, caption=

随机有限断层法模拟汶川地震动场的参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值出处
矩震级7.9文献[8]
断层走向/[倾角/(°)]229/33文献[18]
沿走向×倾向的断层尺寸/km2280×40文献[8]
子断层尺寸/km25×5文献[8]
子断层个数(走向×倾向)56×8计算取值
地壳剪切波速/()3.4文献[10]
破裂传播速度/()3.4×0.8文献[10]
地壳平均密度/()2.7文献[10]
应力降/MPa120文献[19]
Kappa0.03文献[10]
品质因子Q(f)=303f 0.39文献[10]
窗函数Saragoni-Hart文献[8]
几何扩散方程1/R, R≤70 km文献[8]
1/R0, 70 km<R<130 km
1/R0.5, R≥130 km
), ArticleFig(id=1228653725154214014, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=EN, label=Tab.3, caption=

Comparison of strong earthquake records and simulated values of ground motion

, figureFileSmall=null, figureFileBig=null, tableContent=
台站代码台站名称场地条件水平向均值/gal模拟结果/gal误差/%
51MZQ绵竹清平土层730.46788.2227.91
51SFB什邡八角土层595.89368.916-38.09
51WCW汶川卧龙土层819.59883.2677.77
51JYH江油含增土层442.97294.407-33.54
51LXT理县桃平土层341.05265.451-22.17
51LXM理县木卡土层302.92283.073-6.55
51JYD江油地震台土层485.71270.909-44.22
51PWM平武木座土层230.63210.129-8.89
51AXT安县塔水土层250.22194.272-22.36
51JYC江油重华土层287.76219.339-23.78
51DXY大邑银屏土层112.01131.69217.57
51QLY邛崃油榨土层146.62131.692-10.18
51DYB德阳白马土层109.25124.78714.22
), ArticleFig(id=1228653725259071619, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=CN, label=表3, caption=

地震动强震记录与模拟值对比

, figureFileSmall=null, figureFileBig=null, tableContent=
台站代码台站名称场地条件水平向均值/gal模拟结果/gal误差/%
51MZQ绵竹清平土层730.46788.2227.91
51SFB什邡八角土层595.89368.916-38.09
51WCW汶川卧龙土层819.59883.2677.77
51JYH江油含增土层442.97294.407-33.54
51LXT理县桃平土层341.05265.451-22.17
51LXM理县木卡土层302.92283.073-6.55
51JYD江油地震台土层485.71270.909-44.22
51PWM平武木座土层230.63210.129-8.89
51AXT安县塔水土层250.22194.272-22.36
51JYC江油重华土层287.76219.339-23.78
51DXY大邑银屏土层112.01131.69217.57
51QLY邛崃油榨土层146.62131.692-10.18
51DYB德阳白马土层109.25124.78714.22
), ArticleFig(id=1228653726613831815, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=EN, label=Tab.4, caption=

Supplement calculation points information of stochastic finite fault method

, figureFileSmall=null, figureFileBig=null, tableContent=
No.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/gal
10.871042.3176.14650.201314.01395.201924.09194.822538.00118.05
21.02988.8987.74544.191416.02358.962025.53561.002638.49104.22
32.01863.0298.01613.471518.73268.242132.00178.432740.01101.88
43.10831.641010.02510.001619.55219.572234.01146.702840.1796.99
54.54879.881110.18561.451720.01556.962336.94111.442941.0180.00
65.72654.541212.00427.291822.00514.402437.96117.26
), ArticleFig(id=1228653726789992587, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=CN, label=表4, caption=

随机有限断层法补充计算点信息表

, figureFileSmall=null, figureFileBig=null, tableContent=
No.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/galNo.R/kmPGA/gal
10.871042.3176.14650.201314.01395.201924.09194.822538.00118.05
21.02988.8987.74544.191416.02358.962025.53561.002638.49104.22
32.01863.0298.01613.471518.73268.242132.00178.432740.01101.88
43.10831.641010.02510.001619.55219.572234.01146.702840.1796.99
54.54879.881110.18561.451720.01556.962336.94111.442941.0180.00
65.72654.541212.00427.291822.00514.402437.96117.26
), ArticleFig(id=1228653726915821709, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=EN, label=Tab.5, caption=

