关于Coulomb应力变化/扰动作用下的Dieterich余震触发机制的广义解
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摘要
基于单自由度弹簧-滑块模型,滑移速率和状态相依赖的摩擦关系可用于对断层内部地震成核和断层失稳过程的定量化描述.Dieterich(1994)余震触发理论模型首次给出中强震后区域应力场受到静态应力扰动后所导致的区域地震活动性的时空变化特征,近期研究也表明Dieterich理论模型可进一步推广至依赖时间的地震预测模型的建立.本文从简单直观的断层群体化概念模型出发,推导出了包括静态剪应力和正应力扰动作用下广义Dieterich解.同Dieterich经典解相比,广义Coulomb应力变化:ΔCFFG=Δτ-(μ0-α)Δσ取代了Dieterich方程中原有的剪切应力扰动Δτ.从而表明余震发生率R同作用于断层上的正应力的变化(扰动)有着密切的相关性.进一步,我们讨论了传统Coulomb应力变化(扰动)模型在地震预测过程中可能存在的局限性.以1976年MS7.8唐山大地震的主余震序列为例,采用本文中得到的结果,并结合视时窗分段方法,拟合了该地区地震活动性的时间演化过程.结果表明,除Coulomb应力变化(扰动)的影响外,主震前后加载于断层上的剪应力速率变化可对早期余震发生率产生很大影响.
Based on the spring-slide block model,earthquake nucleation related fault self-acceleration to failure could be intuitively and quantitatively described by the rate/state-dependent friction law.In the earthquake triggering model,Dieterich(1994) first proposed that the temporal and spatial evolutions of the seismicity vary with the static shear stress change or perturbation caused by moderate to large earthquakes,which has been used in the physics-based explanation of the Omori′s law.Recent studies also show that the Dieterich′s model can be further extended to time-dependent earthquake forecast modeling.From fault-population-modeling point of view,in this study we have derived a generalized Dieterich solution related to the aftershock triggering process in which the effects of the fault normal and shear stress changes have been involved in the current consideration.Compared with previous Dieterich′s solution,the Coulomb stress change of ΔCFFG=Δτ-(μ0-α)Δσ has been introduced in our solution instead of the only shear stress change of Δτ used in the Dieterich′s model.The results also imply that the normal stress change,Δσ,plays an important role relating to the aftershock seismicity.In addition,we discussed the possible limitations in the calculation of earthquake occurrence rate by using a simple Coulomb Stress Change Model without involving time-dependent non-linear phenomenon in the fault evolution.Using the solution obtained in this study,we fitted the time-dependent seismic variation around Tangshan region due to the 1976 MS7.8 Tangshan earthquake.The results indicated that,around the main fault,the shear stress rate change before and after the mainshock could exhibit a significant impact on the early aftershock rate change,as well as the Coulomb stress change.
Based on the spring-slide block model,earthquake nucleation related fault self-acceleration to failure could be intuitively and quantitatively described by the rate/state-dependent friction law.In the earthquake triggering model,Dieterich(1994) first proposed that the temporal and spatial evolutions of the seismicity vary with the static shear stress change or perturbation caused by moderate to large earthquakes,which has been used in the physics-based explanation of the Omori′s law.Recent studies also show that the Dieterich′s model can be further extended to time-dependent earthquake forecast modeling.From fault-population-modeling point of view,in this study we have derived a generalized Dieterich solution related to the aftershock triggering process in which the effects of the fault normal and shear stress changes have been involved in the current consideration.Compared with previous Dieterich′s solution,the Coulomb stress change of ΔCFFG=Δτ-(μ0-α)Δσ has been introduced in our solution instead of the only shear stress change of Δτ used in the Dieterich′s model.The results also imply that the normal stress change,Δσ,plays an important role relating to the aftershock seismicity.In addition,we discussed the possible limitations in the calculation of earthquake occurrence rate by using a simple Coulomb Stress Change Model without involving time-dependent non-linear phenomenon in the fault evolution.Using the solution obtained in this study,we fitted the time-dependent seismic variation around Tangshan region due to the 1976 MS7.8 Tangshan earthquake.The results indicated that,around the main fault,the shear stress rate change before and after the mainshock could exhibit a significant impact on the early aftershock rate change,as well as the Coulomb stress change.
引文
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[5]Stein R S,Barka A A,Dieterich J H.Progressive failure onthe North Anatolian fault since 1939by earthquake stresstriggering.Geophys.J.Int.,1997,128(3):594-604.
