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Article(id=1322916940599144705, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322916858604696290, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.12.408, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1764604800000, receivedDateStr=2025-12-02, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793337577247, onlineDateStr=2026-10-30, pubDate=1786723200000, pubDateStr=2026-08-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793337577247, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793337577247, creator=13701087609, updateTime=1793337577247, updator=13701087609, issue=Issue{id=1322916858604696290, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='8', pageStart='913', pageEnd='1038', issueExtLink='null', onlineDate='null', pubDate='1786723200000', pubDateStr='2026-08-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793337557698, creator='13701087609', updateTime=1793337557698, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1030, endPage=1038, ext={EN=ArticleExt(id=1322916940762722562, articleId=1322916940599144705, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Robust Location of Micro-Seismic Sources Based on CTCM-Optimized K-means Clustering, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To address the insufficient robustness of traditional micro-seismic source localization methods under noise interference, we propose a robust micro-seismic source localization framework that integrates genetic algorithm (GA) global search with CTCM-optimized K-means clustering. First, an optimization objective function is constructed based on the arrival time difference mathematical model for different four-by-four combinations of measurement points. The genetic algorithm is employed to traverse and solve these cubic quadratic functions with the unknown three-dimensional coordinates of seismic source as independent variables, generating many source approximate solutions. Second, the CTCM algorithm is introduced to optimize the initial K-means clustering centers. The sum of squared error (SSE) of clustering results is used as the dependent variable of optimization objective function, and the state transition correlation matrix is used to enhance the clustering stability of high-dimensional data. Finally, the optimized K-means yields multiple clustering centers. The robust localization strategy is constructed using the median of these center coordinates and the Mahalanobis distance of each point. The median absolute deviation (MAD) is applied to automatically remove outliers, and the weighted arithmetic mean of the remaining clustering centers is the final solution. The results show that GA-CTCM-K-means method achieves superior anomaly elimination and localization performance in one planar simulation case and two real micro-seismic cases, with localization accuracy reaching 9.524 3 m, 137.865 1 m, and 28.100 9 m, respectively, which is superior to traditional methods such as the Geiger method, simplex method, and source scanning method. This method represents a micro-seismic source localization scheme with practical application value.

, authors=Guoqing CHEN1, Cong PANG2, 3, *, Yuxuan LIANG1, Shangdong LI1, Chawei LI2, Sirui LIU2, authorsList=Guoqing CHEN, Cong PANG, Yuxuan LIANG, Shangdong LI, Chawei LI, Sirui LIU, authorCompany=null, correspAuthors=Cong PANG, authorNote=null, 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=1322916944734728471, articleId=1322916940599144705, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=利用CTCM优化K-means聚类研究微震震源稳健定位, columnId=1281933709121138897, journalTitle=大地测量与地球动力学, columnName=地球动力学, runingTitle=null, highlight=null, articleAbstract=

针对传统微震震源定位方法在噪声干扰下鲁棒性不足的问题，提出一种融合遗传算法(genetic algorithm, GA)全局搜索和部落竞争与成员合作算法(competition of tribes and cooperation of members algorithm，CTCM)优化K-means聚类的微震震源稳健定位框架。首先，基于到时差数学模型构建不同测点四四组合的最优化目标函数，通过GA算法遍历求解这些以未知震源三维坐标为自变量的三元二次函数，生成大量震源近似解；然后，引入CTCM对K-means聚类的初始聚类中心进行优化，将聚类结果的误差平方和(sum of squared error, SSE)作为最优化目标函数的因变量，以状态转移相关矩阵提升高维数据的聚类稳定性；最后，执行优化后的K-means得到多个聚类中心，以这些中心坐标的中位数和各点马氏距离构建抗差定位策略，并应用中位数绝对偏差(median absolute deviation, MAD)实现对异常点的自动剔除，其他聚类中心的加权算术平均值即为最终解。结果表明，该方法(GA-CTCM-K-means)在1组平面型仿真实验和2组真实微震案例下均能实现较好的异常剔除和定位效能，定位精度分别可达9.524 3 m、137.865 1 m、28.100 9 m，优于Geiger法、单纯形法、震源扫描法等传统方法，是一种具有一定应用价值的微震震源定位方案。

, authors=陈国庆1, 庞聪2, 3, *, 梁雨萱1, 李尚东1, 李查玮2, 刘斯睿2, authorsList=陈国庆, 庞聪, 梁雨萱, 李尚东, 李查玮, 刘斯睿, authorCompany=null, correspAuthors=庞聪, authorNote=