Correlation coefficients of attenuation models used in this paper

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衰减模型工况类型模型参数
c0c1c2R2
邵广彪模型[6]实测水平2.945-0.018-0.7630.202
实测竖向2.965-0.023-0.7520.256
实测+模拟2.984-0.021-0.7760.245
王国权模型[4]实测水平32.940-11.898334.5980.7490.164
实测竖向34.515-12.133409.5290.6480.138
实测+模拟4.908-1.51517.1180.7800.215
本文模型实测水平3.9886.2728×10-4-0.7440.186
实测竖向4.003-0.004-0.7080.234
实测+模拟4.015-0.002-0.7810.210
), ArticleFig(id=1228653726999707792, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653710990049928, language=CN, label=表5, caption=

本文所用衰减模型相关系数

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衰减模型工况类型模型参数
c0c1c2R2
邵广彪模型[6]实测水平2.945-0.018-0.7630.202
实测竖向2.965-0.023-0.7520.256
实测+模拟2.984-0.021-0.7760.245
王国权模型[4]实测水平32.940-11.898334.5980.7490.164
实测竖向34.515-12.133409.5290.6480.138
实测+模拟4.908-1.51517.1180.7800.215
本文模型实测水平3.9886.2728×10-4-0.7440.186
实测竖向4.003-0.004-0.7080.234
实测+模拟4.015-0.002-0.7810.210
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汶川地震近断层地震动峰值加速度衰减关系研究
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李平 1, 2 , 徐建元 1, 3 , 鞠雅倩 1, 2 , 陈钰鑫 1, 2 , 欧阳刚垒 1, 4 , 宣雨童 1, 2 , 沙明卓 5
振动工程学报 | 2024,37(11): 1875-1883
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振动工程学报 | 2024, 37(11): 1875-1883
汶川地震近断层地震动峰值加速度衰减关系研究
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李平1, 2 , 徐建元1, 3, 鞠雅倩1, 2, 陈钰鑫1, 2, 欧阳刚垒1, 4, 宣雨童1, 2, 沙明卓5
作者信息
  • 1防灾科技学院地质工程学院，河北　三河　065201
  • 2河北省地震灾害防御与风险评价重点实验室， 河北　三河　065201
  • 3江苏省规划设计集团有限公司市政规划与工程设计院，江苏　南京　210019
  • 4核工业井巷建设集团有限公司，浙江　湖州　313001
  • 5沈阳市给排水勘察设计研究院有限公司，辽宁　沈阳　110023

    • 李平（1981—），男，博士，教授。 E-mail： 。

Attenuation relationship of peak ground acceleration near the fault of the Wenchuan earthquake
Ping LI1, 2 , Jian-yuan XU1, 3, Ya-qian JU1, 2, Yu-xin CHEN1, 2, Gang-lei OUYANG1, 4, Yu-tong XUAN1, 2, Ming-zhuo SHA5
Affiliations
  • 1College of Geological Engineering，Institute of Disaster Prevention，Sanhe 065201，China
  • 2Key Laboratory of Earthquake Disaster Prevention and Risk Assessment of Hebei Province，Sanhe 065201，China
  • 3Municipal Planning and Engineering Design Institute，Jiangsu Provincial Planning and Design Group Co.，Ltd.， Nanjing 210019，China
  • 4Nuclear Industry Shaft Construction Group Co.，Ltd.，Huzhou 313001，China
  • 5Shenyang Water Supply & Drainage Prospecting Design Research Institute Co.，Ltd.，Shenyang 110023，China
出版时间: 2024-11-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.11.008
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摘要
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本文选取2008年汶川8.0级特大地震断层距41 km内13个土层台站的强震记录，结合以随机有限断层法模拟得到的29个计算点的强震记录，采用三种近断层地震动衰减模型和第五代地震动参数区划图衰减模型进行了非线性最小二乘法拟合，得到了汶川地震近断层地震动峰值加速度衰减关系，并通过±1倍标准差和相关性系数进行可靠性分析。结果表明，采用不同衰减模型得到的衰减关系有一定的差异：邵广彪模型得到的峰值加速度偏低；王国权模型因没有考虑震级项，其预测结果针对其他震级的地震会产生较大偏差；第五代地震动参数区划图衰减模型得到的峰值加速度偏低。

