断裂分段之间不同相互作用对断裂运动的影响
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摘要
采用速度和状态摩擦本构控制的一维弹簧滑块模型研究断裂分段间相互作用对运动特征的影响,为研究东昆仑活动断裂带库赛湖段和西大滩段2个断裂分段之间的相互影响,采用由弹簧相连的2个滑块模拟断裂分段,通过弹簧滑块系统的动力学分析,将断裂运动性质的描述归结为一组微分方程,数值求解该微分方程组,最终得到断裂运动性质的参数,从而达到确定断裂未来强震复发周期的目的。通过位错模型计算、借鉴前人研究成果以及古地震资料确定模型相关参数。研究断裂分段在不同相互作用下的强震复发周期,模拟表明断裂间不同相互作用对地震复发周期和地震时断裂错动位移的大小没有规律性的影响;只是对地震发生时断裂错动的速度有明显的影响,作用强时,地震发生时断裂错动速度大;反之,地震发生时断裂错动速度小。
In this paper,we apply the spring-block model controlled by the velocity and state depended frictional constitutive relation to research the effect of interaction between two fault segments on their motions.In order to research the effect of interaction between Kusai Lake and Xidatan segment of East Kunlun fault,we use two blocks connected by spring to simulate these two fault segments.Through the dynamical analysis,we get the differential equations to depict fault segment motion.Numerically solving the fault motion equations,we have the parameters of fault motion and determine the recurrence of strong earthquake.With the help of dislocation model research achievements of previous scholar and the data of paleo-earthquakes,we determine the related parameters of spring block model.Through the simulation,we find that the interaction between Kusai Lake and Xidatan fault segment has no regularity effect on recurrent period of earthquake and sliding displacement when earthquake happen,but the strong interaction will make the quick slip velocity of fault and the weak interaction will make the slow one.
In this paper,we apply the spring-block model controlled by the velocity and state depended frictional constitutive relation to research the effect of interaction between two fault segments on their motions.In order to research the effect of interaction between Kusai Lake and Xidatan segment of East Kunlun fault,we use two blocks connected by spring to simulate these two fault segments.Through the dynamical analysis,we get the differential equations to depict fault segment motion.Numerically solving the fault motion equations,we have the parameters of fault motion and determine the recurrence of strong earthquake.With the help of dislocation model research achievements of previous scholar and the data of paleo-earthquakes,we determine the related parameters of spring block model.Through the simulation,we find that the interaction between Kusai Lake and Xidatan fault segment has no regularity effect on recurrent period of earthquake and sliding displacement when earthquake happen,but the strong interaction will make the quick slip velocity of fault and the weak interaction will make the slow one.
引文
[1]Burridge,R,Knopoff,L.Model and theoretical seismicity[J].Bull Seismol Soc Am.,1967,57:341-371.
[2]Carlson,J.M and Langer,J.S.Properties of earthquakes generated by fault dynamics[J].Phys Rev Lett.,1989a,62:2632.
[3]Carlson,J.M and Langer,J.S.Mechanical model of an earthquake fault[J].Phys Rev A.,1989b,40:6740-6484.
[4]Carlson,J.M.Time intervals between characteristic earthquakes and correlations with smaller events:An analysis based on a mechanicalmodel of a fault[J].J.Geophys Res.,1991a,96(3):4255-4267.
[5]Carlson,J.M.Two-dimensional model of a fault[J].Phys Rev A.,1991b,44:6226-6262.
[6]Carlson,J.M,Langer,J.S,Shaw,B.E and Tang,C,Intrinsic properties of a Burridge-Knopoff model of an earthquake fault[J].Phys Rev A.,1991c,44:884-897.
[7]Carlson,J.M,Langer,J.S and Shaw,B.E,Dynamics of earthquake faults[J].Rev Mod Phys.,1994,66:657-670.
[8]Dieterich,J.H.Time-dependent friction and mechanics of stick-slip[J].Pure Appl Geophys,1978,116:790-806.
[9]Dieterich,J.H.Modeling of rock friction,1,Experimental results and constitutive equations[J].J.Geophys.Res.,1979a,84:2161-2168.
[10]Dieterich,J.H.Modeling of rock friction,2,Simulation of preseismic slip[J].J.Geophys.Res.,1979b,84:2169-2175.
[11]Ruina,A.L.Friction laws and instabilities:A quasi-static analysis of some dry friction behavior[D].Ph.D.thesis,Brown Univ.Providence,R.I.1980.
[12]Ruina,A.L.Slip instability and state variable friction laws[J].J.Geophys.Res.,1983,88:359-370.
[13]Rice,J.R and Tse,S T.Dynamic motion of a single degree of freedom system following a rate and state dependent friction law[J].J.Geophys.Res.,1986,91:521-530.
