1976年唐山地震震源动力过程的数值模拟
摘要
用新ＬＤＤＡ（Ｌａｇｒａｎｇｉａｎ Ｄｉｓｃｏｎｔｉｎｕｏｕｓ Ｄｅｆｏｒｍ ａｔｉｏｎ Ａｎａｌｙｓｉｓ）方法模拟了唐山地震断层的破裂、错动和应力释放的整个动力过程． 模拟结果表明， 唐山地震的震源滑动过程在发震断层上各处不一样． 近场位移受断层的曲率影响， 断层凹侧的位移大于断层凸侧的位移． 滑动“过冲现象”在震中处最大， 并向断层两端衰减． 我们发现， 唐山地震断层的破裂速度和应力降与断层上的初始剪应力大小有关． 唐山发震断层的最大动态、准静态位错量和剪应力降均发生在中间部位， 分别是７．１ ｍ 、６．２ ｍ 和８．１ ＭＰａ 、５．４ ＭＰａ， 发震断层的平均准静态位错量和剪应力降分别为４．５ ｍ 和３．３ ＭＰａ， 断层破裂的传播速度从震中向东南和西北方向分别为３．０８ ｋｍ ／ｓ 和１．１８ ｋｍ ／ｓ．
引文
陈运泰, 黄立人, 林邦慧, 等. 1979. 用大地测量资料反演的1976 年唐山地震的位错模式. 地球物理学报, 22(3): 201～216
国家地震局《1976 年唐山地震》编写组. 1982. 1976 年唐山地震. 北京: 地震出版社, 459
黄立人, 王学忠, 刘天奎. 1988. 唐山地震前后的水平形变. 地震学报, 10(4): 375～384
梅世蓉, 梁北援, 朱岳清. 1989. 唐山地震前兆机制的数值模拟. 中国地震, 5(2): 28～34
牛志仁, 陈党民, 李炳乾. 1997. 唐山大地震孕育过程的数值模拟研究. 地震学报, 19(4): 347～358
王仁, 孙荀英, 蔡永恩. 1982. 华北地区近700 年地震序列的数学模拟. 中国科学, B辑, 12(8): 745～753
张之立. 1984. 唐山地震破裂过程的三维分析. 地震学报, 6(1): 22～28
张之立, 王成宝, 方兴, 等. 1989. 唐山地震破裂过程的雁行断裂模式及理论和实验的模拟. 地震学报, 11(3): 291～302
张祖胜, 谢觉民, 徐峰壮, 等. 1981. 唐山7.8 地震的地壳垂直应变. 地球物理学报, 24(2): 182～191
朱岳清, 梅世蓉, 梁北援. 1988. 唐山地震孕育过程的三维有限元分析及其在地震预报研究上的意义. 地球物理学报,31(4): 399～409
Andrew s DJ. 1973. Rupture velocity ofplane strain shearcracks. JGeophysRes, 81(32): 5 679～5 687
Butler R, Stew art G S, Kanam oriH. 1979. The July 27,1976 Tangshan, China Earthquake a com plex sequence ofintraplate events. BullSeism Soc Am er, 69(1): 207～220
CundallPA. 1988. Form ulation ofathree-dim ensionaldistinctelem entm odel, PartⅠ. IntJRock Mech Sci& Geom ech, 25(1): 107～116
Day SM. 1982. Three-dim ensionalsim ulation ofspontaneous rupture: the effect of nonuniform prestress. Bull Seism SocAm er, 72(7): 1 881～1 902
FrankelA. 1993. Three-dim ensionalsim ulationsofground m otions in theSan Bernardino valley, California, forhypotheticalearthquakeson the San Andreas fault. BullSeism Soc Am er, 83(4): 1 020～1 041
Fukuyam a E, MadariagaR. 1998. Rupturedynam icsofaplanarfaultin 3Delastic m edium : rate-and slip-w eakening friction.BullSeism Soc Am er, 88(1): 1～17
Goodm an R E, Taylor R L, Brekke T L. 1968. A m odelfor m echanics of jointed rock. Proc Am er Soc Civ Engr, 94(SM3): 637～659
Hilbert L B, Jr Yi W, Cook N G W, et al. 1994. A new discontinuous finite elem ent m ethod for interaction of m anydeform able bodies in geom echanics. In: Siriw ardane, Zam an eds. Com puter Methods and Advances in Geom echanics.Rotterdam : Balkem a, 931～936
Kim J, Papageorgiou A. 1993. Discrete w avenum ber boundary elem ent m ethod for 3D Scattering problem . J Eng MechASCE, 119(3): 603～624
Liang GP, HeJ. 1993. The non com form ing dom ain decom position m ethod forellipticproblem sw ith Lagrangian m ultipliers.Chinese JNum Math & Appl, 15(1): 8～19
Madariaga R. 1976. Dynam ics ofan expanding circularfault. BullSeism Soc Am er, 66(3): 639～666
Ohm inoto T, Chouet B A. 1997. A free surface boundary condition forincluding 3D topography in the finite differencem ethod. BullSeism Soc Am er, 87(3): 494～515
Olsen K B, Archuleta R J. 1996. 3-Dsim ulation ofearthquakes on the Los Angeles faultsystem . BullSeism Soc Am er, 86(3): 575～596
Printice JK, FikaniM M. 1992. A dom ain decom position technique for com putationalsolid dynam ics. Fifth InternationalSymposium on Dom ain Decom position Methodsfor PartialDifferentialEquations. Philadelphia: SIAM, 541～544
ShiG H, Goodm an R E. 1985. Two-dim ensionaldiscontinuousdeform ation analysis. IntJNumer AnalMeth Geom ech, 9,541～556
