地震发生过程的有限单元法模拟——以苏门答腊俯冲带上的大地震为例
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摘要
地震预报由目前的经验预报走向物理预报,数值模拟地震过程是其中的关键.文中应用统一的数学公式表述了速率相关的摩擦接触中黏着(sticking)和滑移(sliding)这两种不同的运动状态;有限元计算中采用静力显示的时间积分方法,基于R最小策略,控制时间步长以保持力学状态变化稳定,从而保证有限元计算过程平稳、收敛.以2004年发生过Mm=9.3特大地震的苏门答腊俯冲带为例,模拟了俯冲带上俯冲板片与上伏板块之间的闭锁、解锁、滑动到再闭锁这一准周期性过程,即地震的孕育、发生过程.计算结果表明,俯冲带上具有较大尺度、介质均匀、摩擦系数相同的区域是产生大规模、大幅度整体突然滑动(即大地震)的条件;模拟的苏门答腊俯冲带上的大地震在时间上有准周期性,空间上有迁移特征,破裂由深部向浅部进行;此外,俯冲带的几何特征对大地震的震源位置有很大的影响.
Numerical simulation of the earthquake processes is a key method to carry out physical accurate earthquake forecast in the future,but today empirical method is used in earthquake prediction,which is seldom successful. In this paper,we use a unified rate-dependent frictional law to formulate two different frictional states,one is sticking,and the other is sliding. Based on R-minimum,time integration method with static explicit is adopted in finite element analysis in order to make the result convergent in calculation. Take the Sumatra subduction zone as an example,where the major earthquake with M_m 9.3 occurred in 2004,the process of locking,unlocking,and sliding between the subduction plate and the overriding plate is simulated. The result shows that a large space of homogeneous media with the same frictional coefficient is a prerequisite for forming large-scale sudden sliding,which is regarded as an event. The earthquakes simulated by the model on the Sumatra subduction zone have characteristics of quasi-cycle in time and migration in space. The earthquake ruptures propagate upward from bottom. Moreover,the geometry of the subduction zone has much influence on the location of the large event.
Numerical simulation of the earthquake processes is a key method to carry out physical accurate earthquake forecast in the future,but today empirical method is used in earthquake prediction,which is seldom successful. In this paper,we use a unified rate-dependent frictional law to formulate two different frictional states,one is sticking,and the other is sliding. Based on R-minimum,time integration method with static explicit is adopted in finite element analysis in order to make the result convergent in calculation. Take the Sumatra subduction zone as an example,where the major earthquake with M_m 9.3 occurred in 2004,the process of locking,unlocking,and sliding between the subduction plate and the overriding plate is simulated. The result shows that a large space of homogeneous media with the same frictional coefficient is a prerequisite for forming large-scale sudden sliding,which is regarded as an event. The earthquakes simulated by the model on the Sumatra subduction zone have characteristics of quasi-cycle in time and migration in space. The earthquake ruptures propagate upward from bottom. Moreover,the geometry of the subduction zone has much influence on the location of the large event.
引文
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[18]Xing H,Mora P,Makinouchi A.Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault.Pure Appl.Geophys.,2004,161:2091~2102
[19]王瑁成.有限单元法.北京:清华大学出版社,2003Wang MC.Finite Element Method.Beijing:Tsinghua University Press,2003
[20]Dieterich J H.Time-dependent friction and the mechanics of stick-slip.Pure Appl.Geophys.,1978,116:790~806
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[23]Malod J A,Karta K,Beslier M O,et al.From normal to oblique subduction:Tectonic relationships between Java and Sumatra.J.of Southeast Asian Earth Sciences,1995,12(1/2):85~93
[24]Chamot-Rooke N,Pichon X L.GPS determined eastward Sundaland motion with respect to Eurasia confirmed by earthquakes slip vectors at Sunda and Philippine trenches.Earth and Planetary Science Letters,1999,173:439~455
[25]Kopp H,Flueh E R,Klaeschen D,et al.Crustal structure of the central Sunda margin at the onset of oblique subduction.Geophys.J.Int.,2001,147:449~474
[26]Subarya C,Chlieh M,Prawirodirdjo L,et al.Plate-boundary deformation associated with the great Sumatra-Andaman earthquake.Nature,2006,440:46~51
[27]Lay T,Kanamori H,Ammon C J,et al.The great Sumatra-Andaman earthquake of26December2004.Science,2005,308:1127~1133
[28]Bock Y,Prawirodirdjo Y,Stevens C W,et al.Crustal motion in Indonesia from Global Positioning System measurements.J.Geophys.Res.,2003,108(B8),doi:10.1029/2001JB000324.
