滑动弱化模型下的库仑应力变化与远程触发问题
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摘要
地震断层破裂在周围固体介质中能产生静态附加应力场.当依据库仑破裂准则和破裂模型推测构造应力变化,用以判断能否触发某处断层破裂时,这种应力变化称作"库仑破裂应力变化".一次地震产生的"库仑应力变化"被认为能影响下一次地震的发生.讨论了计算"库仑应力变化"所采用的不同模型,指出伏尔泰拉错动模型不能真实反映震源参数,因而所给出的静态附加应力场存在重大缺陷.线弹性断裂力学模型可以与真实应力降联系起来,但不能给出震源参数的约束范围,也存在破裂端部应力奇异性问题.用滑动弱化模式不仅可以消除应力奇异性,而且可以对震源参数给出较合理的约束条件.理论分析表明,计算库仑破裂应力变化必须考虑到模型选择的合理性.另外,无论是哪种模式,利用固体格架破裂计算大地震的库仑应力变化在远场的量值都很低,在一般情况下似乎不足以影响下一次远场地震的发生,迄今为止的岩石试验和实际观测资料也尚不支持这个假说.鉴于全球的地震活动有远场相互关联和呼应,对大地震的远场静态触发作用的解释需要找出其它途径.
Seismic fault failure can generate additional static stress in surrounding solid medium.The stress change,calculated by using certain fault model and following Coulomb fracture criteria,with the aim at testing if it can trigger other fault failures,is called Coulomb failure stress(CFS)change.It is commonly believed that the CFS change generated by an earthquake can affect the occurrence of other remote earthquakes.This paper examines and compares the calculations of CFS change in using three different models.Since the Volterra dislocation model can not accurately represent the source parameters,the additional static stress field given by this model has major flaws.The linear elastic fracture mechanics model can be related to the real stress drop,but can not give the limit range of the source parameters.In addition,it also has the problem of stress singularity at crack ends.The slip-weakening model not only eliminates the stress singularity,but also gives more reasonable constraints on source parameters.However,quantitative analysis shows that in calculating CFS changes the rationality of the fault model must be taken into account,and that for any above model the calculated CFS change induced by a major earthquake in far-field is very low,being not enough to influence the occurrence of another remote earthquake.Up to now rock experiments and actual observations do not support the hypothesis that the Coulomb stress generated by an earthquake can affect the occurrence of a next remote earthquake.Therefore,we need to find new ways to interpret the remote correlation of seismic activities around the world and the cause of static remote triggering of major earthquakes.
Seismic fault failure can generate additional static stress in surrounding solid medium.The stress change,calculated by using certain fault model and following Coulomb fracture criteria,with the aim at testing if it can trigger other fault failures,is called Coulomb failure stress(CFS)change.It is commonly believed that the CFS change generated by an earthquake can affect the occurrence of other remote earthquakes.This paper examines and compares the calculations of CFS change in using three different models.Since the Volterra dislocation model can not accurately represent the source parameters,the additional static stress field given by this model has major flaws.The linear elastic fracture mechanics model can be related to the real stress drop,but can not give the limit range of the source parameters.In addition,it also has the problem of stress singularity at crack ends.The slip-weakening model not only eliminates the stress singularity,but also gives more reasonable constraints on source parameters.However,quantitative analysis shows that in calculating CFS changes the rationality of the fault model must be taken into account,and that for any above model the calculated CFS change induced by a major earthquake in far-field is very low,being not enough to influence the occurrence of another remote earthquake.Up to now rock experiments and actual observations do not support the hypothesis that the Coulomb stress generated by an earthquake can affect the occurrence of a next remote earthquake.Therefore,we need to find new ways to interpret the remote correlation of seismic activities around the world and the cause of static remote triggering of major earthquakes.
引文
陈运泰,许力生,张勇,杜海林,冯万鹏,刘超,李春来,张红霞.2008.2008年5月12日汶川特大地震震源特性分析报告[R/OL].[2009-12-20].www.cea-igp.ac.cn/汶川地震专题/地震情况/初步研究及考察结果(一)PDF.
范天佑.1978.断裂力学基础[M].北京:江苏科学技术出版社:510.
郭增建,秦保燕,徐文耀,汤泉.1973.震源孕育模式的初步探讨[J].地球物理学报,16(1):43--48.
