震源动力学破裂过程数值模拟研究
|
摘要
首先阐述了震源动力学过程研究的重要意义,在此基础上,研究了复杂的断层几何形态及介质模型对动力学破裂过程的影响,并对常用的有限元方法、离散元方法、有限差分方法和边界积分方程方法等进行了相应介绍.讨论了这些数值模拟方法各自的优缺点,建议在方法的选择上应视具体问题及计算的精度而定.最后对动力学数值模拟的关键部分,滑动摩擦准则进行了论述.常用的滑动摩擦准则有滑动弱化准则、速率弱化准则和速率-状态依赖摩擦准则.在单纯考虑某个地震的动力学破裂传播过程时,滑动弱化准则较为常用,其中滑动弱化距离的选取至关重要.但若考虑整个地震循环,速率-状态依赖摩擦准则更为合适.
This paper emphasized the importance of studying dynamic rupture process of earthquake source.In this study,we investigated the influences of complex fault geometry and medium,and introduced some numerical methods,such as finite element method,discrete element method,finite difference method and boundary integral equation method.We further discussed advantages and disadvantages of these methods and suggested that the choice of the methods depend on the concrete problem and calculation accuracy.Finally,we discussed the application of slip friction law to the dynamic simulation.Commonly used friction laws were slip-weakening law,slip rate-weakening law and rate-state dependent friction law.If we simply considered the dynamic rupture process of a single earthquake,slip-weakening law was more widely used,in which choosing reasonable slip weakening distance was very important.However,if we studied a whole seismic cycle,rate and state dependent friction law would be more appropriate.
This paper emphasized the importance of studying dynamic rupture process of earthquake source.In this study,we investigated the influences of complex fault geometry and medium,and introduced some numerical methods,such as finite element method,discrete element method,finite difference method and boundary integral equation method.We further discussed advantages and disadvantages of these methods and suggested that the choice of the methods depend on the concrete problem and calculation accuracy.Finally,we discussed the application of slip friction law to the dynamic simulation.Commonly used friction laws were slip-weakening law,slip rate-weakening law and rate-state dependent friction law.If we simply considered the dynamic rupture process of a single earthquake,slip-weakening law was more widely used,in which choosing reasonable slip weakening distance was very important.However,if we studied a whole seismic cycle,rate and state dependent friction law would be more appropriate.
引文
陈晓非.2010.汶川地震震源破裂动力学研究[J].国际地震动态,(6):8.
何昌荣.2000.断层上的地震成核过程与前兆模拟研究[J].中国地震,16(1):1--13.
李彦恒,史保平,张健.2009.自由表面对地震辐射能的影响:以逆冲断层为例[J].科学通报,54(7):938--943.
刘桂萍,傅征祥,李钢,郝平.2004.摩擦状态-速率依从的区域地震触发模型研究[J].地震,24(1):176--183.
刘启方,丁海平,袁一凡,金星,黄勇.2003.三维地震断层动力破裂的显式并行有限元解法[J].地震工程与工程振动,23(4):22--26.
罗扬.2007.有限差分方法求解断层动力学问题[D].北京:北京大学:12--43.
马胜利,刘力强,马瑾,王凯英,扈小燕,刘天昌,吴秀泉.2003.均匀和非均匀断层滑动失稳成核过程的实验研究[J].中国科学:D辑,33(增刊):45--52.
王威,任青文,张丽峰.2008.远场应变速率对非均质断层滑动成核影响研究[J].水电能源科学,26(3):50--54.
张海明,陈晓非.2003.半空间中平面断层上三维破裂的动力学传播理论研究[C]∥中国地球物理学会编.中国地球物理学会第十九届年会论文集.南京:南京师范大学出版社:521.
朱德瀚,张伟,祝贺君,罗扬,陈晓非.2010.利用曲线网格有限差分方法研究三维倾斜断层的破裂动力学[J].地震学报,32(4):401--411.
祝贺君.2008.使用有限差分方法研究地震波传播和震源动力学问题[D].北京:北京大学:7--38.
Aagaard B.1999.Finite Element Simulation of Earthquakes[D].California:California Institute of Technology:88--123.
