Conjugate earthquake and measurement of friction coefficient in crustal medium
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摘要: 安德逊理论表明地震的共轭破裂现象可以用库仑准则解释，断层面夹角与地下岩石内摩擦系数之间存在简单的定量关系。基于本文提出的通过共轭地震计算介质内摩擦系数的方法，对国内外19个具有X形或不完整的X形（L形）共轭破裂特征的地震进行系统性分析，与震源机制、区域应力轴方向等资料进行对比，确定共轭断层面，进而确定共轭面夹角并计算岩石的内摩擦系数。研究结果进一步证实了天然地震的共轭破裂与实验室岩石破裂具有较好的一致性，给出了库仑准则与安德逊理论在大尺度下也成立的证据，表明通过共轭角确定地下介质的内摩擦系数是对地下介质特性认知的有益补充。Abstract: Anderson’s theory indicates that the conjugate rupture phenomenon of earthquake can be explained by Coulomb’s criterion, and there is a simple quantitative relationship between the angle of fault plane and the friction coefficient of underground rock. Based on the author’s method of calculating the friction coefficient of the medium through conjugate earthquakes, this paper systematically analyzes 19 domestic and foreign earthquakes with X-shaped or incomplete X-shaped （L-shaped） conjugate rupture characteristics. Analyze and compare with the source mechanism, regional stress axis direction and other data to determine the conjugate fault plane, and then determine the angle of the conjugate plane and calculate the internal friction coefficient of the rock. The research results further confirm that the conjugate fracture of natural earthquakes is in good agreement with the laboratory rock fracture, and the Coulomb criterion and Anderson theory are also valid at large scales. It is shown that the internal friction of the underground medium is determined by the conjugate angle. The coefficient is a useful supplement to the cognition of the characteristics of the underground medium.
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图 14 1998年6月4日，11月13日冰岛亨吉德山MW6.4和奥佛斯 MW6.1地震共轭破裂特征分析（修改自Parameswaran et al，2020）
Figure 14. Analysis of conjugate rupture characteristics of the Hengill MW6.4 and Ölfus MW6.1 earthquakes in Iceland on June 4，1998 and November 13，1998 （modified from Parameswaran et al，2020）
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图 1 用莫尔圆表示库仑破裂准则
横坐标表示作用于岩石中某一平面的正应力σn；纵坐标表示作用于某一平面上的剪切应力τ
Figure 1. Coulomb’s failure criterion expressed by Mohr circle
The abscissa represents the normal stress σn acting on a certain plane in the rock，the ordinate represents the shear stress τ acting on a certain plane
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图 2 共轭角2θ与主应力的关系
Figure 2. Relationship between conjugate angle 2θ and principle stress
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图 4 1974年5月11日云南永善—大关MS7.1地震共轭破裂特征分析（修改自刘万琴，陈运泰，1979）
Figure 4. Analysis of conjugate rupture characteristics of MS7.1 earthquake in Yongshan-Daguan，Yunnan on May 11，1974 （modified from Liu，Chen，1979）
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图 5 1995年10月24日云南武定MS6.5地震共轭破裂特征分析（修改自刁桂苓等，1999）
Figure 5. Analysis of conjugate rupture characteristics of the MS6.5 earthquake in Wuding，Yunnan，China on October 24，1995 （modified from Diao et al，1999）
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图 7 2001年4月10日，4月12日，6月8日云南施甸MS5.2，MS5.9和MS5.3地震共轭破裂特征分析（修改自刘翔，赵小艳，2002）
Figure 7. Analysis of conjugate rupture characteristics of the MS5.2，MS5.9 and MS5.3 earthquakes in Shidian，Yunnan on April 10，2001，April 12，2001 and June 8，2001 （modified from Liu，Zhao，2002）
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图 8 1970年11月7日，12月13日川滇盐源—宁蒗MS6.7和MS6.4地震共轭破裂特征分析（修改自程式，任昭明，1990）
Figure 8. Analysis of conjugate rupture characteristics of the MS6.7 and MS6.4 earthquakes in Yanyuan-Ninglang on Novermber 7，1970 and December 13， 1970 （modified from Cheng，Ren，1990）
