Article(id=1322940533060018739, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322940449979244751, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.04.203, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1714320000000, receivedDateStr=2024-04-29, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343202128, onlineDateStr=2026-10-30, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343202128, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343202128, creator=13701087609, updateTime=1793343202128, updator=13701087609, issue=Issue{id=1322940449979244751, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='3', pageStart='221', pageEnd='330', issueExtLink='null', onlineDate='null', pubDate='1741968000000', pubDateStr='2025-03-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343182320, creator='13701087609', updateTime=1793343182320, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=260, endPage=265, ext={EN=ArticleExt(id=1322940533240373812, articleId=1322940533060018739, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Research on Magnitude Estimation Model Using Pd Method in Beijing-Tianjin-Hebei Region, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Based on 963 records of intensity meters and 410 records of strong motion seismographs of 37 earthquakes of ML3.2 to 5.9 in Beijing-Tianjin-Hebei and its surrounding areas from 2019 to 2022, we use the Pd method to establish 36 magnitude estimation models between Pd amplitude within 2 to 7 seconds after P-wave arrival time of vertical waveform and magnitude. By fitting the standard deviation, the optimal filtering frequency bands of intensity meters and strong motion seismographs are determined to be 1 to 3 Hz and 0.5 to 3 Hz respectively. Meanwhile, we establish the magnitude estimation model of intensity meters and strong motion seismographs within 3 seconds after P-wave arrival time using Pd method. The parameter fitting results show that fitting slope and correlation coefficient are high, the standard deviation is small, and the overall reliability is high. The results of reverse and new data verification indicate that the magnitude deviation of Pd method is mainly within ±0.5, which shows that the two models established in this paper are reasonable and can be well applied in Beijing-Tianjin-Hebei region.

, authors=Lichan WANG1, 2, Guoliang MAO1, 2, Yaojia GUO1, 2, Qingxi LIN3, authorsList=Lichan WANG, Guoliang MAO, Yaojia GUO, Qingxi LIN, authorCompany=null, correspAuthors=null, authorNote=

WANG Lichan, senior engineer, majors in earthquake monitoring and early warning, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322940536725840449, articleId=1322940533060018739, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=京津冀地区Pd方法震级估算模型研究, columnId=1322506193558422163, journalTitle=大地测量与地球动力学, columnName=地震地质, runingTitle=null, highlight=null, articleAbstract=

基于2019—2022年京津冀及周边地区37次ML3.2~5.9地震的963个烈度计和410个强震仪台站数据,利用Pd方法建立垂直向波形在P波到时后2~7 s的Pd幅值与震级之间的36种估算模型,通过拟合关系标准差确定烈度计和强震仪的最佳滤波频段分别为1~3 Hz和0.5~3 Hz,同时建立二者在P波到时后3 s内的Pd方法震级估算模型。参数拟合结果表明,模型拟合斜率和相关系数较高,标准差较小,模型整体可靠度较高。反向验证和新数据验证结果显示,与台网编目震级相比,单台Pd方法震级偏差主要集中在±0.5范围内,说明本文建立的2种Pd方法震级估算模型具有可行性,可以较好地应用于京津冀地区。

, authors=王莉婵1, 2, 毛国良1, 2, 郭垚嘉1, 2, 林庆西3, authorsList=王莉婵, 毛国良, 郭垚嘉, 林庆西, authorCompany=null, correspAuthors=null, authorNote=

王莉婵,高级工程师,主要从事地震监测与预警研究,E-mail:

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tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=CN, label=图4, caption=烈度计与强震仪最优回归模型, figureFileSmall=mvp1obayX5kyRiKjB/4mtA==, figureFileBig=05CAfWydV8ClQ8kJbDIU8Q==, tableContent=null), ArticleFig(id=1322940546024612468, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=EN, label=Tab. 1, caption=