汶川地震  /  近断层地震动  /  随机有限断层法  /  衰减关系  /  标准差

In this paper，the strong earthquake records of 13 soil stations within 41 km from the fault of the 2008 Wenchuan 8.0 magnitude earthquake are selected. These records are combined with the strong earthquake records of 29 calculation points obtained by using the stochastic finite fault method simulation. Moreover，nonlinear least squares fitting is performed by using three near-fault ground motion attenuation models and the fifth-generation ground motion parameter zoning map attenuation model to obtain the peak ground motion acceleration of the Wenchuan earthquake near-fault. The attenuation relationships are obtained and analyzed by considering ±1 times standard deviation and correlation coefficients for reliability. The results show that there are some differences in the attenuation relations obtained by different attenuation models. The peak acceleration obtained by the Shao Guangbiao model is low. The prediction results of Wang Guoquan model has a large deviation for other magnitude earthquakes because the magnitude term is not considered. Besides，the peak acceleration of the fifth-generation ground motion parameter zoning map attenuation model is low.

Wenchuan earthquake  /  near-fault seismic ground motion  /  stochastic finite tomography  /  attenuation relationship  /  standard deviation
李平, 徐建元, 鞠雅倩, 陈钰鑫, 欧阳刚垒, 宣雨童, 沙明卓. 汶川地震近断层地震动峰值加速度衰减关系研究. 振动工程学报, 2024 , 37 (11) : 1875 -1883 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.008
Ping LI, Jian-yuan XU, Ya-qian JU, Yu-xin CHEN, Gang-lei OUYANG, Yu-tong XUAN, Ming-zhuo SHA. Attenuation relationship of peak ground acceleration near the fault of the Wenchuan earthquake[J]. Journal of Vibration Engineering, 2024 , 37 (11) : 1875 -1883 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.008
正文
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引言