李世愚,张洪魁,和泰名,赵玉林,钱复业.2009.地球深部流体的状态及其在震源物理中的意义[J].物理,38(2):680--689.
万永革,吴忠良,周公威,黄静,秦立新.2002.地震应力触发研究[J].地震学报,24(5):533--551.
尹祥础.1985.固体力学[M].北京:地震出版社:512.
赵纪东.2010.气候变化可能触发地震和火山[J].国际地震动态,(1):10--13.
Aki K,Richards P G.1980.Quantitativeseismology,theoryand methods[M].San Francisco:W HFreeman and Com-pany:867.
Andrews DJ.1976.Rupture velocity of plane-strain shear cracks[J].J Geophys Res,81(B32):5679--5687.
Chen Y T,Knopoff L.1986.Static shear crack with a zone of slip weakening[J].Geophys J R astr Soc,87(3):1005--1024.
Harris R A.1998.Introduction to special section:Introduction to special section:stress triggers,stress shadows,andimplications for seismic hazards[J].J Geophys Res,103(B10):24347--24358.
Harris R A.2000.Earthquake stress triggers,stress shadows,and seismic hazard[J].Current Science,79(9):1215--1225.
He C R.1995.Slip-weakening constitutive relation and the structure in the vicinity of a shear crack tip[J].Pure ApplGeophys,145(3--4):747--757.
Hill D P,Reasenberg P A,Michael A,Arabaz WJ,Beroza G,Brumbaugh D,Brune J N,Castro R,Davis S,et al.1993.Seismicity remotely triggered by the magnitude7.3Landers,California,earthquake[J].Science,260(5114):1617--1623.
Ida Y.1972.Cohesive force across the tip of a longitudinal shear crack and Griffith's specific surface energy[J].J Geo-phys Res,77(20):3796--3805.
Kanamori H,Anderson D L.1975.Theoretical basis of some empirical relationin seismology[J].Bull SeismSoc Amer,65(5):1073--1095.
Kanamori H.1994.Mechanics of earthquakes[J].Annual Reviewof Earth and Planetary Sciences,22(1):207--237.
Knopoff L,Chen Y T.2009.Single couple component of the far field radiation fromdynamical fractures[J].Bull SeismSoc Amer,99(2B):1091--1102.
Maruyama T.1969.Stress fieldin the neighborhood of a crack[J].东京大学地震研究所汇报,47(1):1--29.
Ohnaka M.2003.Aconstitutive scalinglawand a unified comprehensionfor frictional slipfailure,shear facture of intactrock,and earthquake rupture[J].J Geophys Res,108(B2),2080,doi10.1029/2000JB000123
Pal mer A C,Rice J R.1973.The growth of slip surfacesinthe progressive failure of over-consolid clay[J].Proc Roy SocLondon Ser A,332(1591):527--548.
Rice J R,Samis C G,Parsons R.2005.Off-fault secondaryfailureinduced by a dynamic slip-rupture[J].Bull SeismSocAmer,95(1):109--134,doi10.1785/0120030166
Ruff L J.2002.State of stress within the earth[M]∥Lee W H K,Jennings P,Kisslinger C,Kanamori Heds.Interna-tional Handbook of Earthquake and Engineering Seismology.Amsterdam:Academic Press for International Associ-ation of Seismology and Physics of the Earth's Interior,81A:539.
Starr A T.1928.Slipin a crystal and rupture in a solid due to shear[J].Proc Comb Phil Soc,24(04):489--500.
Westergaard H M.1939.Bearing pressures and cracks[J].J Appl Mechan,6:A49--A53.
Yamashita T.1976.On the dynamic processof fault motion in the presence of friction and inhomogeneous initial stress.Part I:Rupture propagation[J].J Phys Earth,24:417--444
Zoback M D,Zoback ML.2002.State of stressin the earth’s lithosphere[M]∥Lee W H K,Jennings P,Kisslinger C,Kanamori H eds.International Handbook of Earthquake and Engineering Seismology.Amsterdam:AcademicPress for International Association of Seismology and Physics of the Earth’s Interior,81A:559--568.
范天佑.1978.断裂力学基础[M].北京:江苏科学技术出版社:510.