Aagaard B T,Heaton T H,Hall J F.2001.Dynamic earthquake ruptures in the presence of lithostatic normal stresses:Implications for friction models and heat production[J].Bull Seism Soc Amer,91(6):1765--1796.
Andrews D J.1976a.Rupture propagation with finite stress in antiplane[J].J Geophys Res,81(20):3575--3582.
Andrews D J.1976b.Rupture velocity of plane strain shear cracks[J].J Geophys Res,81(32):5679--5687.
Andrews D J.1985.Dynamic plane-strain shear rupture with a slip-weakening friction law calculated by a boundary integral method[J].Bull Seism Soc Amer,75(1):1--21.
Aochi H,Fukuyama E,Matsu′ura M.2000a.Spontaneous rupture propagation on a non-planar fault in 3Delastic medium[J].Pure Appl Geophys,157(11--12):2003--2027.
Aochi H,Fukuyama E,Matsu′ura M.2000b.Selectivity of spontaneous rupture propagation on a branched fault[J].Geophys Res Lett,27(22):3635--3638.
Aochi H,Fukuyama E.2002.Three-dimensional nonplanar simulation of the 1992Landers earthquake[J].J Geophys Res,107(B2):1--12.
Aochi H,Madariaga R.2003.The 1999Izmit,Turkey earthquake:Nonplanar fault structure,dynamic rupture process,and strong ground motion[J].Bull Seism Soc Amer,93(3):1249--1266.
Archuleta R,Frazier G.1978.Three-dimensional numerical simulations of dynamic faulting in a half space[J].Bull Seism Soc Amer,68(3):541--572.
Archuleta R,Day S.1980.Dynamic rupture in a layered medium:The 1966Parkfield earthquake[J].Bull Seism Soc Amer,70(3):671--689.
Beroza G C,Mikumo T.1996.Short slip duration in dynamic rupture in the presence of heterogeneous fault properties[J].J Geophys Res,101(B10):22449--22460.
Carlson J M,Langer J S.1989.Mechanical model of an earthquake fault[J].Phys Rev A,40(11):6470--6484.
Chen X F,Zhang H M.2006.Modeling rupture dynamics of a planar fault in 3-D half space by boundary integral equation method:An overview[J].Pure Appl Geophys,163(2--3):267--299.
Cocco M,Bizzarri A.2002.On the slip-weakening behavior of rate and state dependent constitutive laws[J].Geophys Res Lett,29(11):11-1--11-4.
Cochard A,Madariaga R.1994.Dynamic faulting under rate-dependence friction[J].Pure Appl Geophys,142(3--4):419--445.
Cochard A,Madariaga R.1996.Complexity of seismicity due to highly rate dependent friction[J].J Geophys Res,101(B11):25321--25336.
Dalguer L A,Irikura K,Riera J D,Chiu H C.2001a.Fault dynamic rupture simulation of the hypocenter area of the thrust fault of the 1999Chi--Chi(Taiwan)earthquake[J].Geophys Res Lett,28(7):1327--1330.
Dalguer L A,Irikura K,Riera J D,Chiu H C.2001b.The importance of the dynamic source effects on strong ground motion during the 1999Chi--Chi,Taiwan,earthquake:Brief Interpretation of the damage distribution on buildings[J].Bull Seism Soc Amer,91(5):1112--1127.
Dalguer L A,Irikura K,Zhang W,Riera J D.2002.Distribution dynamic stress changes during 2000Tottori(Japan)earthquake:Brief interpretation of the earthquake sequences foreshocks,mainshock and aftershocks[J].Geophys Res Lett,29(16):5-1--5-4
Das S,Aki K.1977.A numerical study of two-dimensional spontaneous rupture propagation[J].Geophys J Roy astr Soc,50(3):643--668.
David P,Peter M.1999.The lattice solid model to simulate the physics of rocks and earthquakes:Incorporation of friction[J].J Comput Phys,150(2):332--372.
Day S.1977.Finite Element Analysis of Seismic Scattering Problems[D].California:University of California at San Diego:1--44.
Day S M,Dalguer L A,Lapusta N,Liu Y.2005.Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture[J].J Geophys Res,110(B12):B12307,doi:10.1029/2005JB003813.