Comparison with previous research results

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 区域 震级范围 震源距范围/km 地震条数/台站记录数 P波到时后时间/s 地震计类型 拟合斜率 相关系数 标准差
1 京津冀地区 ML3.2~5.9 0~60 37/963 2~7 烈度计 0.65~0.74 0.72~0.82 0.26~0.30
2 京津冀地区 ML3.2~5.9 0~60 37/410 2~7 强震仪 0.87~0.90 0.62~0.73 0.29~0.37
3 鲁甸地区[3] M≥3.0 0~300 11/64 1~3 强震仪 0.50~1.17 0.57~0.74 0.84~0.98
4 芦山地区[4] M4.0~7.0 20~200 -/211 1~3 强震仪 0.32~1.05 0.25~0.64 1.14~1.30
5 云南地区[5] M≥3.5 0~200 -/133 2~4 强震仪 0.60~0.67 0.65~0.83 /
6 四川地区[6] M≥4.0 20~100 -/937 2~4 强震仪 0.25~0.51 0.65~0.82 /
7 汶川地区[10] M4.0~8.0 0~60 218/687 2、4 强震仪 0.67~0.68 / 0.37
8 甘肃及邻区[11] M3.1~6.5 0~100 190/821 1~5、7、10 速度计 0.68~0.71 / 0.29~0.34
), ArticleFig(id=1322940546108498549, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=CN, label=表1, caption=

与前人研究结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 区域 震级范围 震源距范围/km 地震条数/台站记录数 P波到时后时间/s 地震计类型 拟合斜率 相关系数 标准差
1 京津冀地区 ML3.2~5.9 0~60 37/963 2~7 烈度计 0.65~0.74 0.72~0.82 0.26~0.30
2 京津冀地区 ML3.2~5.9 0~60 37/410 2~7 强震仪 0.87~0.90 0.62~0.73 0.29~0.37
3 鲁甸地区[3] M≥3.0 0~300 11/64 1~3 强震仪 0.50~1.17 0.57~0.74 0.84~0.98
4 芦山地区[4] M4.0~7.0 20~200 -/211 1~3 强震仪 0.32~1.05 0.25~0.64 1.14~1.30
5 云南地区[5] M≥3.5 0~200 -/133 2~4 强震仪 0.60~0.67 0.65~0.83 /
6 四川地区[6] M≥4.0 20~100 -/937 2~4 强震仪 0.25~0.51 0.65~0.82 /
7 汶川地区[10] M4.0~8.0 0~60 218/687 2、4 强震仪 0.67~0.68 / 0.37
8 甘肃及邻区[11] M3.1~6.5 0~100 190/821 1~5、7、10 速度计 0.68~0.71 / 0.29~0.34
), ArticleFig(id=1322940546448237174, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=EN, label=Tab. 2, caption=

Statistics on magnitude deviation of single station

, figureFileSmall=null, figureFileBig=null, tableContent=
震级偏差范围 [-1.5, -1.0) [-1.0, -0.5) [-0.5, 0) 0 (0, 0.5] (0.5, 1.0] (1.0, 1.5] 标准偏差
烈度计台站数 8 104 363 9 378 95 6 0.42
强震仪台站数 4 34 152 9 179 29 3 0.41
), ArticleFig(id=1322940546532123256, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=CN, label=表2, caption=

单台震级偏差统计

, figureFileSmall=null, figureFileBig=null, tableContent=
震级偏差范围 [-1.5, -1.0) [-1.0, -0.5) [-0.5, 0) 0 (0, 0.5] (0.5, 1.0] (1.0, 1.5] 标准偏差
烈度计台站数 8 104 363 9 378 95 6 0.42
强震仪台站数 4 34 152 9 179 29 3 0.41
), ArticleFig(id=1322940546863473273, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=EN, label=Tab. 3, caption=

Segmental statistics on magnitude deviation of intensity meters and strong motion seismographs

, figureFileSmall=null, figureFileBig=null, tableContent=
震级范围 震级偏差 烈度计 强震仪
个数 平均偏差 个数 平均偏差
[3.2, 4.0) <0 229 -0.283 6 146 -0.328 0
≥0 239 0.324 7 163 0.283 2
[4.0, 5.0) <0 188 -0.414 3 40 -0.274 4
≥0 164 0.374 7 45 0.278 8
[5.0, 6.0) <0 60 -0.318 1 6 -0.356 7
≥0 83 0.282 7 10 0.247 4
), ArticleFig(id=1322940546930582138, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=CN, label=表3, caption=