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中国学者对近断层地震动衰减规律的研究因缺乏近断层强震记录，以及受限于近断层地震动的复杂性而不够深入。随着近些年破坏性地震的频发，中国学者获取了大量近断层强震记录，关于近断层地震动的研究也取得了一些实质性的突破，得到了一系列研究成果［1-3］。文献［4-5］以中国台湾集集地震发震断层55 km范围内的130个台站记录为数据库，分析了地震动峰值加速度、速度、位移和持时的特征，提出了适用于集集地震的近场地震动衰减关系；邵广彪等［6］基于全球范围内6.0~7.6级且震源深度小于20 km的地震，通过对强震记录峰值加速度进行统计分析，提出了近断层地震动的衰减模型；KOKETSU等［7］利用汶川地震发震断层150 km内54个台站的加速度记录，拟合回归得到了汶川地震近断层地震动的衰减关系。
除了依靠现有强震记录进行回归分析确定地震动衰减关系之外，随机有限断层法在建立地震动衰减关系中也得到广泛应用。傅磊等［8］建立了龙门山地区与高程相关的κ0模型，模拟得到了汶川地震动PGA（峰值加速度）分布；GHASEMI等［9］基于随机有限断层法，模拟了汶川地震近断层150 km内54个台站的PGA，并对模拟结果和经验衰减模型进行了对比分析，验证了模拟结果的准确性；喻烟［10］利用随机有限断层法，模拟出了汶川地震主震地震动场，但并未得到北川老县城的地表地震动。关于汶川地震衰减关系的成果中，并未给出明确的近断层区域划分和适用于汶川地震近断层地震动参数衰减关系的衰减模型。因此，基于已有研究成果，本文利用李明等［11］对近断层区域的划分范围，确定了汶川地震近断层区域在断层距41 km内，并选取了13个土层台站的强震记录，结合以随机有限断层法模拟得到的29个模拟计算点的强震记录，采用王国权衰减模型［4］、邵广彪衰减模型［6］、本文模型和第五代地震动参数区划图衰减模型［12-13］进行非线性最小二乘法拟合，得到了汶川地震近断层地震动峰值加速度衰减关系，并通过±1倍的标准差及相关性系数对拟合曲线的离散程度进行可靠性分析。
1　近断层区域划分及台站选取
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2008年5月12日，四川省汶川县发生8.0级特大地震，震中位于阿坝藏族羌族自治州汶川县映秀镇，震源深度为14 km。根据地质学研究表明：控制本次地震的是北川—映秀断裂带，地表破裂长度约240 km，以逆断层破裂为主并伴有右旋走滑分量［14-15］。此次地震共计触发四川省强震台站141个，参考李明等［11，16］在2010年给出的近断层地震动区域的划分标准，根据USGS场地分类标准、断层类型和矩震级三个指标，确定汶川地震近断层区域为断层距41 km内，选取了近断层41 km内的13个土层台站和2个基岩台站（选取两个基岩台站作为后文的随机有限断层法模拟地震动的参照台站）。本文台站信息来自中国地震局工程力学研究所强震动观测与工程振动研究中心，使用的强震记录数据均已进行基线校正和滤波。本文计算衰减关系采用断层距作为距离项，具体计算方法是以汶川地震地表破裂带作为发震断层在地表的投影位置，根据多个地表破裂带现场调查点的经纬度坐标和台站的经纬度坐标计算地表破裂带现场调查点和台站位置两点之间的距离，取其中的最小值为断层距。台站分布如图1所示，台站信息如表1所示。
2　汶川地震随机有限断层模拟
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本文以2008年汶川特大地震为例，基于文献［17-18］反演得到的单断层位错模型，确定了沿走向280 km和沿倾向40 km的矩形计算区域，计算点共计9060个，如图2所示。参考文献［8-10］的研究成果，确定了模拟汶川特大地震地震动场的参数，如表2所示，表中R为断层距。
由于随机有限断层模拟的是水平向基岩地震动，为了和13个土层台站（Ⅱ类场地）的PGA进行对比分析［20］，利用《中国地震动参数区划图》（GB 18306—2015）［21］中的场地地震动峰值加速度调整系数，采用线性内插法调整得到台站地表的PGA模拟计算结果，如表3所示。表3中除51SFB，51JYH，51JYD台站误差稍大，其余台站的强震记录数据和模拟误差平均在20%左右，误差较大的三个台站可能是由于土层台站位于山地地区，地形地貌对地震动影响显著。