陈国庆，博士，讲师，主要从事数学建模及数据挖掘研究，E-mail：

, correspAuthorsNote=
庞聪，工程师，主要从事人工智能地震学研究，E-mail：
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figureFileSmall=8BzWpD85ZS8o/TlYPBBUqg==, figureFileBig=kZP0ShQG+wXccXU/CpWqrg==, tableContent=null), ArticleFig(id=1322916953035256161, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=CN, label=图10, caption=基于柿竹园矿微震事件和CTCM-K-means的微震震源稳健定位结果, figureFileSmall=8BzWpD85ZS8o/TlYPBBUqg==, figureFileBig=kZP0ShQG+wXccXU/CpWqrg==, tableContent=null), ArticleFig(id=1322916953114947938, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=EN, label=Tab. 1, caption=

Simulation data of micro-seismic sources based on planar array

, figureFileSmall=null, figureFileBig=null, tableContent=
序号拾震器坐标/m到时/s
xyz
11.91 196.22.40.413 1
2852.1851.81.70.379 2
31 195.72.30.90.394 3
4846.3－844.94.20.452 3
5－4.1－1 198.56.30.510 6
6－851.2－845.75.50.538 4
7－1 196.8－3.72.40.523 9
8－845.6852.98.20.476 8
9－1.8597.63.40.246 8
10421.9426.51.20.215 4
11596.34.27.30.231 6
12426.8－420.18.90.279 8
132.5－597.24.00.324 0
14－420.7－427.16.20.346 7
15－598.4－2.99.50.336 9
16－427.5419.83.30.297 9
), ArticleFig(id=1322916953194639715, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=CN, label=表1, caption=

基于平面型台阵的微震震源仿真数据

, figureFileSmall=null, figureFileBig=null, tableContent=
序号拾震器坐标/m到时/s
xyz
11.91 196.22.40.413 1
2852.1851.81.70.379 2
31 195.72.30.90.394 3
4846.3－844.94.20.452 3
5－4.1－1 198.56.30.510 6
6－851.2－845.75.50.538 4
7－1 196.8－3.72.40.523 9
8－845.6852.98.20.476 8
9－1.8597.63.40.246 8
10421.9426.51.20.215 4
11596.34.27.30.231 6
12426.8－420.18.90.279 8
132.5－597.24.00.324 0
14－420.7－427.16.20.346 7
15－598.4－2.99.50.336 9
16－427.5419.83.30.297 9
), ArticleFig(id=1322916953282720100, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=EN, label=Tab. 2, caption=

CTCM-K-means clustering center data of source approximate solutions based on planar array simulation

, figureFileSmall=null, figureFileBig=null, tableContent=
簇群标签聚类中心坐标/m簇群点数
xyz
1185.831 8134.526 9－345.840 1134
2181.946 6132.076 2－69.486 938
3227.178 5161.432 5－652.686 4193
4254.255 8196.226 1－759.900 7137
5259.886 9200.482 5－928.218 684
6413.677 2364.880 9－78.492 31
7211.188 3156.583 2－569.978 5365
8182.371 1142.210 3－214.366 757
9196.531 3148.046 4－441.425 0312
1071.336 2387.820 5－412.395 33
11202.003 7152.129 1－506.209 3485
12318.827 6280.420 7－479.866 711
), ArticleFig(id=1322916953358217573, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=CN, label=表2, caption=

基于平面型台阵仿真的震源近似解CTCM-K-means聚类中心数据

, figureFileSmall=null, figureFileBig=null, tableContent=
簇群标签聚类中心坐标/m簇群点数
xyz
1185.831 8134.526 9－345.840 1134
2181.946 6132.076 2－69.486 938
3227.178 5161.432 5－652.686 4193
4254.255 8196.226 1－759.900 7137
5259.886 9200.482 5－928.218 684
6413.677 2364.880 9－78.492 31
7211.188 3156.583 2－569.978 5365
8182.371 1142.210 3－214.366 757
9196.531 3148.046 4－441.425 0312
1071.336 2387.820 5－412.395 33
11202.003 7152.129 1－506.209 3485
12318.827 6280.420 7－479.866 711
), ArticleFig(id=1322916953429520742, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=EN, label=Tab. 3, caption=

Micro-seismic experimental data from a certain deep mine

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探测器拾震器坐标/m到时/ms
xyz
T14 088.23 548.661.61 093.1
T24 413.13 057.4－2.21 419.0
T34 798.02 904.0－52.41 304.1
T44 280.92 834.0－83.91 224.8
T54 569.82 183.0－199.31 392.1
T63 978.43 774.3151.41 086.5
T74 501.02 442.5－147.51 315.1
T83 874.63 352.667.11 013.8
T95 447.63 138.918.01 445.7
T103 656.93 494.697.8988.5
T114 970.43 086.4－1.21 341.4
T125 181.32 942.3－21.21 396.3
), ArticleFig(id=1322916953513406823, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=CN, label=表3, caption=