[29]Sieh K,Natawidjaja D.Neotectonics of the Sumatranfault,Indonesia.J.Geophys.Res.,2000,105(B12):28295~28326
[30]Schlter HU,Gaedicke C,Roeser HA,et al.Tectonicfeatures of the southern Sumatra-western Java forearc of Indonesia.Tectonics,2002,21(5),doi:10.1029/2001TC901048
[31]Curray J R.Tectonics and history of the Andaman Sea region.J.of Asian Earth Science,2005,25:187~232
[32]Simoes M,Avouac J P,Cattin R,et al.The Sumatra subductionzone:A case for a locked fault zone extending into the mantle.J.Geophys.Res.,2004,109,B10402,doi:10.1029/2003JB002958
[33]Ghose R,Yoshioka S,Oike K.Three-dimensional numerical simulation of the subduction dynamics in the Sunda arc region,Southeast Asia.Tectonophysics,1990,181:223~255
[34]马胜利,刘力强,马瑾等.基于实验结果讨论断层破裂与强震物理过程的若干问题.地学前缘,2003,10(增刊),225~232Ma S L,Liu L Q,Ma J,et al.A discussion on related issues of physical process of faulting and strong earthquake based on experimental results.Earth Science Frontier(in Chinese),2003,10(Suppl.):225~232
[2]Brace WF,Byerlee J D.Stick-slip as a mechanismfor earthquakes.Science,1966,153:990~992
[3]Scholz C H.Earthquake andfriction laws.Nature,1998,391:37~42
[4]Goodman R E,Taylor RL,Brekke TL.Amodel forthe mechanics of jointed rock.J.Soil Mech.And Found.Proc.ASCE,1968,94:637~659
[5]Jungels P H,Frazier G A.Finite element analysis of the residual displacements for an earthquake rupture:source parameters for the San Fernando earthquake.J.Geophys.Res.,1973,78:5062~5083
[6]Bird P.Finite-element modeling of lithosphere deformation:The Zagros collision orogeny.Tectonophysics,1978,50:307~336
[7]Richardson R M.Finite Element Modeling of Stress in the Nazca Plate:Driving Forces and Plate Boundary Earthquakes.Tectonophysics,1978,50:223~248
[8]汪素云,陈培善.中国及邻区现代构造应力场的数值模拟.地球物理学报,1980,23(1):35~45Wang S,Chen P.Simulation of tectonic stress field in the Chinese Continent and adjacent areas.Chinese J.Geophys.(in Chinese),1980,23(1):35~45
[9]王仁,孙荀英,蔡永恩.华北地区近700年地震序列的数学模拟.中国科学(B辑),1982,745~753Wang R,Sun XY,Cai YE.Amathematical simulationof earthquake sequence in North China inthe last700years.Science in China(B Serial),1983,26:103~112
[10]Melosh HJ,Williams C A.Mechanics of graben formation in crustal rocks:A finite element analysis.J.Geophys.Res.,1989,94(B10):13961~13972
[11]Richardson R M,Coblentz D.Stress modeling in the Andes:constraints on the south American intraplater stress magnitudes.J.Geophys.Res.,1994,99:22015~22025
[12]Cai Y,He T,Wang R.Numerical simulation of Dynamic process of the Tangshan earthquake by a new method-LDDA.Pure Appl.Geophys.,2000,157:2083~2104
[13]朱守彪,石耀霖.中国大陆及邻区构造应力场成因的研究.中国科学(D辑),2006,36(12):1077~1082Zhu S B,Shi YL.Originof tectonic stressesinthe Chinese continent and adjacent areas.Science in China(Ser D),2006,36(12):1~7
[14]Yamada Y,Yoshimura N,Sakurai T.Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by finite element method.Int.J.Mech.Sci.,1968,10:343~354