为了验证利用随机有限断层法模拟汶川地震主震地震动场的准确性，本文利用《中国地震烈度表》（GB/T 17742—2020）［22］中的地震烈度对应的地震动峰值（地震动峰值为所对应的仪器测定的地震烈度中值），将汶川地震Ⅸ，Ⅹ，Ⅺ烈度等值线转换为地震动峰值等值线，并与模拟的地震动场等值线进行对比分析，结果如图3所示。模拟得到的汶川地震近场加速度等值线和烈度等值线基本吻合，其中Ⅹ和Ⅺ烈度区的等值线和峰值加速度分区吻合度较高。
汶川地震中近断层41 km内有13个土层台站和2个基岩台站。由于台站仅分布在4~6 km，18~25 km，30~36 km，强震记录数据少且分布不均，所以仅用强震记录数据拟合近断层地震动衰减关系不够精确。本文通过汶川地震随机有限断层法在断层距41 km范围内增加了29个模拟计算点（依据实测台站的位置、模拟计算点的PGA值和断层距确定补充计算点的位置，使其均匀分布在近断层41 km内，便于后文衰减关系的拟合），汶川地震随机有限断层法计算区域和模拟计算点如图4所示。模拟补充基岩处的计算点通过《中国地震动参数区划图》（GB 18306—2015）［21］中的场地地震动峰值加速度调整系数进行调整，采用线性内插法调整得到模拟地表PGA的计算结果如表4所示。
综上分析，以随机有限断层法模拟近断层地震动是可靠的，所得数据可用于后文中的汶川地震近断层衰减关系拟合。
3　近断层地震动衰减关系模型
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目前常用的近断层地震动衰减关系模型有邵广彪衰减模型［6］、王国权衰减模型［4］，本文衰减模型以及第五代地震动参数区划图青藏区短轴衰减模型，具体阐述如下：
邵广彪衰减模型［6］形式为：
式中　 Y为地震动峰值PGA；R为断层距；M为矩震级；H为震源深度；c0~c3为待求的参数；ε为随机误差。
由于本文所研究的是汶川地震主震，式（1）中的变量矩震级、震源深度都是常数，所以经过修改后的衰减模型为：
式中　 为拟合值的标准差。
王国权等［4］基于1999年中国台湾集集（Chi-Chi）地震提出的衰减模型为：
文献［9］提出的PGA衰减模型为：
式中　 a0~a3为待求的参数。
依据已有强震记录提出的近断层地震动PGA衰减模型为（本文所使用的衰减模型）：
第五代地震动参数区划图青藏区短轴衰减模型［20］为：
采用以上三种衰减模型和第五代地震动参数区划图衰减模型，对实测台站的水平向记录、竖向记录、实测台站记录和模拟记录进行非线性最小二乘法拟合（最小二乘法应用到曲线拟合时，当自变量和因变量同时存在均值为零，方差相同的随机误差时，此方法能给出在统计意义上最好的参数拟合结果），回归结果、拟合优度R2和标准差σ如表5所示。第五代地震动参数区划图青藏区短轴衰减模型参数已确定。
4　回归结果分析
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4.1　本文衰减关系与其他衰减关系对比
本文基于以上三种衰减模型和第五代地震动参数区划图衰减模型，分别对实测强震记录和模拟强震记录进行非线性最小二乘法拟合（水平向峰值加速度衰减关系拟合使用13个土层台站的峰值加速度和随机有限断层模拟得到的29个补充记录，竖向地震动峰值加速度进行衰减关系拟合时，仅使用13个土层台站的峰值加速度进行回归拟合），如图5（a），（b）所示，邵广彪［6］和王国权模型［4］的结果对地震动峰值加速度估计过低，而本文模型和第五代地震动参数区划图衰减模型地震动峰值加速度较为接近。如图5（c）所示，使用随机有限断层法对模拟计算点强震记录和实测强震记录进行拟合，除了邵广彪模型［6］对峰值估计过低之外其他三种模型峰值均达到了1.0g左右，所以随着随机有限断层法模拟计算点的补充，近断层区域内衰减规律较为明显，而第五代地震动参数区划图衰减模型和本文模型较为接近，但预测峰值加速度偏低。根据整个汶川地震的宏观现象以及台站记录到的强震记录来看，距离震中最近的卧龙台PGA高达957.7 gal，而远离震中的北川震害情况非常严重，与震中相比甚至更加显著。所以北川老县城的地表地震动估计值要大于卧龙台所记录到的结果，至少要达到1.0g以上。故根据北川老县城的实际震害以及地表地震动估计，本文模型的结果更为合理。
4.2　标准差分析