[14]Cao,T and Aki,K.Seismicity simulation rate-and state-dependent friction[J].Pure Appl Geophys,1986,124:487-513.
[15]Wang Jeen-Hwa.A dynamic study of two one-state-variable,rate-dependent and state-dependent friction laws[J].Bull Seism Soc Am.,2002,92(2):687-694.
[16]张继峰,冯奇.两自由度的Burridge-Knopoff模型的一种近似分析方法[J].力学季刊,2008,29:66-71.
[17]王威,任青文,杜小凯,等.滑动速率及系统刚度对断层滑动性质影响研究[J].南京理工大学学报(自然科学版).2007,31(6):784-788.
[18]范丽琨,蔡岩萍,梁海川,等.东昆仑地质构造及地球动力学演化特征[J].地质调查与研究,2009,33(3):181-186.
[19]胡道功,吴中海,吴珍汉,等.东昆仑断裂带库赛湖段晚第四纪古地震研究[J].第四纪研究,2007,27(1):27-34.
[20]胡道功,叶培盛,吴芳,等.东昆仑断裂带西大滩段晚第四纪古地震研究[J].第四纪研究,2008,28(2):214-221.
[21]青海省地震局,中国地震局地壳应力研究所.东昆仑活动断裂带[M].北京:地震出版社,1999.
[22]刘光勋.东昆仑活动断裂带及其强震活动性[J].中国地震,1996,12(2):119-126.
[23]Aiming Lin,Jianming Guo,Ken-ichi Kano.et al.2006.Average slip rate and recurrence interval of large-magnitude earthquakes on theWestern Segment of the Strike-slip Kunlun Fault,Northern Tibet[J].Bull Seism Soc Am.,96(5):1597-1611.
[24]许洪泰,闵伟.利用地震矩和实时概率模型对中长期地震危险性进行评价-以东昆仑和阿尔金断裂为例[J].地震研究,2007,30(2):120-126.
[25]李海兵,司家亮,潘家伟,等.活动断裂的变形特征及其大地震复发周期的估算[J].地质通报,2008,27(12):1968-1991.
[26]Jianming Guo,Aiming Lin,Tadashi Maruyama.et al.New constrains on recent large earthquakes along the Xidatan-Dongdatan Seg-ment of the Kunlun Fault,Westren China[J].Bull Seism Soc Am.,2006,96(1):48-58.
[27]Van der Woerd J,Ryerson F J,Tapponnier P.et al.Holocene left-slip rate determined by cosmogenic surface dating on the XidatanSegment of the Kunlun fault(Qinghai,China)[J].Geology,1998,26(8):695-698.
[28]吴珍汉,胡道功,吴中海,等.东昆仑南部西大滩断裂的地震鼓包及形成时代[J].地质评论,2006,52(1):15-25.
[29]徐锡伟,陈文彬,于贵华,等.2001年11月14日昆仑山库赛湖地震(MS8.1)地表破裂带的基本特征[J].地震地质,2002,24(1):1-13.
[30]Okada.Y.Surface Deformation due to shear and tensile faults in a half-space[J].Bul1Seis Soc Am.,1985,75:1018-1040.
[31]Okada.Y.Internal deformation due to shear and tensile faults in a half-space[J].Bull Seis Soc Am.,1992,82:1018-1040.
[32]陶玮,沈正康,万永革,等.根据2001年Mw7.8可可西里强震InSAR同震测量结果反演东昆仑断裂两侧地壳弹性介质差异[J].地球物理学报,2007,50(3):744-751.
[33]何昌荣.速度与状态依赖性摩擦本构关系下双滑块系统的相互作用[J].中国科学:D辑,2003,33:53-59.
[2]Carlson,J.M and Langer,J.S.Properties of earthquakes generated by fault dynamics[J].Phys Rev Lett.,1989a,62:2632.
[3]Carlson,J.M and Langer,J.S.Mechanical model of an earthquake fault[J].Phys Rev A.,1989b,40:6740-6484.
[4]Carlson,J.M.Time intervals between characteristic earthquakes and correlations with smaller events:An analysis based on a mechanicalmodel of a fault[J].J.Geophys Res.,1991a,96(3):4255-4267.
[5]Carlson,J.M.Two-dimensional model of a fault[J].Phys Rev A.,1991b,44:6226-6262.
[6]Carlson,J.M,Langer,J.S,Shaw,B.E and Tang,C,Intrinsic properties of a Burridge-Knopoff model of an earthquake fault[J].Phys Rev A.,1991c,44:884-897.
[7]Carlson,J.M,Langer,J.S and Shaw,B.E,Dynamics of earthquake faults[J].Rev Mod Phys.,1994,66:657-670.