[15]Kawka M,Makinouchi A.Shell element formulation in the static explicit FEMcode for simulation for sheet stamping.J.MaterialsProcessing Technology,1995,50:105~115
[16]SFSRG(Sheet Forming Simulation Research Group).ITAS3D User’s Manual,Version2.0,Riken,Japan.1996
[17]Xing H,Makinouchi A.Finite element analysis of a sandwichfriction experiment model of rocks.Pure Appl.Geophys.,2002,159:1985~2009
[18]Xing H,Mora P,Makinouchi A.Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault.Pure Appl.Geophys.,2004,161:2091~2102
[19]王瑁成.有限单元法.北京:清华大学出版社,2003Wang MC.Finite Element Method.Beijing:Tsinghua University Press,2003
[20]Dieterich J H.Time-dependent friction and the mechanics of stick-slip.Pure Appl.Geophys.,1978,116:790~806
[21]Ruina AL.Slip instability and state variable friction laws.J.Geophys.Res.,1983,88:10359~10370
[22]McCaffrey R.Oblique plate convergence,slip vectors,and forearc deformation.J.Geophys.Res.,1992,97(B6):8905~8915
[23]Malod J A,Karta K,Beslier M O,et al.From normal to oblique subduction:Tectonic relationships between Java and Sumatra.J.of Southeast Asian Earth Sciences,1995,12(1/2):85~93
[24]Chamot-Rooke N,Pichon X L.GPS determined eastward Sundaland motion with respect to Eurasia confirmed by earthquakes slip vectors at Sunda and Philippine trenches.Earth and Planetary Science Letters,1999,173:439~455
[25]Kopp H,Flueh E R,Klaeschen D,et al.Crustal structure of the central Sunda margin at the onset of oblique subduction.Geophys.J.Int.,2001,147:449~474
[26]Subarya C,Chlieh M,Prawirodirdjo L,et al.Plate-boundary deformation associated with the great Sumatra-Andaman earthquake.Nature,2006,440:46~51
[27]Lay T,Kanamori H,Ammon C J,et al.The great Sumatra-Andaman earthquake of26December2004.Science,2005,308:1127~1133
[28]Bock Y,Prawirodirdjo Y,Stevens C W,et al.Crustal motion in Indonesia from Global Positioning System measurements.J.Geophys.Res.,2003,108(B8),doi:10.1029/2001JB000324.
[29]Sieh K,Natawidjaja D.Neotectonics of the Sumatranfault,Indonesia.J.Geophys.Res.,2000,105(B12):28295~28326
[30]Schlter HU,Gaedicke C,Roeser HA,et al.Tectonicfeatures of the southern Sumatra-western Java forearc of Indonesia.Tectonics,2002,21(5),doi:10.1029/2001TC901048
[31]Curray J R.Tectonics and history of the Andaman Sea region.J.of Asian Earth Science,2005,25:187~232
[32]Simoes M,Avouac J P,Cattin R,et al.The Sumatra subductionzone:A case for a locked fault zone extending into the mantle.J.Geophys.Res.,2004,109,B10402,doi:10.1029/2003JB002958
[33]Ghose R,Yoshioka S,Oike K.Three-dimensional numerical simulation of the subduction dynamics in the Sunda arc region,Southeast Asia.Tectonophysics,1990,181:223~255
[34]马胜利,刘力强,马瑾等.基于实验结果讨论断层破裂与强震物理过程的若干问题.地学前缘,2003,10(增刊),225~232Ma S L,Liu L Q,Ma J,et al.A discussion on related issues of physical process of faulting and strong earthquake based on experimental results.Earth Science Frontier(in Chinese),2003,10(Suppl.):225~232
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