Day S M.1982a.Three-dimensional finite difference simulation of fault dynamics:rectangular faults with fixed rupture velocity[J].Bull Seism Soc Amer,72(3):705--727.
Day S M.1982b.Three-dimensional simulation of spontaneous rupture:the effect of nonuniform prestress[J].Bull Seism Soc Amer,72(6A):1881--1902.
Dieterich J H.1979.Modeling of rock friction:1.Experimental results and constitutive equations[J].J Geophys Res,84(B5):2161--2168.
Dieterich J H.1992.Earthquake nucleation on faults with rate and state-dependent strength[J].Tectonophysics,211(3--4):115--134.
Duan B C,Oglesby D D.2006.Heterogeneous fault stresses from previous earthquakes and the effect on dynamics of parallel strike-slip faults[J].J Geophys Res,111(B5):B05309,doi:10.1029/2005JB004138.
Duan B C,Oglesby D D.2007.Nonuniform prestress from prior earthquakes and the effects on dynamics of branched fault systems[J].J Geophys Res,112(B5):B05308,doi:10.1029/2006JB004443.
Dunham E M,Belanger D,Cong L,Kozdon J E.2011a.Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity,Part 1:Planar faults[J].Bull Seism Soc Amer,101(5):2296--2307.
Dunham E M,Belanger D,Cong L,Kozdon J E.2011b.Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity,Part 2:Nonplanar faults[J].Bull Seism Soc Amer,101(5):2308--2322.
Fukuyama E,Madariaga R.1995.Integral equation method for plane crack with arbitrary shape in 3Delastic medium[J].Bull Seism Soc Amer,85(2):614--628.
Fukuyama E,Madariaga R.1998.Rupture dynamics of a planar fault in a 3Delastic medium:Rate-and slip-weakening friction[J].Bull Seism Soc Amer,88(1):1--17.
Fukuyama E,Mikumo T.2006.Dynamic rupture propagation during the 1891Nobi,Central Japan,earthquake:A possible extension to the branched faults[J].Bull Seism Soc Amer,96(4A):1257--1266.
Guatteri M,Spudich P.2000.What can strong motion data tell us about slip-weakening fault friction laws?[J].Bull Seism Soc Amer,90(1):98--116.
Harris R A,Archuleta R J,Day S M.1991.Fault steps and the dynamic rupture process:2-D numerical simulations of a spontaneously propagating shear fracture[J].Geophys Res Lett,18(5):893--896.
Harris R A,Day S M.1993.Dynamics of fault interaction:parallel strike-slip faults[J].J Geophys Res,98(B3):4461--4472.
Ida Y.1972.Cohesive force across the tip of a longitudinal shear crack and Griffith’s specific surface energy[J].J Geophys Res,77(20):3796--3805.
Ide S,Takeo M.1997.Determination of constitutive relations of fault slip based on seismic wave analysis[J].J Geophys Res,102(B12):27379--27391.
Kato N,Hirasawa T.1996.Effects of strain rate and strength nonuniformity on the slip nucleation process:A numerical experiment[J].Tectonophysics,265(3--4):299--311.
Kostrov B V.1964.Self-similar problems of propagation of shear cracks[J].J Appl Math Mech,28(5):1077--1087.
Kostrov B V.1966.Unsteady propagation of longitudinal shear cracks[J].J Appl Math Mech,30(6):1241--1248.
Kostrov B V,Das S.1989.Principles of Earthquake Source Mechanics[M].New York:Cambridge University Press:37--52.
Madariaga R.1976.Dynamics of an expanding circular fault[J].Bull Seism Soc Amer,66(3):639--666.
Madariaga R,Olsen K B.2000.Criticality of rupture dynamics in 3-D[J].Pure Appl Geophys,157(11--12):1981--2001.
Marone C,Kilgore B.1993.Scaling of the critical slip distance for seismic faulting with shear strain in fault zones[J].Nature,362:618--621.
Mikumo T,Hirahara K,Miyatake T.1987.Dynamic fault rupture processes in heterogeneous media[J].Tectonophysics,144(1--3):19--36.