烈度计与强震仪震级偏差分段统计结果

, figureFileSmall=null, figureFileBig=null, tableContent=
震级范围 震级偏差 烈度计 强震仪
个数 平均偏差 个数 平均偏差
[3.2, 4.0) <0 229 -0.283 6 146 -0.328 0
≥0 239 0.324 7 163 0.283 2
[4.0, 5.0) <0 188 -0.414 3 40 -0.274 4
≥0 164 0.374 7 45 0.278 8
[5.0, 6.0) <0 60 -0.318 1 6 -0.356 7
≥0 83 0.282 7 10 0.247 4
), ArticleFig(id=1322940547299680891, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=EN, label=Tab. 4, caption=

Validation results of the model

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 日期 震级ML 参考地名 烈度计 强震仪
Pd平均震级 使用台站数量 震级偏差 Pd平均震级 使用台站数量 震级偏差
1 2023-01-24 3.3 河北磁县 3.08 18 -0.22 3.11 6 -0.19
2 2023-01-30 3.2 河北蠡县 3.10 17 -0.10 3.17 12 -0.03
3 2023-02-12 3.6 北京房山 3.41 15 -0.19 3.24 38 -0.14
4 2023-03-25 3.9 河北临城 3.74 34 -0.16 3.79 7 -0.11
5 2023-04-05 3.7 河北灵寿 3.48 54 -0.22 3.29 8 -0.41
6 2023-07-31 3.4 河北张北 3.15 10 -0.25 3.34 11 -0.06
7 2023-08-06 3.7 山东平原 3.80 13 0.10 3.55 9 -0.15
8 2023-09-01 3.4 北京昌平 3.49 19 0.09 3.42 69 0.02
), ArticleFig(id=1322940547400344188, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, language=CN, label=表4, caption=

模型验证结果

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 日期 震级ML 参考地名 烈度计 强震仪
Pd平均震级 使用台站数量 震级偏差 Pd平均震级 使用台站数量 震级偏差
1 2023-01-24 3.3 河北磁县 3.08 18 -0.22 3.11 6 -0.19
2 2023-01-30 3.2 河北蠡县 3.10 17 -0.10 3.17 12 -0.03
3 2023-02-12 3.6 北京房山 3.41 15 -0.19 3.24 38 -0.14
4 2023-03-25 3.9 河北临城 3.74 34 -0.16 3.79 7 -0.11
5 2023-04-05 3.7 河北灵寿 3.48 54 -0.22 3.29 8 -0.41
6 2023-07-31 3.4 河北张北 3.15 10 -0.25 3.34 11 -0.06
7 2023-08-06 3.7 山东平原 3.80 13 0.10 3.55 9 -0.15
8 2023-09-01 3.4 北京昌平 3.49 19 0.09 3.42 69 0.02
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京津冀地区Pd方法震级估算模型研究
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王莉婵 1, 2 , 毛国良 1, 2 , 郭垚嘉 1, 2 , 林庆西 3
大地测量与地球动力学 | 地震地质 2025,45(3): 260-265
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大地测量与地球动力学 |地震地质 2025 , 45 (3) : 260 -265
京津冀地区Pd方法震级估算模型研究
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[Author(id=1322940537732473421, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=wlc84872583@163.com, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322940537858302544, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940533060018739, authorId=1322940537732473421, language=EN, stringName=Lichan WANG, firstName=Lichan, middleName=null, lastName=WANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, 2, address=1 Hebei Hongshan National Observatory on Thick Sediments and Seismic Hazards, 1540 West-Quanbei Street, Xingtai 054000, China
2 Hebei Earthquake Agency, 262 Huaizhong Road, Shijiazhuang 050021, China, bio={"content":"

WANG Lichan, senior engineer, majors in earthquake monitoring and early warning, E-mail:

"}, bioImg=null, bioContent=

WANG Lichan, senior engineer, majors in earthquake monitoring and early warning, E-mail:

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2 河北省地震局, 石家庄市槐中路262号, 050021, bio={"content":"

王莉婵,高级工程师,主要从事地震监测与预警研究,E-mail:

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王莉婵,高级工程师,主要从事地震监测与预警研究,E-mail:

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王莉婵1, 2 , 毛国良1, 2, 郭垚嘉1, 2, 林庆西3
作者信息
  • 1 河北红山巨厚沉积与地震灾害国家野外科学观测研究站, 河北省邢台市泉北西大街1540号, 054000
  • 2 河北省地震局, 石家庄市槐中路262号, 050021
  • 3 广东省地震局, 广州市先烈中路81号, 510070
作者简介:

王莉婵,高级工程师,主要从事地震监测与预警研究,E-mail:

Research on Magnitude Estimation Model Using Pd Method in Beijing-Tianjin-Hebei Region
Lichan WANG1, 2 , Guoliang MAO1, 2, Yaojia GUO1, 2, Qingxi LIN3
Affiliations
  • 1 Hebei Hongshan National Observatory on Thick Sediments and Seismic Hazards, 1540 West-Quanbei Street, Xingtai 054000, China
  • 2 Hebei Earthquake Agency, 262 Huaizhong Road, Shijiazhuang 050021, China
  • 3 Guangdong Earthquake Agency, 81 Mid-Xianlie Road, Guangzhou 510070, China
  • WANG Lichan, senior engineer, majors in earthquake monitoring and early warning, E-mail:

出版时间: 2025-03-15 doi: 10.14075/j.jgg.2024.04.203
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基于2019—2022年京津冀及周边地区37次ML3.2~5.9地震的963个烈度计和410个强震仪台站数据,利用Pd方法建立垂直向波形在P波到时后2~7 s的Pd幅值与震级之间的36种估算模型,通过拟合关系标准差确定烈度计和强震仪的最佳滤波频段分别为1~3 Hz和0.5~3 Hz,同时建立二者在P波到时后3 s内的Pd方法震级估算模型。参数拟合结果表明,模型拟合斜率和相关系数较高,标准差较小,模型整体可靠度较高。反向验证和新数据验证结果显示,与台网编目震级相比,单台Pd方法震级偏差主要集中在±0.5范围内,说明本文建立的2种Pd方法震级估算模型具有可行性,可以较好地应用于京津冀地区。

京津冀地区  /  地震预警  /  Pd方法  /  震级估算模型

Based on 963 records of intensity meters and 410 records of strong motion seismographs of 37 earthquakes of ML3.2 to 5.9 in Beijing-Tianjin-Hebei and its surrounding areas from 2019 to 2022, we use the Pd method to establish 36 magnitude estimation models between Pd amplitude within 2 to 7 seconds after P-wave arrival time of vertical waveform and magnitude. By fitting the standard deviation, the optimal filtering frequency bands of intensity meters and strong motion seismographs are determined to be 1 to 3 Hz and 0.5 to 3 Hz respectively. Meanwhile, we establish the magnitude estimation model of intensity meters and strong motion seismographs within 3 seconds after P-wave arrival time using Pd method. The parameter fitting results show that fitting slope and correlation coefficient are high, the standard deviation is small, and the overall reliability is high. The results of reverse and new data verification indicate that the magnitude deviation of Pd method is mainly within ±0.5, which shows that the two models established in this paper are reasonable and can be well applied in Beijing-Tianjin-Hebei region.