Sim o JC, Wriggers P, Taylor R L. 1985. A perturbed Lagrangian form ulation for the finite elem ent solution of contactproblem . Com p Meth ApplMech Engr, 50, 163～180
国家地震局《1976 年唐山地震》编写组. 1982. 1976 年唐山地震. 北京: 地震出版社, 459
黄立人, 王学忠, 刘天奎. 1988. 唐山地震前后的水平形变. 地震学报, 10(4): 375～384
梅世蓉, 梁北援, 朱岳清. 1989. 唐山地震前兆机制的数值模拟. 中国地震, 5(2): 28～34
牛志仁, 陈党民, 李炳乾. 1997. 唐山大地震孕育过程的数值模拟研究. 地震学报, 19(4): 347～358
王仁, 孙荀英, 蔡永恩. 1982. 华北地区近700 年地震序列的数学模拟. 中国科学, B辑, 12(8): 745～753
张之立. 1984. 唐山地震破裂过程的三维分析. 地震学报, 6(1): 22～28
张之立, 王成宝, 方兴, 等. 1989. 唐山地震破裂过程的雁行断裂模式及理论和实验的模拟. 地震学报, 11(3): 291～302
张祖胜, 谢觉民, 徐峰壮, 等. 1981. 唐山7.8 地震的地壳垂直应变. 地球物理学报, 24(2): 182～191
朱岳清, 梅世蓉, 梁北援. 1988. 唐山地震孕育过程的三维有限元分析及其在地震预报研究上的意义. 地球物理学报,31(4): 399～409
Andrew s DJ. 1973. Rupture velocity ofplane strain shearcracks. JGeophysRes, 81(32): 5 679～5 687
Butler R, Stew art G S, Kanam oriH. 1979. The July 27,1976 Tangshan, China Earthquake a com plex sequence ofintraplate events. BullSeism Soc Am er, 69(1): 207～220
CundallPA. 1988. Form ulation ofathree-dim ensionaldistinctelem entm odel, PartⅠ. IntJRock Mech Sci& Geom ech, 25(1): 107～116
Day SM. 1982. Three-dim ensionalsim ulation ofspontaneous rupture: the effect of nonuniform prestress. Bull Seism SocAm er, 72(7): 1 881～1 902
FrankelA. 1993. Three-dim ensionalsim ulationsofground m otions in theSan Bernardino valley, California, forhypotheticalearthquakeson the San Andreas fault. BullSeism Soc Am er, 83(4): 1 020～1 041
Fukuyam a E, MadariagaR. 1998. Rupturedynam icsofaplanarfaultin 3Delastic m edium : rate-and slip-w eakening friction.BullSeism Soc Am er, 88(1): 1～17
Goodm an R E, Taylor R L, Brekke T L. 1968. A m odelfor m echanics of jointed rock. Proc Am er Soc Civ Engr, 94(SM3): 637～659
Hilbert L B, Jr Yi W, Cook N G W, et al. 1994. A new discontinuous finite elem ent m ethod for interaction of m anydeform able bodies in geom echanics. In: Siriw ardane, Zam an eds. Com puter Methods and Advances in Geom echanics.Rotterdam : Balkem a, 931～936
Kim J, Papageorgiou A. 1993. Discrete w avenum ber boundary elem ent m ethod for 3D Scattering problem . J Eng MechASCE, 119(3): 603～624
Liang GP, HeJ. 1993. The non com form ing dom ain decom position m ethod forellipticproblem sw ith Lagrangian m ultipliers.Chinese JNum Math & Appl, 15(1): 8～19
Madariaga R. 1976. Dynam ics ofan expanding circularfault. BullSeism Soc Am er, 66(3): 639～666
Ohm inoto T, Chouet B A. 1997. A free surface boundary condition forincluding 3D topography in the finite differencem ethod. BullSeism Soc Am er, 87(3): 494～515
Olsen K B, Archuleta R J. 1996. 3-Dsim ulation ofearthquakes on the Los Angeles faultsystem . BullSeism Soc Am er, 86(3): 575～596
Printice JK, FikaniM M. 1992. A dom ain decom position technique for com putationalsolid dynam ics. Fifth InternationalSymposium on Dom ain Decom position Methodsfor PartialDifferentialEquations. Philadelphia: SIAM, 541～544
ShiG H, Goodm an R E. 1985. Two-dim ensionaldiscontinuousdeform ation analysis. IntJNumer AnalMeth Geom ech, 9,541～556
Sim o JC, Wriggers P, Taylor R L. 1985. A perturbed Lagrangian form ulation for the finite elem ent solution of contactproblem . Com p Meth ApplMech Engr, 50, 163～180
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