Mikumo T,Kim B O,Fukuyama E,Yagi Y.2003.Stress breakdown time and slip-weakening distance inferred from slipvelocity functions on earthquake faults[J].Bull Seism Soc Amer,93(1):264--282.
Miyatake T.1980a.Numerical simulations of earthquake source process by a three-dimensional crack model:PartⅠ.Rupture process[J].J Phys Earth,28:565--598.
Miyatake T.1980b.Numerical simulations of earthquake source process by a three-dimensional crack model:PartⅡ.Seismic wave and spectrum[J].J Phys Earth,28:599--616.
Nielsen S B.1998.Free surface effects on the propagation of dynamic rupture[J].Geophys Res Lett,25(1):125--128.
Oglesby D D,Archuleta R J,Nielsen S B.1998.Earthquakes on dipping faults:The effects of broken symmetry[J].Science,280(5366):1055--1059.
Oglesby D D,Archuleta R J,Nielsen S B.2000a.The three-dimensional dynamics of dipping faults[J].Bull Seism Soc Amer,90(3):616--628.
Oglesby D D,Archuleta R J,Nielsen S B.2000b.The dynamics of dipping faulting:Explorations in two dimensions[J].J Geophys Res,105(B6):13643--13653.
Oglesby D D,Day S M.2001a.The effect of fault geometry on the 1999Chi--Chi(Taiwan)earthquake[J].Geophys Res Lett,28(9):1831--1834.
Oglesby D,Day S M.2001b.Fault geometry and the dynamics of the 1999Chi--Chi(Taiwan)earthquake[J].Bull Seism Soc Amer,91(5):1099--1111.
Ohnaka M.1992.Earthquake source nucleation:A physical model for short term precursors[J].Tectonophysics,211(1--4):149--178.
Okubo P G.1989.Dynamic rupture modeling with laboratory-derived constitutive relations[J].J Geophys Res,94(B9):12321--12335.
Parsons T,Toda S,Stein R S,Barka A,Dieterich J H.2000.Heightened odds of large earthquakes near Istanbul:An interaction-based probability calculation[J].Science,288(5466):661--665.
Pitarka A.1999.3Delastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing[J].Bull Seism Soc Amer,89(1):54--68.
Quin H.1990.Dynamic stress drop and rupture dynamics of the October 15,1979Imperial Valley,California,earthquake[J].Tectonophysics,175(1--3):93--117.
Ruina A.1983.Slip instabilities and state variable friction laws[J].J Geophys Res,88(B12):10359--10370.
Scholz C H.1998.Earthquakes and friction laws[J].Nature,391:37--42.
Scholz C H.1989.The Mechanics of Earthquake and Faulting[M].New York:Cambridge University Press:179--206.
Shen Z K,Sun J B,Zhang P Z,Wan Y,Wang M,Bürgmann R,Zeng Y H,Gan W J,Liao H,Wang Q L.2009.Slip maxima at fault junctions and rupturing of barriers during the 2008 Wenchuan earthquake[J].Nature Geoscience,(2):718--724.
Tada T,Yamashita T.1997.Nonhypersingular boundary integral equations for two-dimensional non-planar crack analysis[J].Geophys J Int,130(2):269--282.
Tada T,Fukuyama E,Madariaga R.2000.Non-hyper singular boundary integral equations for 3-D non-planar crack dynamics[J].Computational Mechanics,25(6):613--626.
Toda S,Stein R S,Sagiya T.2002.Evidence from the AD 2000Izu islands earthquake swarm that stressing rate governs seismicity[J].Nature,419(6902):58--61.
Tse S T,Rice J R.1986.Crustal earthquake instability in relation to the depth variation of frictional slip properties[J].J Geophys Res,91(B9):9452--9472.
Wald D J,Heaton T H.1994.Spatial and temporal distribution of slip for the 1992Landers,Californica,earthquake[J].Bull Seism Soc Amer,84(3):668--691.
Yamashita T,Umeda Y.1994.Earthquake rupture complexity due to dynamic nucleation and interaction of subsidiary faults[J].Pure Appl Geophys,143(1--3):89--116.