某深部开采矿井微震实验数据

, figureFileSmall=null, figureFileBig=null, tableContent=
探测器拾震器坐标/m到时/ms
xyz
T14 088.23 548.661.61 093.1
T24 413.13 057.4－2.21 419.0
T34 798.02 904.0－52.41 304.1
T44 280.92 834.0－83.91 224.8
T54 569.82 183.0－199.31 392.1
T63 978.43 774.3151.41 086.5
T74 501.02 442.5－147.51 315.1
T83 874.63 352.667.11 013.8
T95 447.63 138.918.01 445.7
T103 656.93 494.697.8988.5
T114 970.43 086.4－1.21 341.4
T125 181.32 942.3－21.21 396.3
), ArticleFig(id=1322916953584709992, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916940599144705, language=EN, label=Tab. 4, caption=

CTCM-K-means clustering center data of source approximate solutions based on deep mine micro-seismic events

, figureFileSmall=null, figureFileBig=null, tableContent=
簇群标签聚类中心坐标/m簇群点数
xyz
13 891.635 03 282.702 1113.287 230
23 219.727 43 985.706 6173.983 140
33 186.439 83 661.288 897.646 337
43 782.581 53 505.173 4449.519 97
53 969.452 03 993.021 2241.869 921
63 064.854 23 917.081 2468.860 78
73 661.186 73 499.621 9100.419 8123
83 047.745 63 000.937 8226.461 612
93 446.412 63 546.723 7119.819 285
103 038.634 53 582.020 1223.133 032
113 017.240 23 839.804 5116.003 672
123 902.888 73 049.473 5465.450 728
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基于深部开采矿井微震事件的震源近似解CTCM-K-means聚类中心数据

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簇群标签聚类中心坐标/m簇群点数
xyz
13 891.635 03 282.702 1113.287 230
23 219.727 43 985.706 6173.983 140
33 186.439 83 661.288 897.646 337
43 782.581 53 505.173 4449.519 97
53 969.452 03 993.021 2241.869 921
63 064.854 23 917.081 2468.860 78
73 661.186 73 499.621 9100.419 8123
83 047.745 63 000.937 8226.461 612
93 446.412 63 546.723 7119.819 285
103 038.634 53 582.020 1223.133 032
113 017.240 23 839.804 5116.003 672
123 902.888 73 049.473 5465.450 728
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Micro-seismic event data of polymetallic mine in shizhuyuan

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编号探测器拾震器坐标/m到时/ms
xyz
T19#8 761.06 614.0522.034.9
T221#8 737.06 609.0565.036.6
T35#8 666.06 600.0520.039.3
T417#8 668.06 599.0565.041.1
T54#8 641.06 515.0520.042.3
T68#8 691.06 684.0520.044.5
T72#8 721.06 449.0520.047.8
T826#8 702.06 604.0647.050.0
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柿竹园多金属矿微震事件数据

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编号探测器拾震器坐标/m到时/ms
xyz
T19#8 761.06 614.0522.034.9
T221#8 737.06 609.0565.036.6
T35#8 666.06 600.0520.039.3
T417#8 668.06 599.0565.041.1
T54#8 641.06 515.0520.042.3
T68#8 691.06 684.0520.044.5
T72#8 721.06 449.0520.047.8
T826#8 702.06 604.0647.050.0
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CTCM-K-means clustering center data of source approximate solutions based on micro-seismic events in Shizhuyuan mine

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簇群标签聚类中心坐标/m簇群点数
xyz
18 664.311 06 538.463 15203
28 644.204 36 605.462 2629.324 44
38 724.051 86 558.534 7532.427 120
48 720.130 56 639.921 9540.433 710
58 729.374 96 588.496 3641.462 04
68 685.027 46 624.726 3564.010 74
78 705.454 16 659.365 6624.860 41
88 657.803 26 647.965 6563.670 83
98 741.609 56 527.422 6541.804 721
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基于柿竹园矿微震事件的震源近似解CTCM-K-means聚类中心数据

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簇群标签聚类中心坐标/m簇群点数
xyz
18 664.311 06 538.463 15203
28 644.204 36 605.462 2629.324 44
38 724.051 86 558.534 7532.427 120
48 720.130 56 639.921 9540.433 710
58 729.374 96 588.496 3641.462 04
68 685.027 46 624.726 3564.010 74
78 705.454 16 659.365 6624.860 41
88 657.803 26 647.965 6563.670 83
98 741.609 56 527.422 6541.804 721
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Comparison of results from multiple micro-seismic source localization methods