Beijing-Tianjin-Hebei region  /  earthquake early warning  /  Pd method  /  magnitude estimation model
王莉婵, 毛国良, 郭垚嘉, 林庆西. 京津冀地区Pd方法震级估算模型研究. 大地测量与地球动力学, 2025 , 45 (3) : 260 -265 . DOI: 10.14075/j.jgg.2024.04.203
Lichan WANG, Guoliang MAO, Yaojia GUO, Qingxi LIN. Research on Magnitude Estimation Model Using Pd Method in Beijing-Tianjin-Hebei Region[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (3) : 260 -265 . DOI: 10.14075/j.jgg.2024.04.203
随着国家地震烈度速报与预警工程的完成,地震预警已经成为社会公众服务的重要产品之一。地震预警信息可为政府应急决策提供依据,减少人员伤亡和财产损失,为重大工程提供安全保障服务,减轻直接地震灾害及次生灾害损失[1]。完整的地震预警系统一般包括实时地震定位、实时震级计算、烈度估计和信息发布等重要功能模块,其中实时震级计算最重要,也是最困难的部分[2]。震级的准确度对于地震危害判断和灾后救援等具有重要作用,因此预警震级的精度是科研工作者的重点研究对象。
目前国内预警震级计算方法中,应用最多的是τpmax、τc和Pd方法。研究表明[3-6],3种方法中Pd方法与震级的相关性最高,离散程度最小,在监测台网密集地区中应用效果最好,其最优拟合时间窗为3~4 s。由于Pd方法稳定性好,可靠性高,即使采用单个台站计算震级,其结果的离散程度也优于其他算法,且Pd参数获取方法也较为简单,因此张红才等[2]推荐将Pd方法作为我国地震预警系统中优先采用的震级计算方法之一。
京津冀地区近年来虽少有大震发生,但小震频发,且部分地区小震震感明显,容易引起公众恐慌,需要提供精度较高的地震预警信息。而目前预警网的震级估计一般依靠经验公式,存在一定的离散性;同时,地震预警参数具有一定的区域适用性,即在不同地质、地形和发震构造条件影响下,不同地区的震级估算模型也会有所差别[7],如2020-07-12河北古冶5.1级地震预警首报仅为3.8级。因此,从技术层面和社会服务层面出发,基于京津冀地区地震资料,建立符合本地区预警震级估算模型的需求非常迫切。为此,本文基于京津冀地区历年预警事件波形数据,建立本地化的Pd方法震级估算模型并进行相应分析。
对地震数据进行高通滤波处理后,生成的位移记录中P波触发3 s内的位移幅值Pd与地震震级和震源距R之间存在如下关系[8-9]:
$\lg P_{\mathrm{d}}=A+B M+C \lg R$
式中,Pd为采用2阶高通Butterworth滤波器(低频截止频率为0.075 Hz)滤波后的位移记录中P波触发若干秒内的峰值位移;M为事件震级;R为震源距;A、B、C为需要求取的各项拟合参数。
收集2019年以来京津冀地区记录的37次M2.5 (ML3.2,后文震级标度统一为ML)以上地震数据,作为本研究的基础。图1为地震震中分布。
由于预警主要针对大地震,前人研究也主要是基于6级以上地震,滤波频段一般为0.075 Hz至高频,或0.075~3 Hz以及0.25~3 Hz等[4-5, 10-12],低频段信息较多。但受限于近年京津冀及周边地区大震较少,本研究中地震目录多集中在ML4.0左右,而河北预警网当前使用的地震计均为加速度计,其记录频段范围更偏向于高频。为了能更好地建立拟合关系,本文在多种滤波频段内(0.075~3 Hz、0.25~3 Hz、0.5~1.5 Hz、0.5~3 Hz、1~3 Hz、1~6 Hz)得到P波到时后2~7 s内P波最大位移幅值Pd,估算不同Pd与震源距、震级之间的拟合关系。
在数据整理过程中发现,河北预警网中的加速度计分为烈度计与强震仪2种,二者记录数据质量区别较大,为建立精度更高的Pd方法模型,本文对2种仪器分别开展研究。以2020-07-12河北古冶5.1级地震(河北台网编目结果为ML5.3)为例,对震源距60 km范围内的台站波形进行数据预处理,包括基线校正、去除仪器响应等。预处理完成后,去除基线漂移,然后人工拾取P波到时,采用上述6种频段滤波,得到位移模量曲线(图2)。可以看出,在相对较低和较高滤波频段内,滤波后波形中P波起始位置的清晰度均低于中间滤波频段,且1~6 Hz滤波频段内背景噪声更多,因此中间滤波频段更具优势。