Zhang H M,Chen X F.2006a.Dynamic rupture on a planar fault in three-dimensional half space:Ⅰ.Theory[J].Geophys J Int,164(3):633--652.
Zhang H M,Chen X F.2006b.Dynamic rupture on a planar fault in three-dimensional half space:Ⅱ.Validations and numerical experiments[J].Geophys J Int,167(2):917--932.
Zhang W,Chen X F.2006c.Traction image method for irregular free surface boundaries in finite difference seismic wave simulation[J].Geophys J Int,167(1):337--353.
Zhang W B,Iwata T,Irikura K,Sekiguchi H,Bouchon M.2003.Heterogeneous distribution of the dynamic source parameters of the 1999Chi--Chi,Taiwan,earthquake[J].J Geophys Res,108(B5):2232.
Zhang W B,Iwata T,Irikura K.2006.Dynamic simulation of a dipping fault using a three-dimensional finite difference method with nonuniform grid spacing[J].J Geophys Res,111(B5):B05301,doi:10.1029/2005JB003725.
Zhang W B,Iwata T,Irikura K.2010.Dynamic simulation of the 1999Chi--Chi,Taiwan,earthquake[J].J Geophys Res,115(B4):B04305,doi:10.1029/2008JB006201.
何昌荣.2000.断层上的地震成核过程与前兆模拟研究[J].中国地震,16(1):1--13.
李彦恒,史保平,张健.2009.自由表面对地震辐射能的影响:以逆冲断层为例[J].科学通报,54(7):938--943.
刘桂萍,傅征祥,李钢,郝平.2004.摩擦状态-速率依从的区域地震触发模型研究[J].地震,24(1):176--183.
刘启方,丁海平,袁一凡,金星,黄勇.2003.三维地震断层动力破裂的显式并行有限元解法[J].地震工程与工程振动,23(4):22--26.
罗扬.2007.有限差分方法求解断层动力学问题[D].北京:北京大学:12--43.
马胜利,刘力强,马瑾,王凯英,扈小燕,刘天昌,吴秀泉.2003.均匀和非均匀断层滑动失稳成核过程的实验研究[J].中国科学:D辑,33(增刊):45--52.
王威,任青文,张丽峰.2008.远场应变速率对非均质断层滑动成核影响研究[J].水电能源科学,26(3):50--54.
张海明,陈晓非.2003.半空间中平面断层上三维破裂的动力学传播理论研究[C]∥中国地球物理学会编.中国地球物理学会第十九届年会论文集.南京:南京师范大学出版社:521.
朱德瀚,张伟,祝贺君,罗扬,陈晓非.2010.利用曲线网格有限差分方法研究三维倾斜断层的破裂动力学[J].地震学报,32(4):401--411.
祝贺君.2008.使用有限差分方法研究地震波传播和震源动力学问题[D].北京:北京大学:7--38.
Aagaard B.1999.Finite Element Simulation of Earthquakes[D].California:California Institute of Technology:88--123.
Aagaard B T,Heaton T H,Hall J F.2001.Dynamic earthquake ruptures in the presence of lithostatic normal stresses:Implications for friction models and heat production[J].Bull Seism Soc Amer,91(6):1765--1796.
Andrews D J.1976a.Rupture propagation with finite stress in antiplane[J].J Geophys Res,81(20):3575--3582.
Andrews D J.1976b.Rupture velocity of plane strain shear cracks[J].J Geophys Res,81(32):5679--5687.
Andrews D J.1985.Dynamic plane-strain shear rupture with a slip-weakening friction law calculated by a boundary integral method[J].Bull Seism Soc Amer,75(1):1--21.
Aochi H,Fukuyama E,Matsu′ura M.2000a.Spontaneous rupture propagation on a non-planar fault in 3Delastic medium[J].Pure Appl Geophys,157(11--12):2003--2027.
Aochi H,Fukuyama E,Matsu′ura M.2000b.Selectivity of spontaneous rupture propagation on a branched fault[J].Geophys Res Lett,27(22):3635--3638.
Aochi H,Fukuyama E.2002.Three-dimensional nonplanar simulation of the 1992Landers earthquake[J].J Geophys Res,107(B2):1--12.