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[7]Hardebeck J L.Stress triggering and earthquake probabilityestimates.J.Geophys.Res.,2004,109(B4):B04310,doi:10.1029/2003JB002437.
[8]Parsons T.Significance of stress transfer in time-dependentearthquake probability calculations.J.Geophys.Res.,2005,110(B5):B05S02,doi:10.1029/2004JB003190.
[9]Gomberg J,Belardinelli M,Cocco M,et al.Time-dependentearthquake probabilities.J.Geophys.Res.,2005,110(B5):B05S04,doi:10.1029/2004JB003405.
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[14]Ruina A.Slip instability and state variable friction laws.J.Geophys.Res.,1983,88(B12):359-310.
[15]Dieterich J H.Modeling of rock friction 1.Experimentalresults and constitutive equations.J.Geophys.Res.,1979,84(B5):2161-2168.
[16]Dieterich J H.Earthquake nucleation on faults with rate-andstate-dependent strength.Tectonophysics,1992,211(1-4):115-134.
[17]Dieterich J H.A model for the nucleation of earthquake slip.Earthquake Source Mechanics,1986,37:37-47.
[18]Scholz C H.Earthquakes and friction laws.Nature,1998,391(6662):37-42.
[19]Ziv A,Rubin A.Implications of rate-and-state friction forproperties of aftershock sequence:Quasi-static inherentlydiscrete simulations.J.Geophys.Res.,2003,108(B1),doi:10.1029/2001JB001219.
[20]Byerlee J.Friction of rocks.Pure Appl.Geophys.,1978,116(4-5):615-626.
[21]Perfettini H,Avouac J.Postseismic relaxation driven bybrittle creep:A possible mechanism to reconcile geodeticmeasurements and the decay rate of aftershocks,applicationto the Chi-Chi earthquake,Taiwan.J.Geophys.Res.,2004,109(B2),doi:10.1029/2003JB002488.
[22]Kaneko Y.Investigations of earthquake source processesbased on fault models with variable friction rheology[Ph.D.thesis].California:California Institute of Technology,2009.
[23]尤惠川,徐锡伟,吴建平等.唐山地震深浅构造关系研究.地震地质,2002,24(4):571-582.You H C,Xu X W,Wu J P,et al.Study on the relationshipbetween shallow and deep structures in the 1976 Tangshanearthquake area.Seismology and Geology(in Chinese),2002,24(4):571-582.
[24]Huang B S,Yeh Y T.The fault ruptures of the 1976Tangshan earthquake sequence inferred from coseismiccrustal deformation.Bull.Seismol.Soc.Amer.,1997,87(4):1046-1057.
[25]Butler R,Stewart G S,Kanamori H.The July 27,1976Tangshan,China earthquake-A complex sequence ofintraplate events.Bull.Seismol.Soc.Amer.,1979,69(1):207-220.
[26]邓起东,徐锡伟,于贵华.中国大陆活动断裂的分区特征及其成因.∥中国活动断层研究.北京:地震出版社,1994:1-14.Deng Q D,Xu X W,Yu G H.Characteristics ofregionalization of active faults in China and their genesis(inChinese).∥China Active Faults Reserch.Beijing:SeismologicalPress,1994:1-14.
[27]Robinson R,Zhou S.Stress interactions within theTangshan,China,earthquake sequence of 1976.Bull.Seismol.Soc.Amer.,2005,95(6):2501-2505.
[28]万永革,沈正康,曾跃华等.唐山地震序列应力触发的粘弹性力学模型研究.地震学报,2008,30(6):581-593.Wan Y G,Shen Z K,Zeng Y H,et al.Study on visco-elasticstress triggering model of the 1976 Tangshan earthquakesequence.Acta Seismologica Sinica(in Chinese),2008,30(6):581-593.
[29]Cui X F,Xie F R,Zhang H Y.Recent tectonic stress fieldzoning in Sichuan-Yunnan region and its dynamic interest.Acta Seismologica Sinica,2006,19(5):485-496.
[30]Segall P,Desmarais E K,Shelly D,et al.Earthquakestriggered by silent slip events on Kilauea volcano,Hawaii.Nature,2006,442(7098):71-74.