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方法定位误差/m
Geiger法81.731 8
单纯形法30.993 5
震源扫描法78.050 6
TDOA法30.553 9
双差定位法33.049 2
爬山法31.599 0
GA-CTCM-K-means28.100 9
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多种微震震源定位方法结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
方法定位误差/m
Geiger法81.731 8
单纯形法30.993 5
震源扫描法78.050 6
TDOA法30.553 9
双差定位法33.049 2
爬山法31.599 0
GA-CTCM-K-means28.100 9
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利用CTCM优化K-means聚类研究微震震源稳健定位
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陈国庆 1 , 庞聪 2, 3, * , 梁雨萱 1 , 李尚东 1 , 李查玮 2 , 刘斯睿 2
大地测量与地球动力学 | 地球动力学 2026,46(8): 1030-1038
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大地测量与地球动力学 |地球动力学 2026 , 46 (8) : 1030 -1038
利用CTCM优化K-means聚类研究微震震源稳健定位
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陈国庆1 , 庞聪2, 3, * , 梁雨萱1, 李尚东1, 李查玮2, 刘斯睿2
作者信息
  • 1 成都锦城学院数学建模研究中心, 成都, 611731
  • 2 中国地震局地震研究所, 武汉, 430071
  • 3 武汉引力与固体潮国家野外科学观测研究站, 武汉, 430071
通讯作者:
庞聪，工程师，主要从事人工智能地震学研究，E-mail：
作者简介:

陈国庆，博士，讲师，主要从事数学建模及数据挖掘研究，E-mail：

Robust Location of Micro-Seismic Sources Based on CTCM-Optimized K-means Clustering
Guoqing CHEN1 , Cong PANG2, 3, * , Yuxuan LIANG1, Shangdong LI1, Chawei LI2, Sirui LIU2
Affiliations
  • 1 Mathematical Modeling Research Center, Chengdu Jincheng College, Chengdu 611731, China
  • 2 Institute of Seismology, CEA, Wuhan 430071, China
  • 3 Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station, Wuhan 430071, China
出版时间: 2026-08-15 doi: 10.14075/j.jgg.2025.12.408
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摘要
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针对传统微震震源定位方法在噪声干扰下鲁棒性不足的问题，提出一种融合遗传算法(genetic algorithm, GA)全局搜索和部落竞争与成员合作算法(competition of tribes and cooperation of members algorithm，CTCM)优化K-means聚类的微震震源稳健定位框架。首先，基于到时差数学模型构建不同测点四四组合的最优化目标函数，通过GA算法遍历求解这些以未知震源三维坐标为自变量的三元二次函数，生成大量震源近似解；然后，引入CTCM对K-means聚类的初始聚类中心进行优化，将聚类结果的误差平方和(sum of squared error, SSE)作为最优化目标函数的因变量，以状态转移相关矩阵提升高维数据的聚类稳定性；最后，执行优化后的K-means得到多个聚类中心，以这些中心坐标的中位数和各点马氏距离构建抗差定位策略，并应用中位数绝对偏差(median absolute deviation, MAD)实现对异常点的自动剔除，其他聚类中心的加权算术平均值即为最终解。结果表明，该方法(GA-CTCM-K-means)在1组平面型仿真实验和2组真实微震案例下均能实现较好的异常剔除和定位效能，定位精度分别可达9.524 3 m、137.865 1 m、28.100 9 m，优于Geiger法、单纯形法、震源扫描法等传统方法，是一种具有一定应用价值的微震震源定位方案。

微震震源定位  /  到时差模型  /  CTCM算法  /  K-means聚类  /  遗传算法  /  稳健定位  /  中位数绝对偏差

To address the insufficient robustness of traditional micro-seismic source localization methods under noise interference, we propose a robust micro-seismic source localization framework that integrates genetic algorithm (GA) global search with CTCM-optimized K-means clustering. First, an optimization objective function is constructed based on the arrival time difference mathematical model for different four-by-four combinations of measurement points. The genetic algorithm is employed to traverse and solve these cubic quadratic functions with the unknown three-dimensional coordinates of seismic source as independent variables, generating many source approximate solutions. Second, the CTCM algorithm is introduced to optimize the initial K-means clustering centers. The sum of squared error (SSE) of clustering results is used as the dependent variable of optimization objective function, and the state transition correlation matrix is used to enhance the clustering stability of high-dimensional data. Finally, the optimized K-means yields multiple clustering centers. The robust localization strategy is constructed using the median of these center coordinates and the Mahalanobis distance of each point. The median absolute deviation (MAD) is applied to automatically remove outliers, and the weighted arithmetic mean of the remaining clustering centers is the final solution. The results show that GA-CTCM-K-means method achieves superior anomaly elimination and localization performance in one planar simulation case and two real micro-seismic cases, with localization accuracy reaching 9.524 3 m, 137.865 1 m, and 28.100 9 m, respectively, which is superior to traditional methods such as the Geiger method, simplex method, and source scanning method. This method represents a micro-seismic source localization scheme with practical application value.