Aochi H,Madariaga R.2003.The 1999Izmit,Turkey earthquake:Nonplanar fault structure,dynamic rupture process,and strong ground motion[J].Bull Seism Soc Amer,93(3):1249--1266.
Archuleta R,Frazier G.1978.Three-dimensional numerical simulations of dynamic faulting in a half space[J].Bull Seism Soc Amer,68(3):541--572.
Archuleta R,Day S.1980.Dynamic rupture in a layered medium:The 1966Parkfield earthquake[J].Bull Seism Soc Amer,70(3):671--689.
Beroza G C,Mikumo T.1996.Short slip duration in dynamic rupture in the presence of heterogeneous fault properties[J].J Geophys Res,101(B10):22449--22460.
Carlson J M,Langer J S.1989.Mechanical model of an earthquake fault[J].Phys Rev A,40(11):6470--6484.
Chen X F,Zhang H M.2006.Modeling rupture dynamics of a planar fault in 3-D half space by boundary integral equation method:An overview[J].Pure Appl Geophys,163(2--3):267--299.
Cocco M,Bizzarri A.2002.On the slip-weakening behavior of rate and state dependent constitutive laws[J].Geophys Res Lett,29(11):11-1--11-4.
Cochard A,Madariaga R.1994.Dynamic faulting under rate-dependence friction[J].Pure Appl Geophys,142(3--4):419--445.
Cochard A,Madariaga R.1996.Complexity of seismicity due to highly rate dependent friction[J].J Geophys Res,101(B11):25321--25336.
Dalguer L A,Irikura K,Riera J D,Chiu H C.2001a.Fault dynamic rupture simulation of the hypocenter area of the thrust fault of the 1999Chi--Chi(Taiwan)earthquake[J].Geophys Res Lett,28(7):1327--1330.
Dalguer L A,Irikura K,Riera J D,Chiu H C.2001b.The importance of the dynamic source effects on strong ground motion during the 1999Chi--Chi,Taiwan,earthquake:Brief Interpretation of the damage distribution on buildings[J].Bull Seism Soc Amer,91(5):1112--1127.
Dalguer L A,Irikura K,Zhang W,Riera J D.2002.Distribution dynamic stress changes during 2000Tottori(Japan)earthquake:Brief interpretation of the earthquake sequences foreshocks,mainshock and aftershocks[J].Geophys Res Lett,29(16):5-1--5-4
Das S,Aki K.1977.A numerical study of two-dimensional spontaneous rupture propagation[J].Geophys J Roy astr Soc,50(3):643--668.
David P,Peter M.1999.The lattice solid model to simulate the physics of rocks and earthquakes:Incorporation of friction[J].J Comput Phys,150(2):332--372.
Day S.1977.Finite Element Analysis of Seismic Scattering Problems[D].California:University of California at San Diego:1--44.
Day S M,Dalguer L A,Lapusta N,Liu Y.2005.Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture[J].J Geophys Res,110(B12):B12307,doi:10.1029/2005JB003813.
Day S M.1982a.Three-dimensional finite difference simulation of fault dynamics:rectangular faults with fixed rupture velocity[J].Bull Seism Soc Amer,72(3):705--727.
Day S M.1982b.Three-dimensional simulation of spontaneous rupture:the effect of nonuniform prestress[J].Bull Seism Soc Amer,72(6A):1881--1902.
Dieterich J H.1979.Modeling of rock friction:1.Experimental results and constitutive equations[J].J Geophys Res,84(B5):2161--2168.
Dieterich J H.1992.Earthquake nucleation on faults with rate and state-dependent strength[J].Tectonophysics,211(3--4):115--134.
Duan B C,Oglesby D D.2006.Heterogeneous fault stresses from previous earthquakes and the effect on dynamics of parallel strike-slip faults[J].J Geophys Res,111(B5):B05309,doi:10.1029/2005JB004138.
Duan B C,Oglesby D D.2007.Nonuniform prestress from prior earthquakes and the effects on dynamics of branched fault systems[J].J Geophys Res,112(B5):B05308,doi:10.1029/2006JB004443.
