Geometry of Seismogenic Faults Determination of the 2021 Maduo Earthquake Sequence by Fuzzy Clustering Algorithm
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摘要: 为更深入理解青海玛多区域的地质构造，准确确定该区域的各个分支断层面形状以及断层面参数是关键.本研究按照成丛小震发生在断层面邻近区域的原则，基于模糊聚类算法聚类数据并确定断层面的方法对2021年青海玛多Ms7.4级地震序列进行断层面形状求解，得到了各个分级下的断层结构.然后将研究区域的应力场投影到获得的断层面上，得到了各个断层面的相对剪应力和正应力.结果表明本次地震主干断层面破裂长度为163.71 km，总体走向为285.81°，倾角为85.62°，断层面主要分布于昆仑山口‒江错断裂上.该地震序列的东西两侧表现有明显的分叉现象，针对这一较为复杂的断层结构，通过区域划分和模糊聚类数目的各种尝试，得到了划分为6个断层面的模糊聚类求解断层面结果.将研究区域的构造应力场结果投影到6个断层面上，发现这些断层面上相对剪应力普遍大于相对正应力.由此推断本次地震主要是由构造应力场作用引起，而位于西端分叉处北支的小断裂是主破裂引发的分支破裂，由于本次破裂具有左旋走滑运动性质，使断层东段东北部出现了尾端拉张，导致东段分叉上形成了两个小断层.本研究中通过模糊聚类方法得出的断层参数与其他机构作者数据一致性较高.该方法基于大量地震序列数据可较为准确地得出断层面信息且可操作性高，在未来地震构造、断层面确定以及分析中具有重要意义.Abstract: To gain a deeper understanding of the geological structure in the Maduo region of Qinghai, it is crucial to accurately determine the shapes and parameters of each branch fault planes in the area. Based on the principle that clusters of small earthquakes occur near the fault plane, by using the fuzzy clustering algorithm to cluster the seismic event, the geometry parameters of the fault planes of the 2021 Ms7.4 Qinghai Maduo earthquake sequence are determined. By projecting the stress field in study area onto the obtained fault planes, the relative shear stress and normal stress of each fault plane are obtained. The results show that the overall fault plane of these 2021 Maduo earthquake is mainly distributed on the Kunlun Pass-Jiangcuo fault, with rupture length of 163.71 km, strike of 285.81°, and dip angle of 85.62°. There are obvious bifurcations on the east and west sides of the earthquake distribution area. For the complex fault structure, we made various attempts through the fuzzy clustering algorithm, and obtained the fault plane solution by fuzzy clustering with 6 fault planes. By projecting the tectonic stress field onto the 6 obtained fault planes, we found that the relative shear stress on these fault planes is generally greater than the relative normal stress. Therefore, it is speculated that the earthquake was mainly caused by the tectonic stress field, and the small fault in the north branch at the western end of the bifurcation is the branch rupture caused by the main rupture. Due to the left-lateral strike-slip nature of this rupture, tail extension appeared in the northeastern part of the eastern segment of the fault, resulting in the formation of the 2 small faults on the bifurcation of the eastern segment. The fault parameters obtained by the fuzzy clustering method in this study are also highly consistent with the data of other authors and institutions. This method is an accurate and maneuverable method to obtain fault plane information based on a large amount of seismic sequence data. This method will have important significance for seismic structure, fault plane determination and analysis in the future.
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图 1 青海玛多地震分布图(断层采用邓起东等，2002)
图中右上方为研究区域位置，图中黑线为断层，淡蓝色表示河流湖泊，红色小圆点为每个余震的位置，黄色五角星为主震的位置，黄色三角形为玛多县的位置
Fig. 1. Distribution of the 2021 Qinghai Maduo earthquake (after Deng et al., 2002)
图 2 整体聚类为1确定的断层面和地震位置的平面图(a)和立体图(b)
方框为确定的断层面，其周围的红色圆圈为聚类所用的属于断层面的数据
Fig. 2. The determined fault planes and hypocenters in map view (a) and in 3-D (b) (the overall clustering=1)
图 3 研究区内地震分段图
图中由蓝色线条围成的6个矩形区域对应6个断层分段，图中黑线为断层，淡蓝色表示河流湖泊，黄色小圆点为每次地震事件的位置
Fig. 3. Seismic segmentation map in the study area
图 4 按4个断层面处理的主破裂地震数据确定的断层面和地震位置的平面图(a)和立体图(b、c)
蓝色叉号为聚类过程断定的离群事件.其余图例同图 2，断层面按照大写英文字母A、B、C、D等标记
Fig. 4. Determined fault planes and hypocenters in map view(a) and in 3-D (b、c) in main rupture area and 4 fault planes
图 5 分区域操作所选区域图(a)、(d)和(g)，分区域确定的断层面平面图(b)、(e)和(h)以及相应立体图(c)、(f)和(i)
图例同图 2