通过上述处理,37次地震最终得到963个烈度计和410个强震仪台站数据,数据量相对丰富,并且数据记录相对震源距呈高斯分布,震级主要集中在ML4.5以下。
以上述数据为基础,根据式(1)进行最小二乘拟合,得到各项系数。为只研究震级ML与早期P波震相幅值的关系,在式(1)基础上,对震源距进行校正,将其统一校正到“参考”震源距10 km[10, 13],可以得到:
$\lg P_{\mathrm{d}}^{10 \mathrm{~km}}=a M+b$
针对烈度计与强震仪分别建立36种Pd方法估算模型,各自对应一个标准差。据此开展反向验证,即根据式(2)计算37次地震中963个烈度计和410个强震仪台站的36种单台Pd方法震级,与编目震级对比,计算单台震级偏差,同时分析估算模型与震级偏差的标准差。由图3可知,每种滤波频段的标准差都随P波到时增加而变小,这是因为随着时间变长,原本表征震级的S波被纳入分析范围内,因此拟合结果越来越好,这也说明在预警系统中可以不断更新震级,从而提高震级的可靠性。另外,图中数据也清晰地展示出本文所选数据在0.075~3 Hz滤波频段内标准差最大,故该频段无法用于本文震级估算模型的建立。
从图3可以看出,对于烈度计而言,0.5~3 Hz与1~3 Hz滤波频段效果较好;对于强震仪而言,0.5~3 Hz、1~3 Hz与1~6 Hz滤波频段效果较好。考虑到预警系统的时效性,本文以P波到时后3 s为数据基础,选择此时标准差最小的滤波频段建立各自的Pd方法震级估算模型,其中烈度计选择1~3 Hz,强震仪为0.5~3 Hz。图4为2种地震计震级估算模型拟合关系图,包含模型参数及参数误差和标准差,其中各项系数的偏差和标准差代表式(1)中未考虑到的其他因素对结果的影响,如介质衰减、场地效应和震源辐射花样等[10]。
本文使用的地震数据仅37条,数据量相对偏少。为验证结果的可靠性,将本文所选滤波频段内2~7 s的拟合结果与前人研究成果进行对比(表1)。结果表明,本文建立的模型中,烈度计的拟合斜率在0.7左右,相关系数在0.8左右,标准差均低于0.3;强震仪的拟合斜率接近0.9,相关系数在0.7左右,标准差均低于0.4。在不考虑震级和震源距范围的情况下,虽然本文使用的地震条数较少,但数据记录较多,并且相对于以往研究成果,拟合斜率和相关系数较高,且分布较集中,同时标准差也较小,说明本文研究结果可靠度高。本文选择的地震数据并未按主余震或地域进行区分,表明Pd算法在京津冀地区的整体适用性较好。
依据图4中模型参数分别计算烈度计和强震仪台站的Pd方法震级,并与编目震级对比,进行反向验证。由表2可知,2种地震计的单台Pd方法震级偏差主要集中在±0.5范围内,占比分别为77.88%、82.92%。将编目震级分成[3.2,4.0)、[4.0,5.0)、[5.0,6.0)共3个震级范围,统计各个震级段内对应的2种地震计的单台Pd方法震级偏差,结果见表3。可以看出,在不同震级段内,2种地震计的Pd方法所得震级偏差分布均匀,平均偏差也基本一致,最大平均偏差为-0.414 3,由此也说明本文建立的模型(图4)具有可行性。
根据单台Pd方法计算每次地震的平均震级,其中烈度计震级偏差小于±0.3占比83.78%,小于±0.5占比100%;强震仪震级偏差小于±0.3占比83.78%,小于±0.5占比97.30%。选取其中2次ML5.0以上地震(2020-07-12河北唐山古冶ML5.3地震,河北台网编目结果;2023-08-06山东平原ML5.9地震,山东台网编目结果),分别计算震中距最近的6个烈度计与强震仪台站的平均震级,唐山地震平均震级分别为ML5.1、ML5.3,平原地震平均震级分别为ML6.1、ML5.9,计算精度得到明显提升。以上结果表明,本文建立的Pd方法震级估算模型具有可行性。
选择2023-01—10京津冀地区ML3.2以上地震作为验证数据,以预警系统触发到时为起始时间,得到不同到时的最大位移量Pd,并计算烈度计和强震仪台站的36种预警震级,同样与编目震级进行对比,分析震级偏差的标准差。与上文一致,烈度计在0.5~3 Hz与1~3 Hz,强震仪在0.5~3 Hz、1~3 Hz与1~6 Hz滤波频段内标准差最小。与编目震级对比可知,烈度计台站震级偏差小于±0.5占比83.33%,强震仪台站震级偏差小于±0.5占比78.13%。根据单台Pd方法震级结果计算每次地震的平均震级,其中烈度计震级偏差小于±0.3占比100%;强震仪震级偏差小于±0.3占比75%,小于±0.5占比100%。由表4可以看出,烈度计台站数量整体多于强震仪,因此前者震级偏差更稳定。