micro-seismic source localization  /  arrival time difference model  /  CTCM algorithm  /  K-means clustering  /  genetic algorithm  /  robust localization  /  median absolute deviation
陈国庆, 庞聪, 梁雨萱, 李尚东, 李查玮, 刘斯睿. 利用CTCM优化K-means聚类研究微震震源稳健定位. 大地测量与地球动力学, 2026 , 46 (8) : 1030 -1038 . DOI: 10.14075/j.jgg.2025.12.408
Guoqing CHEN, Cong PANG, Yuxuan LIANG, Shangdong LI, Chawei LI, Sirui LIU. Robust Location of Micro-Seismic Sources Based on CTCM-Optimized K-means Clustering[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (8) : 1030 -1038 . DOI: 10.14075/j.jgg.2025.12.408
正文
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微震监测技术是矿山安全监测、地质工程稳定性分析及油气储层评价的核心手段，通过对岩体破裂产生的弹性波信号进行采集与分析，能够反演岩体内部应力状态、定位破裂发生位置并评估岩体稳定性水平。在该技术体系中，震源定位精度直接决定了微震监测技术的应用效果，精确的震源位置信息不仅能揭示岩体破裂的空间分布规律，还能为灾害预警和防控提供关键的决策依据[1-3]。
传统方法(如Geiger法、双差定位法、单纯形法等)依赖初至波到时数据的精确拾取、相邻微震事件的关联性识别或可靠的传感器布设方案，在实际工程中常面临挑战：1)传感器布设受场地条件限制导致的观测数据稀疏性；2)岩体非均质性引起的波速模型不确定性；3)背景噪声与波形混叠造成的到时拾取误差；4)复杂地质条件导致的波传播路径异常。这些因素导致定位结果易受误差较大的离群值干扰，从而降低了方法的工程适用性和结果可靠性[4-6]。值得注意的是，在强噪声干扰或复杂地质条件下，基于单一数学模型的传统定位方法对异常值极为敏感，微小的时间拾取误差可能被放大为数十米的空间定位偏差。因此，开发一种能够抑制异常值干扰、适应波速变化且不依赖高精度初至拾取的稳健型定位方法，成为微震监测领域亟待解决的关键科学问题。
近年来，聚类分析(如K-means、DBSCAN、LOF-K-means)被尝试用于解集筛选和震源定位，但传统聚类对初始中心敏感且难以处理高维非线性结构[7-8]；而启发式搜索与优化方法(如粒子群算法、GA算法、偏移叠加定位等)具有全局最优搜索、避免初值依赖、适应低信噪比等特点，可辅助聚类算法获取有针对性的超参数，实现高质量聚类。针对传统微震定位方法在解算稳健性和异常值敏感方面的不足，本文提出一种融合GA算法[9-10]多解搜索与CTCM优化聚类的稳健定位框架，通过引入CTCM算法[11-13]，重构近似解集相似性评估架构，优化K-means聚类[14-16]的初始中心选择，显著降低聚类结果对噪声和异常值的敏感性。最终实现近视解空间扩展、智能寻优聚类与统计抗差等三重优化，提升复杂噪声环境下的定位性能。
1 微震震源定位的到时差数学模型
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到时差模型是微震震源定位中的经典模型，其核心思想是不依赖地震波的绝对到达时间，而是利用地震波到达不同监测点的相对时间差进行定位。通过到时差模型构建最优化算法的适应度函数，函数自变量为反演模型的待求解参数，因变量为P波波速v和震源近似解坐标O(x0, y0, z0)，适应度函数中的已知参数为微震监测台阵测点坐标Ti(xi, yi, zi)、地震波初至到时ti等。由微震发生时刻t0和上述参数建立以下地震波传播理论公式：
$l_i=\sqrt{\left(x_i-x_0\right)^2+\left(y_i-y_0\right)^2+\left(z_i-z_0\right)^2}$
$l_i=v \cdot\left(t_i-t_0\right)$
$T_k=t_i-t_j, i \neq j$
$L_k=l_i-l_j=v \cdot T_k, i \neq j$
式中，li为第i个监测单元(xi, yi, zi)到微震震源(x0, y0, z0)的空间距离，i=1, 2, ⋯, m，其中m为接收到有效地震波信号的拾震器数量；v为地震波速度；Tk为2个监测单元记录到的首波到时之差；Lk为某2个采集单元与实际震源位置的空间距离之差；t0为微震事件的真实发生时间。最后得到到时差模型，表达式为：
$f_{\mathrm{TDA}}=\sum\limits_{k=1}^M\left(T_k-\frac{L_k}{v}\right)^2$
式中, M为全部拾震器序号的非重复组合数。
2 利用CTCM算法优化K-means聚类的微震震源稳健定位原理
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2.1 CTCM基本原理
CTCM是一种智能优化算法[11-13]，该算法受古代部落之间竞争及部落内成员合作行为的双层机制启发而得，核心参数包括团队数量、团队成员数、惯性权重、团队协作因子、全局竞争因子等，具有种群多样性强、不易早熟收敛、全局寻优能力突出等优势。
2.2 GA-CTCM-K-means微震震源稳健定位原理