[31]仲秋,史保平.1976年Ms7.8唐山地震余震序列持续时间及对地震危险性分析的意义.地震学报,2012,34(4):494-508.Zhong Q,Shi B P.Aftershock time duration of the 1976Ms7.8 Tangshan earthquake and implication for seismichazard.Acta Seismologica Sinica(in Chinese),2012,34(4):494-508.
[32]秦四清,徐锡伟,胡平等.孕震断层的多锁固段脆性破裂机制与地震预测新方法的探索.地球物理学报,2010,53(4):1001-1014,doi:10.3969/j.issn.0001-5733.2010.04.025.Qin S Q,Xu X W,Hu P,et al.Brittle failure mechanism ofmultiple locked patches in a seismogenic fault system andexploration on a new way for earthquake prediction.ChineseJ.Geophys.(in Chinese),2010,53(4):1001-1014,doi:10.3969/j.issn.0001-5733.2010.04.025.
[33]Steven C J,Lynn R S.Evolving towards a critical point:areview of accelerating seismic moment/energy release prior tolarge and great Earthquakes.Pure Appl.Geophys.,1999,155(4):279-306.
[34]蒋长胜,赵祎喆,王行舟.亚洲地区Benioff应变释放和强震活动的周期性特征研究.地震,2010,30(3):72-80.Jiang C S,Zhao Y Z,Wang X Z.Benioff strain release andperiodic characteristics of strong earthquake activities inAsia.Earthquake(in Chinese),2010,30(3):72-80.
[2]Dieterich J.A constitutive law for rate of earthquakeproduction and its application to earthquake clustering.J.Geophys.Res.,1994,99(B2):2601-2601.
[3]King G C P,Stein R S,Lin J.Static stress changes and thetriggering of earthquakes.Bull.Seismol.Soc.Amer.,1994,84(3):935-953.
[4]Harris R A,Simpson R W.Changes in static stress onsouthern California faults after the 1992Landers earthquake.J.Geophys.Res.,1992,103(B10):24439-24451.
[5]Stein R S,Barka A A,Dieterich J H.Progressive failure onthe North Anatolian fault since 1939by earthquake stresstriggering.Geophys.J.Int.,1997,128(3):594-604.
[6]Parsons T,Toda S,Stein R S,et al.Heightened odds oflarge earthquakes near Istanbul:an interaction-basedprobability calculation.Science,2000,288(5466):661-665.
[7]Hardebeck J L.Stress triggering and earthquake probabilityestimates.J.Geophys.Res.,2004,109(B4):B04310,doi:10.1029/2003JB002437.
[8]Parsons T.Significance of stress transfer in time-dependentearthquake probability calculations.J.Geophys.Res.,2005,110(B5):B05S02,doi:10.1029/2004JB003190.
[9]Gomberg J,Belardinelli M,Cocco M,et al.Time-dependentearthquake probabilities.J.Geophys.Res.,2005,110(B5):B05S04,doi:10.1029/2004JB003405.
[10]Working Group on California Earthquake Probabilities.Probabilities of large earthquakes in the San Francisco Bayregion.Calitbmia,U.S.Geol.Surv.Circ.1053,1990.
[11]Harris R A.Introduction to special section:Stress triggers,stress shadows,and implications for seismic hazard.J.Geophys.Res.,1998,103(B10):24347-24358.
[12]Toda S,Stein R S,Reasenberg P A,et al.Stress transferredby the 1995 Mw=6.9Kobe,Japan,shock-Effect on aftershocksand future earthquake probabilities.J.Geophys.Res.,1998,103(B10):24543-24565.
[13]Dieterich J H,Kilgore B.Implications of fault constitutiveproperties for earthquake prediction.Proceedings of theNational Academy of Sciences,1996,93(9):3787-3794.
[14]Ruina A.Slip instability and state variable friction laws.J.Geophys.Res.,1983,88(B12):359-310.
[15]Dieterich J H.Modeling of rock friction 1.Experimentalresults and constitutive equations.J.Geophys.Res.,1979,84(B5):2161-2168.
[16]Dieterich J H.Earthquake nucleation on faults with rate-andstate-dependent strength.Tectonophysics,1992,211(1-4):115-134.
[17]Dieterich J H.A model for the nucleation of earthquake slip.Earthquake Source Mechanics,1986,37:37-47.
[18]Scholz C H.Earthquakes and friction laws.Nature,1998,391(6662):37-42.