本文将实测强震记录和模拟强震记录分别用邵广彪衰减模型［6］、王国权衰减模型［4］和本文模型进行预测值和观测值的对比分析，结果如图6~8所示，图中实线为拟合曲线，虚线为估计值的±1倍标准差值。由图6可知，邵广彪模型［6］的观测值大部分均处在±1倍标准差内，只有极少数大于预测值范围，增加随机有限断层模拟点强震记录之后拟合结果有明显提高但是整体趋势变化不大［23-24］。由图7可知，王国权衰减模型［4］拟合曲线与其他三种模型拟合曲线相比整体趋势过低，尤其是竖向观测值不符合实测记录以及震害特征，增加了模拟计算点强震记录之后整体趋势变化较大，对峰值的估计增大了0.2g左右，但是由于王国权衰减模型［4］没有考虑震级项，故而预测结果对于其他震级的地震会产生较大偏差。由图8可知，本文结果对PGA的估计值较为合理，符合北川老县城的震害特征，整体衰减趋势较快，观测值大部分处在±1倍标准差内，增加了模拟计算点强震记录之后，整体趋势相似性较高，且拟合优度接近0.8，标准差也在0.2左右，不仅说明本文模型可以很好地估计汶川地震近断层区域内的PGA，同时也反映了北川老县城地表地震动的经验估计。所以本文模型的估计值整体上较为合理，符合汶川地震近断层PGA特征。
5　结论与展望
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本文选取了汶川地震近断层内13个土层台站的强震记录，结合以随机有限断层法模拟得到的29个模拟计算点的强震记录，使用邵广彪模型［6］、王国权模型［4］、本文模型以及第五代地震动参数区划图衰减模型［11-12］，对水平和竖向峰值加速度进行非线性最小二乘法拟合，利用相关性系数和±1倍标准差进行了可靠性分析，得出以下结论：
（1） 本文衰减模型对实测台站水平向记录、竖向记录的拟合回归结果较为合理，绝大多数峰值加速度观测值分布在本文衰减模型±1倍标准差以内。断层距1 km范围内峰值加速度达到了1.0g，符合北川老县城的实际震害情况，基本达到了预测值范围。
（2） 在实测台站强震记录和模拟强震记录中，邵广彪模型的估值过低不符合实际震害特征，王国权模型因没有考虑震级项导致预测结果对于其他震级的地震会产生较大偏差，而本文模型和第五代地震动参数区划图衰减模型的结果较为合理，但是第五代地震动参数区划图衰减模型对于本文模型来说峰值较低，所以本文模型较适用于汶川特大地震近断层区域的峰值加速度预测。
本文并未讨论模拟地震动计算点参与到衰减关系拟合中可能存在的误差，本文模型适用性较为单一，仅适用于汶川地震近断层41 km内的衰减关系拟合。对随机有限断层法补充计算点位置的确定并未做深入研究，可能会造成一些误差。断层上下盘的震害程度不同，本文因数据点数量有限并未在衰减关系中考虑上下盘效应的影响。未来工作可以从以上问题入手，进行更加深入的讨论和研究。
基金
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  • 河北省高等学校科学技术研究计划项目(ZD2022166)
  • 中国地震局地震科技星火计划资助项目(XH204401)
  • 防灾科技学院研究生创新基金资助项目(ZY20220323)
文献
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2024年第37卷第11期
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文章信息
doi: 10.16385/j.cnki.issn.1004-4523.2024.11.008
  • 接收时间：2023-03-20
  • 首发时间：2026-02-12
  • 出版时间：2024-11-28
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  • 收稿日期：2023-03-20
  • 修回日期：2023-06-06
基金
河北省高等学校科学技术研究计划项目(ZD2022166)
中国地震局地震科技星火计划资助项目(XH204401)
防灾科技学院研究生创新基金资助项目(ZY20220323)
作者信息
    1防灾科技学院地质工程学院，河北　三河　065201
    2河北省地震灾害防御与风险评价重点实验室， 河北　三河　065201
    3江苏省规划设计集团有限公司市政规划与工程设计院，江苏　南京　210019
    4核工业井巷建设集团有限公司，浙江　湖州　313001
    5沈阳市给排水勘察设计研究院有限公司，辽宁　沈阳　110023
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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