GA-CTCM-K-means微震震源稳健定位流程如图 1所示，可分为5个紧密相连的步骤。
步骤1：震源近似解解算。基于已知的首波到时数据和台阵测点三维坐标值，利用到时差模型构建四四组合的三元二次非线性方程，作为最优化算法的适应度函数，其数值理论上为0。通过GA算法[9-10]依次对这些适应度函数进行全局寻优，满足最大迭代次数且停止优化后可得到大量微震震源近似解。这可有效避免传统线性方法对初值的依赖性，并生成大量覆盖真实震源区的近似解集合。
步骤2：CTCM优化K-means初始聚类中心。初始化CTCM算法的种群大小(团队数量以及每个团队的成员数量)、最大迭代次数、搜索空间范围等参数，将K-means聚类结果的SSE作为适应度函数，SSE越小则适应度越高；迭代结束后，选择全局最优解(即SSE最小的初始中心点)作为K-means初始聚类中心。
步骤3：计算聚类中心。根据上一步骤得到的最优化结果，将其代入标准K-means算法中替换原本的随机性初始聚类中心，得到若干个聚类中心。
步骤4：异常值剔除。针对震源近似解集合中混有部分异常解且空间分布复杂的特性，需要采取合适措施予以剔除，并使震源附近的有效簇群不被意外过滤。设计以聚类中心中位数和马氏距离为基础的抗差定位策略，结合MAD实现对异常点的自动识别与剔除，从而在最终估计阶段抑制异常值干扰。
1) 将上一步骤得到的所有聚类中心piC=($\hat{x}_c, \hat{y}_c, \hat{z}_c $)(1≤c≤J)按行向量构建成中心点矩阵 C，计算其中位数并作为参考中心向量$\bar{\boldsymbol{C}}= \operatorname{median}(\boldsymbol{C})=\left(\bar{x}_c, \bar{y}_c, \bar{z}_c\right)$。
2) 分别计算各个聚类中心piC与参考中心$ \bar{\boldsymbol{C}}$的差值矩阵 diff和MAD，然后利用点除法得到尺度差值矩阵 scaled_diff，在此基础上经过矩阵元素平方、按行求和、按行开方计算 scaled_diff的欧氏距离，最终得到每个聚类中心piC的马氏距离。
3) 利用MAD_dist计算异常值剔除的阈值threshold，其中MAD_dist表示对距离(distance)计算MAD，阈值系数一般为3(对应99.7%置信区间)，偏差估计常数为1.482 6，用于将MAD转换为对正态分布标准偏差的一致估计。将马氏距离大于异常值阈值的聚类中心piC予以剔除，其他J*个聚类中心记为有效聚类中心点。主要公式如下：
$\boldsymbol{C}=\left[\begin{array}{c}p_1^C \\p_2^C \\\vdots \\p_J^C\end{array}\right]=\left[\begin{array}{ccc}\hat{x}_1 & \hat{y}_1 & \hat{z}_1 \\\hat{x}_2 & \hat{y}_2 & \hat{z}_2 \\& \vdots & \\\hat{x}_J & \hat{y}_J & \hat{z}_J\end{array}\right]$
$\mathbf{diff}=\boldsymbol{C}-\bar{\boldsymbol{C}}$
$\mathrm{MAD}=1.482\;6 \times \operatorname{median}\left(\left|p_i^C-\operatorname{median}(\boldsymbol{C})\right|\right)$
$\mathbf{scaled\_diff}=\mathbf{diff} \cdot / \mathrm{MAD}=\left[\begin{array}{ccc}\Delta x_1^C & \Delta y_1^C & \Delta z_1^C \\\Delta x_2^C & \Delta y_2^C & \Delta z_2^C \\& \vdots & \\\Delta x_J^C & \Delta y_J^C & \Delta z_J^C\end{array}\right]$
$\text { distance }=\left[\begin{array}{c}\sqrt{\left(\Delta x_1^C\right)^2+\left(\Delta y_1^C\right)^2+\left(\Delta z_1^C\right)^2} \\\sqrt{\left(\Delta x_2^C\right)^2+\left(\Delta y_2^C\right)^2+\left(\Delta z_2^C\right)^2} \\\vdots \\\sqrt{\left(\Delta x_J^C\right)^2+\left(\Delta y_J^C\right)^2+\left(\Delta z_J^C\right)^2}\end{array}\right]$
$\begin{gathered}\text { threshold }=\text { median }(\text { distance })+3 \times \\1.482\;6 \times \text { MAD_dist }\end{gathered}$
步骤5：对其他聚类中心进行加权算术平均，得到最终的震源解。由于聚类中心位置及其附属簇点数量反映了震源近似解在空间上的聚集密度和命中概率，如果简单地对有效聚类中心计算算术平均值，就无法准确表达有效聚类中心的全部分布信息。本文引入聚集权重因子γj，用以表示每个有效聚类中心所属聚类簇群的近似解数量权重占比，得到最终解Pfinal。