[8]Dieterich,J.H.Time-dependent friction and mechanics of stick-slip[J].Pure Appl Geophys,1978,116:790-806.
[9]Dieterich,J.H.Modeling of rock friction,1,Experimental results and constitutive equations[J].J.Geophys.Res.,1979a,84:2161-2168.
[10]Dieterich,J.H.Modeling of rock friction,2,Simulation of preseismic slip[J].J.Geophys.Res.,1979b,84:2169-2175.
[11]Ruina,A.L.Friction laws and instabilities:A quasi-static analysis of some dry friction behavior[D].Ph.D.thesis,Brown Univ.Providence,R.I.1980.
[12]Ruina,A.L.Slip instability and state variable friction laws[J].J.Geophys.Res.,1983,88:359-370.
[13]Rice,J.R and Tse,S T.Dynamic motion of a single degree of freedom system following a rate and state dependent friction law[J].J.Geophys.Res.,1986,91:521-530.
[14]Cao,T and Aki,K.Seismicity simulation rate-and state-dependent friction[J].Pure Appl Geophys,1986,124:487-513.
[15]Wang Jeen-Hwa.A dynamic study of two one-state-variable,rate-dependent and state-dependent friction laws[J].Bull Seism Soc Am.,2002,92(2):687-694.
[16]张继峰,冯奇.两自由度的Burridge-Knopoff模型的一种近似分析方法[J].力学季刊,2008,29:66-71.
[17]王威,任青文,杜小凯,等.滑动速率及系统刚度对断层滑动性质影响研究[J].南京理工大学学报(自然科学版).2007,31(6):784-788.
[18]范丽琨,蔡岩萍,梁海川,等.东昆仑地质构造及地球动力学演化特征[J].地质调查与研究,2009,33(3):181-186.
[19]胡道功,吴中海,吴珍汉,等.东昆仑断裂带库赛湖段晚第四纪古地震研究[J].第四纪研究,2007,27(1):27-34.
[20]胡道功,叶培盛,吴芳,等.东昆仑断裂带西大滩段晚第四纪古地震研究[J].第四纪研究,2008,28(2):214-221.
[21]青海省地震局,中国地震局地壳应力研究所.东昆仑活动断裂带[M].北京:地震出版社,1999.
[22]刘光勋.东昆仑活动断裂带及其强震活动性[J].中国地震,1996,12(2):119-126.
[23]Aiming Lin,Jianming Guo,Ken-ichi Kano.et al.2006.Average slip rate and recurrence interval of large-magnitude earthquakes on theWestern Segment of the Strike-slip Kunlun Fault,Northern Tibet[J].Bull Seism Soc Am.,96(5):1597-1611.
[24]许洪泰,闵伟.利用地震矩和实时概率模型对中长期地震危险性进行评价-以东昆仑和阿尔金断裂为例[J].地震研究,2007,30(2):120-126.
[25]李海兵,司家亮,潘家伟,等.活动断裂的变形特征及其大地震复发周期的估算[J].地质通报,2008,27(12):1968-1991.
[26]Jianming Guo,Aiming Lin,Tadashi Maruyama.et al.New constrains on recent large earthquakes along the Xidatan-Dongdatan Seg-ment of the Kunlun Fault,Westren China[J].Bull Seism Soc Am.,2006,96(1):48-58.
[27]Van der Woerd J,Ryerson F J,Tapponnier P.et al.Holocene left-slip rate determined by cosmogenic surface dating on the XidatanSegment of the Kunlun fault(Qinghai,China)[J].Geology,1998,26(8):695-698.
[28]吴珍汉,胡道功,吴中海,等.东昆仑南部西大滩断裂的地震鼓包及形成时代[J].地质评论,2006,52(1):15-25.
[29]徐锡伟,陈文彬,于贵华,等.2001年11月14日昆仑山库赛湖地震(MS8.1)地表破裂带的基本特征[J].地震地质,2002,24(1):1-13.
[30]Okada.Y.Surface Deformation due to shear and tensile faults in a half-space[J].Bul1Seis Soc Am.,1985,75:1018-1040.
[31]Okada.Y.Internal deformation due to shear and tensile faults in a half-space[J].Bull Seis Soc Am.,1992,82:1018-1040.
[32]陶玮,沈正康,万永革,等.根据2001年Mw7.8可可西里强震InSAR同震测量结果反演东昆仑断裂两侧地壳弹性介质差异[J].地球物理学报,2007,50(3):744-751.
[33]何昌荣.速度与状态依赖性摩擦本构关系下双滑块系统的相互作用[J].中国科学:D辑,2003,33:53-59.
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