Fig. 5. Sub-regional operation selected area map (a), (d) and (g); sub-regional fault plane plan (b), (e) and (h); corresponding 3-D map (c), (f) and (i)
图 6 中东段区域地震分布在水平面(a)、断层面(b)和垂直于断层面的横断面(c)上的投影以及小地震与断层面距离的分布情况(d)
圆圈表示精确定位余震，粗实线表示确定的断层面边界；AA'为断层上边界的端点
Fig. 6. Distribution of relocated aftershocks near the ME segment (a), vertical cross-section along the fault plane (b), vertical cross-section perpendicular to the fault plane (c) and histogram of small earthquakes sorted by their distances to the fault plane (d)
图 7 2021年青海玛多Ms7.4级地震中心震源机制解(a)及空间三维辐射花样(b)
图a中的两条黑色弧线分别表示中心震源机制的两个节面，绿色弧线形成的区域表示其不确定性范围；红色、蓝色和黄色的点分别表示中心震源机制解的P轴、T轴和B轴，其周围相同颜色的封闭曲线表示其不确定性范围；绿点和黑点分别表示各个机构及作者得到的震源机制解的P轴和T轴的投影；紫色弧线表示各个机构及作者得到的震源机制节面.图b中蓝色和红色部分分别表示压缩区域和膨胀区域
Fig. 7. Center focal mechanism solution (a) and spatial 3-D radiation pattern (b) of the 2021 Qinghai Maduo Ms7.4 earthquake
图 8 6个断层的相对剪应力情况(a)及相对正应力情况(b)
底图颜色表示相对应力值的大小；NS为正走滑型，SS为走滑型，NF为正断型，U为未定型，TS为逆走滑型，TF为逆断型
Fig. 8. Relative shear stress (a) and relative normal stress (b) of six faults
表 1 用于模糊聚类算法得出的6段断层面的小震个数以及所得断层面走向、倾角、长度
Table 1. The number of small earthquakes and the strike, dip angle and length of the six fault planes determined using fuzzy clustering algorithm
分段 小震个数 走向(°) 倾角(°) 长度(km) 西1段 263 101.15 81.11 33.66 西2段 304.58 85.12 32.87 中西段 722 101.93 83.08 26.79 中东段 291.45 86.74 51.73 东1段 202 106.64 87.46 28.25 东2段 90.08 86.14 36.65 
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表 2 使用相同余震资料反演得到此次地震的断层面走向、倾角和位置
Table 2. The fault plane strike, dip and location of this earthquake determined by using the same aftershock data
分段 小震个数 走向 倾角 断层面位置 值(°) 标准差(°) 值(°) 标准差(°) 纬度(°) 经度(°) 深度(km) 西段1 264 103.26 0.61 80.35 1.33 34.82 97.51 1.42 34.80 97.50 17.44 34.73 97.86 17.44 34.75 97.86 1.42 西段2 28 122.51 0.94 87.13 1.59 34.98 97.64 1.49 34.97 97.63 24.20 34.80 97.95 24.20 34.81 97.96 1.49 中西段 222 102.55 1.00 88.44 1.75 34.74 97.93 1.66 34.73 97.93 17.45 34.69 98.18 17.45 34.69 98.18 1.66 中东段 453 290.60 0.20 85.87 0.66 34.48 98.94 1.59 34.49 98.95 22.68 34.70 98.26 22.68 34.69 98.25 1.60 东1 39 95.64 1.78 88.97 1.35 34.43 99.01 0.48 34.42 99.01 28.97 34.40 99.25 28.97 34.41 99.25 0.48 东2 155 87.42 0.64 88.37 0.81 34.46 98.97 2.07 34.45 98.97 28.42 34.46 99.26 28.42 34.47 99.26 2.07
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表 3 不同机构及作者给出的青海玛多地震震源机制解及得到的中心震源机制解的标准差
Table 3. The focal mechanism solutions of the Qinghai Maduo earthquake and the standard deviation of the obtained central focal mechanism solutions given by different institutions and authors
序号 机构或学者 震源机制解 作为初始解得到的中心震源机制 作为初始解得到的标准差S(°) 震源机制与中心震源机制的最小三维空间旋转角(°) 走向(°) 倾角(°) 滑动角(°) 走向(°) 倾角(°) 滑动角(°) 1 USGS 92 67 ‒40 101.93 83.78 ‒3.48 16.780 795 38.95 2 中国地震局地球物理研究所 101 87 ‒7 101.91 83.74 ‒3.78 16.780 872 4.81 3 张志朋等（2022） 284.2 89.6 1 101.89 83.79 ‒176.52 90.137 244 7.33 4 张喆和许力生（2021） 281 88 1 101.89 83.78 ‒176.53 90.137 718 8.64 5 王卫民* 103.1 83.5 6.5 101.89 83.77 ‒3.49 16.780 878 9.92 6 中国地震台网中心 102 81 ‒11 101.9 83.75 ‒3.48 16.780 879 8.03 7 GCMT 282 83 ‒9 101.9 83.72 ‒176.55 90.141 548 18.16 8 CPPT 104 75 14 101.93 83.79 ‒3.48 16.780 798 19.31 9 GFZ 102 84 ‒3 101.89 83.75 ‒3.5 16.780 894 0.52 注：王卫民*的结果由个人通讯获得，未发表；CPPT. https://emsc-csem.org/Earthquake_data/tensors.php?date=2021-05-22&agency=CPPT ；GFZ.https://geofon.gfz-potsdam.de/eqexplorer/events/gfz2021jxef/momenttensor .
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表 4 利用模糊聚类方法结果计算出的滑动角和应力情况
Table 4. Slip angle and stress parameters calculated using fuzzy clustering method results
分段 走向(°) 倾角(°) 滑动角(°) 相对剪应力 相对正应力 剪滑角(°) 西1段 101.15 81.11 14.18 0.891 ‒0.23 14.9 西2段 304.58 85.12 28.06 0.533 ‒0.851 18.6 中西段 101.93 83.08 12.33 0.875 ‒0.268 13.3 中东段 291.45 86.74 1.82 0.729 ‒0.569 1.8 东1段 106.64 87.46 8.11 0.818 ‒0.429 8.1 东2段 90.08 86.14 15.37 0.809 0.050 15.4
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