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图 9 2001年2月14日，2月23日四川雅江MS5.0和MS6.0地震共轭破裂特征分析（修改自魏亚玲等，2001）
Figure 9. Analysis of conjugate rupture characteristics of the MS5.0 and MS6.0 earthquakes in Yajiang，Sichuan on February 14，2001 and February 23，2001 （modified from Wei et al，2001）
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图 10 2005年11月26日江西九江—瑞昌MS5.7地震共轭破裂特征分析（修改自吕坚等，2008）
Figure 10. Analysis of conjugate rupture characteristics of the MS5.7 earthquake in Jiujiang−Ruichang，Jiangxi，China on November 26，2005 （modified from Lü et al，2008）
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图 12 2018年6月17日日本大阪MW5.5地震共轭破裂特征分析（修改自Li et al，2019）
Figure 12. Analysis of conjugate rupture characte-ristics of the MW5.5 earthquake in Osaka，Japan on June 17， 2018 （modified from Li et al，2019）
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图 13 2014年5月5日泰国清莱府湄佬县MW6.2地震共轭破裂特征分析（修改自Pananont et al，2017）。右下角三角图表明大部分震源机制为走滑类型
Figure 13. Analysis of conjugate rupture characteristics of the MW6.2 earthquake in Mae Lao，Chiang Rai，Thailand on May 5，2014 （modified from Pananont et al，2017）. The triangle diagram in thelower right corner shows that most of the focal mechanisms are strike-slip type
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图 15 2016年8月24日意大利中部MW6.0地震共轭破裂特征分析（修改自Porreca et al，2018）
Figure 15. Analysis of conjugate rupture characteristics of the MW6.0 earthquake in central Italy on August 24，2016 （modified from Porreca et al，2018）
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图 16 1979年3月15日美国加州Homestead Valley ML4.9，ML5.2，ML4.5，ML4.9地震序列共轭破裂特征分析 （修改自Stein，Lisowski，1983）
Figure 16. Analysis of conjugate rupture characteristics of ML4.9，ML5.2，ML4.5，ML4.9 earthquake sequence in Homestead Valley，California，USA on March 15，1979 （modified from Stein，Lisowski，1983）
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图 17 1984年11月23日美国加州Round Valley ML5.8地震共轭破裂特征分析（修改自Priestley et al，1988）
Figure 17. Analysis of conjugate rupture characteristics of ML5.8 earthquake in Round Valley，California，USA on November 23th，1984 （modified from Priestley et al，1988）
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图 18 1987年11月17日美国阿拉斯加湾MW7.2地震序列共轭破裂特征分析（修改自Hwang，Kanamori，1992）
Figure 18. Analysis of conjugate rupture characteristics of the MW7.2 earthquake sequence in Gulf of Alaska， USA on November 17，1987 （modified from Hwang，Kanamori，1992）
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图 19 1992年4月23日美国加州兰德斯MW6.1地震序列共轭破裂特征分析（修改自Hauksson et al，1993）
Figure 19. Analysis of conjugate rupture characteristics of the MW6.1 earthquake sequence in Landers， California，USA on April 23，1992 （modified from Hauksson et al，1993）
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图 20 1994年9月12日美国内华达州双泉平原 MW5.8地震共轭破裂特征分析（修改自Amelung，Bell，2003）
Figure 20. Analysis of conjugate rupture characteristics of the MW5.8 earthquake in Double Spring Flat， Nevada，USA on September 12，1994 （modified from Amelung，Bell，2003）
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图 21 1994年5月26日，2004年2月24日和2016年1月25日摩洛哥胡塞马 MW6.1，MW6.5和MW6.4地震序列共轭破裂特征分析（修改自 Kariche et al，2018）
Figure 21. Analysis of conjugate rupture characteristics of the MW6.1，MW6.5 and MW6.4 earthquake sequences in Al Hociema，Morocco on May 26，1994，February 24，2004，and January 25，2016 （modified from Kariche et al，2018）
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