[19]Ziv A,Rubin A.Implications of rate-and-state friction forproperties of aftershock sequence:Quasi-static inherentlydiscrete simulations.J.Geophys.Res.,2003,108(B1),doi:10.1029/2001JB001219.
[20]Byerlee J.Friction of rocks.Pure Appl.Geophys.,1978,116(4-5):615-626.
[21]Perfettini H,Avouac J.Postseismic relaxation driven bybrittle creep:A possible mechanism to reconcile geodeticmeasurements and the decay rate of aftershocks,applicationto the Chi-Chi earthquake,Taiwan.J.Geophys.Res.,2004,109(B2),doi:10.1029/2003JB002488.
[22]Kaneko Y.Investigations of earthquake source processesbased on fault models with variable friction rheology[Ph.D.thesis].California:California Institute of Technology,2009.
[23]尤惠川,徐锡伟,吴建平等.唐山地震深浅构造关系研究.地震地质,2002,24(4):571-582.You H C,Xu X W,Wu J P,et al.Study on the relationshipbetween shallow and deep structures in the 1976 Tangshanearthquake area.Seismology and Geology(in Chinese),2002,24(4):571-582.
[24]Huang B S,Yeh Y T.The fault ruptures of the 1976Tangshan earthquake sequence inferred from coseismiccrustal deformation.Bull.Seismol.Soc.Amer.,1997,87(4):1046-1057.
[25]Butler R,Stewart G S,Kanamori H.The July 27,1976Tangshan,China earthquake-A complex sequence ofintraplate events.Bull.Seismol.Soc.Amer.,1979,69(1):207-220.
[26]邓起东,徐锡伟,于贵华.中国大陆活动断裂的分区特征及其成因.∥中国活动断层研究.北京:地震出版社,1994:1-14.Deng Q D,Xu X W,Yu G H.Characteristics ofregionalization of active faults in China and their genesis(inChinese).∥China Active Faults Reserch.Beijing:SeismologicalPress,1994:1-14.
[27]Robinson R,Zhou S.Stress interactions within theTangshan,China,earthquake sequence of 1976.Bull.Seismol.Soc.Amer.,2005,95(6):2501-2505.
[28]万永革,沈正康,曾跃华等.唐山地震序列应力触发的粘弹性力学模型研究.地震学报,2008,30(6):581-593.Wan Y G,Shen Z K,Zeng Y H,et al.Study on visco-elasticstress triggering model of the 1976 Tangshan earthquakesequence.Acta Seismologica Sinica(in Chinese),2008,30(6):581-593.
[29]Cui X F,Xie F R,Zhang H Y.Recent tectonic stress fieldzoning in Sichuan-Yunnan region and its dynamic interest.Acta Seismologica Sinica,2006,19(5):485-496.
[30]Segall P,Desmarais E K,Shelly D,et al.Earthquakestriggered by silent slip events on Kilauea volcano,Hawaii.Nature,2006,442(7098):71-74.
[31]仲秋,史保平.1976年Ms7.8唐山地震余震序列持续时间及对地震危险性分析的意义.地震学报,2012,34(4):494-508.Zhong Q,Shi B P.Aftershock time duration of the 1976Ms7.8 Tangshan earthquake and implication for seismichazard.Acta Seismologica Sinica(in Chinese),2012,34(4):494-508.
[32]秦四清,徐锡伟,胡平等.孕震断层的多锁固段脆性破裂机制与地震预测新方法的探索.地球物理学报,2010,53(4):1001-1014,doi:10.3969/j.issn.0001-5733.2010.04.025.Qin S Q,Xu X W,Hu P,et al.Brittle failure mechanism ofmultiple locked patches in a seismogenic fault system andexploration on a new way for earthquake prediction.ChineseJ.Geophys.(in Chinese),2010,53(4):1001-1014,doi:10.3969/j.issn.0001-5733.2010.04.025.
[33]Steven C J,Lynn R S.Evolving towards a critical point:areview of accelerating seismic moment/energy release prior tolarge and great Earthquakes.Pure Appl.Geophys.,1999,155(4):279-306.
[34]蒋长胜,赵祎喆,王行舟.亚洲地区Benioff应变释放和强震活动的周期性特征研究.地震,2010,30(3):72-80.Jiang C S,Zhao Y Z,Wang X Z.Benioff strain release andperiodic characteristics of strong earthquake activities inAsia.Earthquake(in Chinese),2010,30(3):72-80.
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