Dunham E M,Belanger D,Cong L,Kozdon J E.2011a.Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity,Part 1:Planar faults[J].Bull Seism Soc Amer,101(5):2296--2307.
Dunham E M,Belanger D,Cong L,Kozdon J E.2011b.Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity,Part 2:Nonplanar faults[J].Bull Seism Soc Amer,101(5):2308--2322.
Fukuyama E,Madariaga R.1995.Integral equation method for plane crack with arbitrary shape in 3Delastic medium[J].Bull Seism Soc Amer,85(2):614--628.
Fukuyama E,Madariaga R.1998.Rupture dynamics of a planar fault in a 3Delastic medium:Rate-and slip-weakening friction[J].Bull Seism Soc Amer,88(1):1--17.
Fukuyama E,Mikumo T.2006.Dynamic rupture propagation during the 1891Nobi,Central Japan,earthquake:A possible extension to the branched faults[J].Bull Seism Soc Amer,96(4A):1257--1266.
Guatteri M,Spudich P.2000.What can strong motion data tell us about slip-weakening fault friction laws?[J].Bull Seism Soc Amer,90(1):98--116.
Harris R A,Archuleta R J,Day S M.1991.Fault steps and the dynamic rupture process:2-D numerical simulations of a spontaneously propagating shear fracture[J].Geophys Res Lett,18(5):893--896.
Harris R A,Day S M.1993.Dynamics of fault interaction:parallel strike-slip faults[J].J Geophys Res,98(B3):4461--4472.
Ida Y.1972.Cohesive force across the tip of a longitudinal shear crack and Griffith’s specific surface energy[J].J Geophys Res,77(20):3796--3805.
Ide S,Takeo M.1997.Determination of constitutive relations of fault slip based on seismic wave analysis[J].J Geophys Res,102(B12):27379--27391.
Kato N,Hirasawa T.1996.Effects of strain rate and strength nonuniformity on the slip nucleation process:A numerical experiment[J].Tectonophysics,265(3--4):299--311.
Kostrov B V.1964.Self-similar problems of propagation of shear cracks[J].J Appl Math Mech,28(5):1077--1087.
Kostrov B V.1966.Unsteady propagation of longitudinal shear cracks[J].J Appl Math Mech,30(6):1241--1248.
Kostrov B V,Das S.1989.Principles of Earthquake Source Mechanics[M].New York:Cambridge University Press:37--52.
Madariaga R.1976.Dynamics of an expanding circular fault[J].Bull Seism Soc Amer,66(3):639--666.
Madariaga R,Olsen K B.2000.Criticality of rupture dynamics in 3-D[J].Pure Appl Geophys,157(11--12):1981--2001.
Marone C,Kilgore B.1993.Scaling of the critical slip distance for seismic faulting with shear strain in fault zones[J].Nature,362:618--621.
Mikumo T,Hirahara K,Miyatake T.1987.Dynamic fault rupture processes in heterogeneous media[J].Tectonophysics,144(1--3):19--36.
Mikumo T,Kim B O,Fukuyama E,Yagi Y.2003.Stress breakdown time and slip-weakening distance inferred from slipvelocity functions on earthquake faults[J].Bull Seism Soc Amer,93(1):264--282.
Miyatake T.1980a.Numerical simulations of earthquake source process by a three-dimensional crack model:PartⅠ.Rupture process[J].J Phys Earth,28:565--598.
Miyatake T.1980b.Numerical simulations of earthquake source process by a three-dimensional crack model:PartⅡ.Seismic wave and spectrum[J].J Phys Earth,28:599--616.
Nielsen S B.1998.Free surface effects on the propagation of dynamic rupture[J].Geophys Res Lett,25(1):125--128.
Oglesby D D,Archuleta R J,Nielsen S B.1998.Earthquakes on dipping faults:The effects of broken symmetry[J].Science,280(5366):1055--1059.
Oglesby D D,Archuleta R J,Nielsen S B.2000a.The three-dimensional dynamics of dipping faults[J].Bull Seism Soc Amer,90(3):616--628.
Oglesby D D,Archuleta R J,Nielsen S B.2000b.The dynamics of dipping faulting:Explorations in two dimensions[J].J Geophys Res,105(B6):13643--13653.
