自维持断层蠕滑过程和余震发生率的衰减特征——以汶川M_W7.9地震序列为例
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摘要
基于Dieterich地震活动性理论,本文推导出计算余震发生率和余震累积次数的一般表达式,其中主震后发震断层内部的剪切应力随时间的演化过程遵从Jeffreys-Lomnitz蠕变模型,且与修正Omori定律直接相关。修正Omori定律中的p值与震后断层的短时应力加卸载过程正相关。采用Rubin和Ampuero给出的震后断层自维持蠕滑模型本文得出计算余震发生率的近似表达式,并对2008年汶川地震序列进行拟合。结果表明,p值的大小直接对应了速率-状态摩擦定律中摩擦参量b/a,而修正Omori定律中的c值则与速率-状态摩擦定律中的临界滑移Dc相关。对于汶川余震序列而言,拟合结果显示b/a约为1.13,Dc约为2—3 cm。Rubin-Ampuero震后自维持蠕滑描述了震后孕震层内部短暂的速率变化特征,是孕震断层演化过程不可缺少的环节。
Based on the Dieterich seismicity theory, this study derived a general formula used to calculate decay rate and cumulative frequency of aftershocks following a mainshock,of which the shear stress variation in the fault plane follows the Jeffreys-Lomnitz creep law and is directly related to the modified Omori law. The p value in the modified Omori law is positively correlated with post earthquake loading and unloading process of the transient stress. Combined with the postseismic slip model proposed by Rubin and Ampuero,this study obtained approximate formulas to describe the variation of seismicity and to fit aftershock sequence following the2008 M_W7.9 Wenchuan earthquake. The results show that the p value is directly associated with the ratio of b/a, where a and b are the frictional parameters used in rate-and state-dependent friction,and the c value used in the modified Omori law is associated with Dc,a critical creep distance described by rate-and state-dependent friction. For the M_W7.9 Wenchuan earthquake sequence,the fitting results indicate the ratio of b/a and Dc are about 1.13 and 2 to 3 cm,respectively. It needs to be emphasized that postseismic creep proposed by Rubin and Ampuero is an inherent stage during earthquake cycle,which describes characteristics of the transient velocity change in seismogenic zone after the mainshock.
Based on the Dieterich seismicity theory, this study derived a general formula used to calculate decay rate and cumulative frequency of aftershocks following a mainshock,of which the shear stress variation in the fault plane follows the Jeffreys-Lomnitz creep law and is directly related to the modified Omori law. The p value in the modified Omori law is positively correlated with post earthquake loading and unloading process of the transient stress. Combined with the postseismic slip model proposed by Rubin and Ampuero,this study obtained approximate formulas to describe the variation of seismicity and to fit aftershock sequence following the2008 M_W7.9 Wenchuan earthquake. The results show that the p value is directly associated with the ratio of b/a, where a and b are the frictional parameters used in rate-and state-dependent friction,and the c value used in the modified Omori law is associated with Dc,a critical creep distance described by rate-and state-dependent friction. For the M_W7.9 Wenchuan earthquake sequence,the fitting results indicate the ratio of b/a and Dc are about 1.13 and 2 to 3 cm,respectively. It needs to be emphasized that postseismic creep proposed by Rubin and Ampuero is an inherent stage during earthquake cycle,which describes characteristics of the transient velocity change in seismogenic zone after the mainshock.
引文
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Barbot S,Fialko Y,Bock Y.2009.Postseismic deformation due to the MW6.0 2004 Parkfield earthquake:Stress-driven creep on a fault with spatially variable rate-and-state friction parameters[J].J Geophys Res,114(B7):B07405.
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田勤俭,刁桂苓,郝平,冯向东,孙晴.2009.汶川8.0级地震及余震破裂的地质构造特征[J].地震,29(1):141-148.Tian Q J,Diao G L,Hao P,Feng X D,Sun Q.2009.Earthquake geology of the Wenchuan M8.0 mainshock and its aftershocks[J].Earthquake,29(1):141-148(in Chinese).
张培震,徐锡伟,闻学泽,冉勇康.2008.2008年汶川8.0级地震发震断裂的滑动速率、复发周期和构造成因[J].地球物理学报,54(4):1066-1073.Zhang P Z,Xu X W,Wen X Z,Ran Y K.2008.Slip rates and recurrence intervals of the Longmenshan active fault zone,and tectonic implications for the mechanism of the May 12 Wenchuan earthquake,2008,Sichuan,China[J].Chinese Journal of Geophysics,54(4):1066-1073(in Chinese).
张勇,冯万鹏,许力生,周成虎,陈运泰.2008.2008年汶川大地震的时空破裂过程[J].中国科学:D辑,38(10):1186-1194.Zhang Y,Feng W P,Xu L S,Zhou C H,Chen Y T.2009.Spatial and temporal rupture process of 2008 MW7.8 Wenchuan earthquake,China[J].Science in China:Series D,52(2):145-154.