郭增建,秦保燕,徐文耀,汤泉.1973.震源孕育模式的初步探讨[J].地球物理学报,16(1):43--48.
李世愚,张洪魁,和泰名,赵玉林,钱复业.2009.地球深部流体的状态及其在震源物理中的意义[J].物理,38(2):680--689.
万永革,吴忠良,周公威,黄静,秦立新.2002.地震应力触发研究[J].地震学报,24(5):533--551.
尹祥础.1985.固体力学[M].北京:地震出版社:512.
赵纪东.2010.气候变化可能触发地震和火山[J].国际地震动态,(1):10--13.
Aki K,Richards P G.1980.Quantitativeseismology,theoryand methods[M].San Francisco:W HFreeman and Com-pany:867.
Andrews DJ.1976.Rupture velocity of plane-strain shear cracks[J].J Geophys Res,81(B32):5679--5687.
Chen Y T,Knopoff L.1986.Static shear crack with a zone of slip weakening[J].Geophys J R astr Soc,87(3):1005--1024.
Harris R A.1998.Introduction to special section:Introduction to special section:stress triggers,stress shadows,andimplications for seismic hazards[J].J Geophys Res,103(B10):24347--24358.
Harris R A.2000.Earthquake stress triggers,stress shadows,and seismic hazard[J].Current Science,79(9):1215--1225.
He C R.1995.Slip-weakening constitutive relation and the structure in the vicinity of a shear crack tip[J].Pure ApplGeophys,145(3--4):747--757.
Hill D P,Reasenberg P A,Michael A,Arabaz WJ,Beroza G,Brumbaugh D,Brune J N,Castro R,Davis S,et al.1993.Seismicity remotely triggered by the magnitude7.3Landers,California,earthquake[J].Science,260(5114):1617--1623.
Ida Y.1972.Cohesive force across the tip of a longitudinal shear crack and Griffith's specific surface energy[J].J Geo-phys Res,77(20):3796--3805.
Kanamori H,Anderson D L.1975.Theoretical basis of some empirical relationin seismology[J].Bull SeismSoc Amer,65(5):1073--1095.
Kanamori H.1994.Mechanics of earthquakes[J].Annual Reviewof Earth and Planetary Sciences,22(1):207--237.
Knopoff L,Chen Y T.2009.Single couple component of the far field radiation fromdynamical fractures[J].Bull SeismSoc Amer,99(2B):1091--1102.
Maruyama T.1969.Stress fieldin the neighborhood of a crack[J].东京大学地震研究所汇报,47(1):1--29.
Ohnaka M.2003.Aconstitutive scalinglawand a unified comprehensionfor frictional slipfailure,shear facture of intactrock,and earthquake rupture[J].J Geophys Res,108(B2),2080,doi10.1029/2000JB000123
Pal mer A C,Rice J R.1973.The growth of slip surfacesinthe progressive failure of over-consolid clay[J].Proc Roy SocLondon Ser A,332(1591):527--548.
Rice J R,Samis C G,Parsons R.2005.Off-fault secondaryfailureinduced by a dynamic slip-rupture[J].Bull SeismSocAmer,95(1):109--134,doi10.1785/0120030166
Ruff L J.2002.State of stress within the earth[M]∥Lee W H K,Jennings P,Kisslinger C,Kanamori Heds.Interna-tional Handbook of Earthquake and Engineering Seismology.Amsterdam:Academic Press for International Associ-ation of Seismology and Physics of the Earth's Interior,81A:539.
Starr A T.1928.Slipin a crystal and rupture in a solid due to shear[J].Proc Comb Phil Soc,24(04):489--500.
Westergaard H M.1939.Bearing pressures and cracks[J].J Appl Mechan,6:A49--A53.
Yamashita T.1976.On the dynamic processof fault motion in the presence of friction and inhomogeneous initial stress.Part I:Rupture propagation[J].J Phys Earth,24:417--444
Zoback M D,Zoback ML.2002.State of stressin the earth’s lithosphere[M]∥Lee W H K,Jennings P,Kisslinger C,Kanamori H eds.International Handbook of Earthquake and Engineering Seismology.Amsterdam:AcademicPress for International Association of Seismology and Physics of the Earth’s Interior,81A:559--568.
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