$\gamma_j=\frac{\operatorname{num}\left(p_j^C\right)}{\sum\limits_{j=1}^{J^*} \operatorname{num}\left(p_j^C\right)} $
$P_{\text {final }}=\sum\limits_{j=1}^{J^*}\left(\gamma_j \times p_j^C\right)$
式中，num(·)表示该有效聚类中心pjC所属簇群的震源近似解数量。
3 微震震源正反演仿真实验
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基于仿真原理设计1组平面型台阵正反演仿真实验，为模仿真实场景，生成的数据含有一定噪声成分，假设P波在地质介质中的传播速度为213.3 m/s(对应某些软岩或煤层)，发震地点固定为三维点(200.7, 150.4, －500.5)，在微震台阵边缘上均匀布设16个监测单元，台阵正反演仿真数据如表 1所示。
图 2为基于平面型台阵仿真和GA算法求解到时差模型的震源近似解分布，图 3为基于平面型台阵仿真和CTCM-K-means的震源近似解聚类散点图，表 2为基于平面型台阵仿真的震源近似解CTCM-K-means聚类中心数据，图 4为基于平面型台阵仿真和CTCM-K-means的微震震源稳健定位结果。
由图 2~4和表 2可知：
1) 本轮定位过程历时76.746 6 s，共产生1 820个震源近似解和12个聚类中心，各中心所属簇群的近似解数量分别为134、38、193、137、84、1、365、57、312、3、485、11，各簇群平均深度分别为－345.8±32.5 m、－69.5±44.7 m、－652.7±30.1 m、－759.9±39.6 m、－928.2±46.7 m、－78.5 m、－570.0±20.5 m、－214.4±38.5 m、－441.4±22.6 m、－412.4±43.9 m、－506.2±18.6 m、－479.9±78.6 m。
2) 根据近似解所属聚类中心，在近似解矩阵基础上替换并重建182 0×3阶聚类中心矩阵，将其中位数中心(202.003 7, 152.129 1, －506.209 3) 作为参考点，计算得到X、Y、Z方向的MAD分别为9.184 6 m、4.454 1 m、64.784 3 m，结合各重建近似解与参考点的差值矩阵，计算得到马氏距离的MAD为1.723 1 m，异常值阈值为9.386 8 m。
3) 该模型利用阈值共剔除异常近似解236个，对其他近似解求算术平均得到最终定位结果为(203.553 9, 151.157 8, －491.445 0)，定位误差为9.524 3 m。
4 实例验证与分析
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为验证本文提出的新型微震震源定位方法在不同实际监测条件下的性能与鲁棒性，设计并引入2组在台阵形状、尺寸及测点数量上均存在显著差异的微震事件数据集。这一对比设计的核心目的在于：1)检验GA-CTCM-K-means框架对非理想、不规则台阵布局的适应能力，避免所提方法仅在特定“完美”台阵下有效；2)测试台站数量与空间覆盖范围变化对定位精度与稳定性的具体影响，从而明确该方法的优势区间与应用边界。
CTCM算法参数设置：团队数量为5，各团队个体数为10，迭代次数为50，惯性权重为0.7，团队协作因子为1.5，全局竞争因子为1.5。GA算法参数设置：迭代次数为20，种群数目为50，交配概率为0.8，变异概率为0.2，连续不进化的中断数为500。
4.1 工程案例一
引入某深部开采矿井微震实验数据[4-6]进行定位实验，该深部矿井共布设12台拾震器，人工爆破震源三维坐标为(3 500.0, 3 520.5, 102.0), 发震时刻为00:00，微震事件发生后记录到12个地震波到时有效数据，具体如表 3所示。
图 5为基于深部开采矿井微震事件和GA算法求解到时差模型的震源近似解分布，图 6为基于深部开采矿井微震事件和CTCM-K-means的震源近似解聚类散点图，表 4为基于深部开采矿井微震事件的震源近似解CTCM-K-means聚类中心数据，图 7为基于深部开采矿井微震事件和CTCM-K-means的微震震源稳健定位结果。
由图 5~7和表 4可知：
1) 本轮定位过程历时48.610 5 s，共产生495个震源近似解和12个聚类中心，各中心所属簇群的近似解数量分别为30、40、37、7、21、8、123、12、85、32、72、28，各簇群平均深度分别为113.3±79.4 m、174.0±81.5 m、97.6±51.6 m、449.5±60.9 m、241.9±150.4 m、468.9±72.2 m、100.4±33.7 m、226.5±245.2 m、119.8±74.1 m、223.1±168.0 m、116.0±64.3 m、465.5±49.7 m。
2) 根据近似解所属聚类中心，在近似解矩阵基础上替换并重建495×3阶聚类中心矩阵，将其中位数中心(3 446.412 6, 3 546.723 7, 116.003 6) 作为参考点，计算得到X、Y、Z方向的MAD分别为226.685 1 m、114.565 1 m、15.583 8 m，结合各重建近似解与参考点的差值矩阵，计算得到马氏距离的MAD为1.595 4 m，异常值阈值为10.128 8 m。
3) 该模型利用阈值共剔除异常近似解43个，对其他近似解求算术平均得到最终定位结果为(203.553 9, 151.157 8, －491.445 0)，定位误差为137.865 1 m。
4.2 工程案例二