张致伟,程万正,阮祥,吴朋.2009.汶川8.0级地震前龙门山断裂带的地震活动性和构造应力场特征[J].地震学报,31(2):117-127.Zhang Z W,Cheng W Z,Ruan X,Wu P.2009.Seismicity and tectonic stress of the Longmenshan fault zone before 2008 Wenchuan MS8.0 earthquake[J].Acta Seismologica Sinica,31(2):117-127(in Chinese).
Ader T J,Lapusta N,Avouac J P,Ampuero J P.2014.Response of rate-and-state seismogenic faults to harmonic shear-stress perturbations[J].Geophys J Int,198(1):385-413.
Ariyoshi K,Hori T,Ampuero J P,Kaneda Y,Matsuzawa T,Hino R,Hasegawa A.2009.Influence of interaction between small asperities on various types of slow earthquakes in a 3-D simulation for a subduction plate boundary[J].Gondwana Res,16(3/4):534-544.
Barbot S,Fialko Y,Bock Y.2009.Postseismic deformation due to the MW6.0 2004 Parkfield earthquake:Stress-driven creep on a fault with spatially variable rate-and-state friction parameters[J].J Geophys Res,114(B7):B07405.
Beeler N M,Lockner D A.2003.Why earthquakes correlate weakly with the solid Earth tides:Effects of periodic stress on the rate and probability of earthquake occurrence[J].J Geophys Res,108(B8):2391.
Beeler N M.2004.Review of the physical basis of laboratory-derived relations for brittle failure and their implications for earthquake occurrence and earthquake nucleation[J].Pure Appl Geophys,161(9/10):1853-1876.
Bizzarri A.2012.What can physical source models tell us about the recurrence time of earthquakes?[J].Earth-Sci Rev,115(4):304-318.
Blanpied M L,Tullis T E,Weeks J D.1998.Effects of slip,slip rate,and shear heating on the friction of granite[J].J Geophys Res,103(B1):489-511.
Dieterich J H.1978.Preseismic fault slip and earthquake prediction[J].J Geophys Res,83(B8):3940-3948.
Dieterich J H.1992.Earthquake nucleation on faults with rate-and state-dependent strength[J].Tectonophysics,211(1/2/3/4):115-134.
Dieterich J.1994.A constitutive law for rate of earthquake production and its application to earthquake clustering[J].J Geophys Res,99(B2):2601-2618.
Dieterich J H.2007.Applications of rate-and state-dependent friction to models of fault slip and earthquake occurrence[G]//Treatise on Geophysics,Volume 4:Earthquake Seismology.Amsterdam:Elsevier:107-129.
Freed A M.2005.Earthquake triggering by static,dynamic,and postseismic stress transfer[J].Ann Rev Earth Planet Sci,33:335-367.
Freedman D,Pisani R,Purves R.2007.Statistics[M].New York:W W Norton&Company Inc:185-187.
Gomberg J,Reasenberg P,Cocco M,Belardinelli M E.2005.A frictional population model of seismicity rate change[J].J Geophys Res,110(B5):B05S03.
Hainzl S,Marsan D.2008.Dependence of the Omori-Utsu law parameters on main shock magnitude:Observations and modeling[J].J Geophys Res,113(B10):B10309.
Hainzl S,Steacy S,Marsan D.2010.Seismicity models based on Coulomb stress calculations[EB/OL].[2010-10-10].http://www.corssa.org/export/sites/corssa/.galleries/articles-pdf/Hainzl-et-al-2010-CORSSA-Coulomb-models.pdf.
Hainzl S,Christophersen A,Rhoades D,Harte D.2016.Statistical estimation of the duration of aftershock sequences[J].Geophys J Int,205(2):1180-1189.
He C R,Luo L,Hao Q M,Zhou Y S.2013.Velocity-weakening behavior of plagioclase and pyroxene gouges and stabilizing effect of small amounts of quartz under hydrothermal conditions[J].J Geophys Res,118(7):3408-3430.
Helmstetter A,Shaw B E.2009.Afterslip and aftershocks in the rate-and-state friction law[J].J Geophys Res,114(B1):B01308.
Hirose T,Shimamoto T.2005.Slip-weakening distance of faults during frictional melting as inferred from experimental and natural pseudotachylytes[J].Bull Seismol Soc Am,95(5):1666-1673.
Hsu Y J,Segall P,Yu S B,Kuo L C,Williams C A.2007.Temporal and spatial variations of post-seismic deformation following the 1999 Chi-Chi,Taiwan earthquake[J].Geophys J Int,169(2):367-379.
Hsu Y J,Simons M,Avouac J P,Galetzka J,Sieh K,Chlieh M,Natawidjaja D,Prawirodirdjo L,Bock Y.2006.Frictional afterslip following the 2005 Nias-Simeulue earthquake,Sumatra[J].Science,312(5782):1921-1926.
Huang Y,Wu J P,Zhang T Z,Zhang D N.2008.Relocation of the M8.0 Wenchuan earthquake and its aftershock sequence[J].Science in China:Series D,51(12):1703-1711.
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.
Jia K,Zhou S Y,Zhuang J C,Jiang C S.2014.Possibility of the independence between the 2013 Lushan earthquake and the2008 Wenchuan earthquake on Longmenshan fault,Sichuan,China[J].Seismol Res Lett,85(1):60-67.
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