根据震源能量辐射花样可知,台站数量越多,其分布均匀度越高,平均震级偏差会越小;反之,则容易导致震级偏差增大。因此针对强震仪中台站数量少于15个的6次地震(表4中序号为1、2、4~7)进行分析,发现台站震级基本随震源距变大而增大。但对于2023-04-05河北灵寿ML3.7地震(序号为5),使用的8个台站主要集中于震中一侧,具体表现为3个震源距较小(11 km、25 km、27 km)台站的震级偏小(ML3.05、ML3.35、ML3.27)。在震源距较大的5个台站中,3个台站的震级明显偏小,分别为ML2.84、ML2.79、ML2.85,对应的方位角分别为179°、195°、351°,原因为该方位震源辐射能量较弱,导致震级偏小;剩余2个台站的震源距及方位角分别为43.7 km、145°和53.8 km、155°,震级偏大,分别为ML4.00、ML4.20,由此导致该地震的平均震级偏差相对较大,为-0.41。而其他使用台站数量较少的地震(序号为1、2、4、6、7),因台站分布情况较好,且震源距多大于30 km,因此震级偏差相对较小。
1) 与前人研究结果相比,本文建立Pd方法震级估算模型过程中使用的地震数据震级偏小,在ML3.2~5.9之间;地震条数较少,但台站数量相对较多且分布范围较大,分布在京津冀及周边地区;滤波频段主要偏向于较高频段。另外,本文按照仪器类型进行分类研究,建立烈度计与强震仪2种估算模型,估算模型的拟合斜率都大于0.6,且强震仪的拟合斜率接近0.9,标准差均低于0.4,模型可靠度较高,不仅说明Pd方法在京津冀高密度台网地区适用性较好,也表明分类建立模型有助于提高震级估算精度。
2) 在反向验证及新数据验证中,与原编目结果相比,单台Pd方法震级偏差与平均Pd方法震级偏差主要集中在±0.5以内,应用效果较好。尤其是本文研究的震级主要集中在ML4.0左右,最大震级为ML5.9,在2次ML5.0以上地震中平均Pd方法震级偏差均在±0.2以内,应用效果良好。但后续仍需不断增加震例,尤其是6级以上地震,通过对高低频滤波频段进行分析,探寻Pd方法在京津冀地区的优势滤波频段和震级饱和情况,并实时更新,以期达到更优的预警效果。
3) 由于震级测定涉及多个方面,如场地条件、震源过程、传播介质和仪器响应等,简单的P波起始振幅并不能保证全部还原震级情况,因此Pd方法存在较大的离散性[10]。本文建立的模型显示,随着P波到时的增加,拟合情况也越来越好,但考虑到预警的时效性,建议预警首报可以采用P波到时后3 s的数据计算震级,后续实时更新,同时也可以考虑加入其他相关参数,不断提升预警震级的准确度。
  • 河北省地震科技星火计划(DZ202108100004)
  • 中国地震局地震科技星火计划(XH23005A)
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2025年第45卷第3期
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doi: 10.14075/j.jgg.2024.04.203
  • 接收时间:2024-04-29
  • 首发时间:2026-10-30
  • 出版时间:2025-03-15
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  • 收稿日期:2024-04-29
基金
The Spark Program of Earthquake Technology of Hebei Province(DZ202108100004)
河北省地震科技星火计划(DZ202108100004)
The Spark Program of Earthquake Technology of CEA(XH23005A)
中国地震局地震科技星火计划(XH23005A)
作者信息
    1 河北红山巨厚沉积与地震灾害国家野外科学观测研究站, 河北省邢台市泉北西大街1540号, 054000
    2 河北省地震局, 石家庄市槐中路262号, 050021
    3 广东省地震局, 广州市先烈中路81号, 510070
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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
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