The magnitude distribution law of characteristic earthquakes in Chinese mainland
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摘要: 根据特征地震的震级分布符合正态分布的基本假设，对特征地震的震级分布规律进行定量化研究.考虑到原地复发型大地震的震级数据稀少，提出利用大地震的同震位移转换得到震级数据，再对不同观测点所得到的震级数据进行归一化处理，使所有归一化震级数据均服从均值为0的同分布，进而可以统计得到反映特征地震震级变异性的标准差σ.最后基于广泛搜集的中国大陆54个特征地震的同震位移，利用本文给出的统计方法得到一个通用的标准差σ=0.08，为进一步研究特征地震的发生概率模型提供了重要依据.Abstract: Based on the fundamental assumption that the magnitude distribution of characteristic earthquakes obeys the normal distribution, the quantification research are carried out on the magnitude distribution of characteristic earthquakes. Given sparse magnitude data of large earthquakes recurrence in situ, this paper uses magnitude data converted by coseismic displacement data, and each magnitude obeys identical distribution after normalization, then the standard deviation σ which reflects the variability of the normalized magnitude can be got by statistic analysis. Using the approach proposed in this paper, analysis of coseismic displacements of 54 characteristic earthquakes in Chinese mainland suggests a generic value of σ=0.08, which provides an important basis for further studying occurrence probabilistic model of characteristic earthquakes.
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Keywords:
- characteristic earthquake /
- magnitude /
- coseismic displacement /
- small sample
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图 1 特征地震模型(引自Schwartz，Coppersmith，1984)
Figure 1. Characteristic earthquake model (after Schwartz, Coppersmith, 1984)
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图 2 抽取2次(a)，3次(b)，4次(c)，5次(d)地震事件的Mk值初始分布(上)和基于小样本的分布(下)，图中n为地震事件个数
Figure 2. The initiatory distribution of Mk (upper panels) and the distribution of Mk based on small sample (lower panels) for 2-event (a), 3-event (b), 4-event (c) and 5-event (d) synthetic earthquakes
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图 3 本文所统计的54个特征地震的Mk值分布直方图
Figure 3. Histogram of Mk values for 54 characteristic earthquakes
表 1 本文所用的中国大陆16个断层上的同震位移数据
Table 1 The data of coseismic displacement on 16 faults of Chinese mainland used in this paper
断层(段) 同震位移/m 归一化无量纲震级 修正系数ρ 数据来源 1.50 -0.0183 鲜水河断裂炉霍段 1.70 0.0179 1.22 钱洪等(1990) 1.60 0.0004 鲜水河断裂道孚段 0.78 0.0644 1.41 Papadimitriou et al (2004) 0.50 -0.0644 夏垫断裂(东柳河屯探槽) 1.75 0.0313 1.41 冉永康等(1997) 1.41 -0.0312 1.0 -0.1022 1.2 -0.0494 夏垫断裂(齐心庄探槽) 1.8 0.0680 1.15 江娃利等(2000) 1.9 0.0836 0.34 0.0697 0.30 0.0335 包代河断裂 0.20 -0.0839 1.15 董治平等(2002) 0.25 -0.0192 0.8 -0.1100 0.8 -0.1100 北京南口-孙河断裂 1.0 -0.0454 1.12 张世民等(2008) 1.8 0.1248 1.9 0.1405 2.6 0.0920 色尔腾山山前断裂大佘太段 1.6 -0.0485 1.15 陈立春等(2003) 2.2 0.0437 1.4 -0.0872 2.6 0.1328 1.8 0.0263 色尔滕山山前断裂乌兰忽洞段 1.3 -0.0679 1.15 陈立春等(2003) 1.2 -0.0911 1.5 -0.0392 2.0 0.0441 贺兰山东麓断裂中北段 2.0 0.0441 1.15 邓起东等(1984) 1.45 -0.0490 贺兰山东麓断裂南段 0.34 -0.1343 1.41 杜鹏等(2009) 0.86 0.1343 1.5 -0.0454 灵武断裂 1.8 0.0074 1.22 柴炽章等(2001) 2.0 0.0379 2.0 0.0287 山西大同盆地恒山北缘断裂 1.5 -0.0555 1.22 江娃利等(2003) 2.0 0.0278 3.2 0.0238 山西交城断裂带 2.5 -0.0477 1.22 谢新生等(2007) 3.2 0.0328 云南龙蟠-乔后断裂剑川段 1.0 0.0476 1.41 汤勇等(2014) 0.72 -0.0476 海原断裂全段 5.6 -0.0323 1.41 冉永康和邓起东(1998) 7.0 0.0323 1.5 -0.0278 海原断裂中段 1.5 -0.0278 1.22 冉永康和邓起东(1998) 2.0 0.0555 6.0 0.0132 郯城断裂中断 5.0 -0.0396 1.15 王华林(1995) 6.0 0.0132 6.0 0.0132 
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