Oglesby D D,Day S M.2001a.The effect of fault geometry on the 1999Chi--Chi(Taiwan)earthquake[J].Geophys Res Lett,28(9):1831--1834.
Oglesby D,Day S M.2001b.Fault geometry and the dynamics of the 1999Chi--Chi(Taiwan)earthquake[J].Bull Seism Soc Amer,91(5):1099--1111.
Ohnaka M.1992.Earthquake source nucleation:A physical model for short term precursors[J].Tectonophysics,211(1--4):149--178.
Okubo P G.1989.Dynamic rupture modeling with laboratory-derived constitutive relations[J].J Geophys Res,94(B9):12321--12335.
Parsons T,Toda S,Stein R S,Barka A,Dieterich J H.2000.Heightened odds of large earthquakes near Istanbul:An interaction-based probability calculation[J].Science,288(5466):661--665.
Pitarka A.1999.3Delastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing[J].Bull Seism Soc Amer,89(1):54--68.
Quin H.1990.Dynamic stress drop and rupture dynamics of the October 15,1979Imperial Valley,California,earthquake[J].Tectonophysics,175(1--3):93--117.
Ruina A.1983.Slip instabilities and state variable friction laws[J].J Geophys Res,88(B12):10359--10370.
Scholz C H.1998.Earthquakes and friction laws[J].Nature,391:37--42.
Scholz C H.1989.The Mechanics of Earthquake and Faulting[M].New York:Cambridge University Press:179--206.
Shen Z K,Sun J B,Zhang P Z,Wan Y,Wang M,Bürgmann R,Zeng Y H,Gan W J,Liao H,Wang Q L.2009.Slip maxima at fault junctions and rupturing of barriers during the 2008 Wenchuan earthquake[J].Nature Geoscience,(2):718--724.
Tada T,Yamashita T.1997.Nonhypersingular boundary integral equations for two-dimensional non-planar crack analysis[J].Geophys J Int,130(2):269--282.
Tada T,Fukuyama E,Madariaga R.2000.Non-hyper singular boundary integral equations for 3-D non-planar crack dynamics[J].Computational Mechanics,25(6):613--626.
Toda S,Stein R S,Sagiya T.2002.Evidence from the AD 2000Izu islands earthquake swarm that stressing rate governs seismicity[J].Nature,419(6902):58--61.
Tse S T,Rice J R.1986.Crustal earthquake instability in relation to the depth variation of frictional slip properties[J].J Geophys Res,91(B9):9452--9472.
Wald D J,Heaton T H.1994.Spatial and temporal distribution of slip for the 1992Landers,Californica,earthquake[J].Bull Seism Soc Amer,84(3):668--691.
Yamashita T,Umeda Y.1994.Earthquake rupture complexity due to dynamic nucleation and interaction of subsidiary faults[J].Pure Appl Geophys,143(1--3):89--116.
Zhang H M,Chen X F.2006a.Dynamic rupture on a planar fault in three-dimensional half space:Ⅰ.Theory[J].Geophys J Int,164(3):633--652.
Zhang H M,Chen X F.2006b.Dynamic rupture on a planar fault in three-dimensional half space:Ⅱ.Validations and numerical experiments[J].Geophys J Int,167(2):917--932.
Zhang W,Chen X F.2006c.Traction image method for irregular free surface boundaries in finite difference seismic wave simulation[J].Geophys J Int,167(1):337--353.
Zhang W B,Iwata T,Irikura K,Sekiguchi H,Bouchon M.2003.Heterogeneous distribution of the dynamic source parameters of the 1999Chi--Chi,Taiwan,earthquake[J].J Geophys Res,108(B5):2232.
Zhang W B,Iwata T,Irikura K.2006.Dynamic simulation of a dipping fault using a three-dimensional finite difference method with nonuniform grid spacing[J].J Geophys Res,111(B5):B05301,doi:10.1029/2005JB003725.
Zhang W B,Iwata T,Irikura K.2010.Dynamic simulation of the 1999Chi--Chi,Taiwan,earthquake[J].J Geophys Res,115(B4):B04305,doi:10.1029/2008JB006201.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心