为进一步分析本文方法在不同微震事件数据下的定位实用性和模型兼容性，采用区别于工程案例一的湖南柿竹园微震实验数据[4-6]进行实验验证，其实际发震位置为(8 732.70, 6 570.60, 511.30)，共记录到8个地震波到时数据(表 5)。
图 8为基于柿竹园矿微震事件和GA算法求解到时差模型的震源近似解分布，表 6为基于柿竹园矿微震事件的震源近似解CTCM-K-means聚类中心数据，图 9为基于柿竹园矿微震事件和CTCM-K-means的震源近似解聚类散点图，图 10为基于柿竹园矿微震事件和CTCM-K-means的微震震源稳健定位结果。
由图 8~10和表 6可知：
1) 本轮定位过程历时4.308 7 s，共产生70个震源近似解和9个聚类中心，各中心所属簇群的近似解数量分别为3、4、20、10、4、4、1、3、21，各簇群平均深度分别为520.0 m、629.3±18.8 m、532.4±11.8 m、540.4±12.0 m、641.5±8.6 m、564.0±11.6 m、624.9±0.0 m、563.7±28.1 m、541.8±9.1 m。
2) 全部聚类中心的中位数中心为(8 724.051 8, 6 558.534 7, 541.804 7)，将其作为参考点计算各点的马氏距离，得到马氏距离的MAD为0.414 2 m，异常值阈值为3.256 6 m。
3) 该模型利用阈值共剔除异常近似解19个，对其他近似解求算术平均得到最终定位结果为(8 730.5, 6 561.7, 537.9)，定位误差为28.100 9 m。
为分析GA-CTCM-K-means模型与传统算法的定位性能差异，采用Geiger法、单纯形法、震源扫描法、TDOA法、双差定位法、爬山法等多种定位方法进行比较，实验均使用湖南柿竹园矿微震事件数据，计算结果如表 7所示。可以看出，GA-CTCM-K-means相对其他传统定位方法具有显著的震源计算优势，定位误差在30 m以内。
5 结语
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针对传统微震震源定位方法在噪声干扰下易失稳、鲁棒性不足的核心问题，提出一种融合GA算法全局搜索与CTCM优化K-means聚类的稳健定位算法(GA-CTCM-K-means)。该模型的关键之处在于构建了一个“全局初筛-智能聚类-抗差估计”的多阶段优化流程。
GA-CTCM-K-means方法在1例平面型仿真实验和2例真实微震案例下均实现了显著的异常点剔除和震源定位效果，定位精度分别可达9.524 3 m、137.865 1 m、28.100 9 m，并且分别剔除236、43、19个异常近似解，被证实是一种适宜小型台网、具有一定抗异能力的微震震源定位方案。此外，2组工程微震实验结果表明，不同的台阵分布和测点数量在一定程度上会制约定位精度的提升。
尽管本文提出的方法具有良好效果，但在后续研究中仍可进一步深化与拓展：1)当前框架涉及GA的全局搜索和CTCM的迭代优化，计算成本相对较高。未来可探索并行计算或自适应迭代终止策略，以提升方法的实时性。2)利用深度学习网络(如自动编码器)对初代近似解集合进行降维和特征学习，以辅助或改进聚类过程，进一步提升方法在极端噪声条件下的适应性。
基金
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  • 四川省科技厅软科学项目(2023JDR0271)
  • 成都锦城学院博士专项(2025JCKY(B)0018)
  • 武汉引力与固体潮国家野外科学观测研究站开放基金(WHYWZ202406)
  • 中国地震局地震监测预警工作任务(CEA-JCYJ-202601025)
  • 湖北省重点实验室定向委托项目(2025CSA083)
  • 应急管理部国家自然灾害防治研究院基本科研业务专项(ZDJ2025-58)
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doi: 10.14075/j.jgg.2025.12.408
  • 接收时间：2025-12-02
  • 首发时间：2026-10-30
  • 出版时间：2026-08-15
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  • 收稿日期：2025-12-02
基金
四川省科技厅软科学项目(2023JDR0271)
成都锦城学院博士专项(2025JCKY(B)0018)
武汉引力与固体潮国家野外科学观测研究站开放基金(WHYWZ202406)
中国地震局地震监测预警工作任务(CEA-JCYJ-202601025)
湖北省重点实验室定向委托项目(2025CSA083)
应急管理部国家自然灾害防治研究院基本科研业务专项(ZDJ2025-58)
作者信息
    1 成都锦城学院数学建模研究中心, 成都, 611731
    2 中国地震局地震研究所, 武汉, 430071
    3 武汉引力与固体潮国家野外科学观测研究站, 武汉, 430071

通讯作者:

庞聪，工程师，主要从事人工智能地震学研究，E-mail：
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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2025.12.408
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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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