改进的传染型余震序列模型
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摘要
将有限幂律公式(LPL)应用到传染型余震序列模型(ETAS)中,并对原ETAS模型加以改进。以台湾集集地震早期余震序列为例,对原ETAS模型与改进的ETAS模型进行了对比分析,结果表明改进的ETAS模型要优于原ETAS模型。
Since the earliest aftershocks are always less frequent than predicted by the modified Omori law due to the purely physical causes of aftershock shortage,and since the Limited Power Law (LPL) formula performs better than the Omori law for the earliest aftershocks,this paper modifies the Epidemic Type Aftershock Sequence (ETAS) model for the aftershock rate by using the LPL formula in place of the modified Omori law. The parameters are estimated by the maximum likelihood method. The model is then applied to the Chi-Chi sequence and the resulting AIC values show that the new model performs better than the original ETAS model for the earliest aftershocks.
Since the earliest aftershocks are always less frequent than predicted by the modified Omori law due to the purely physical causes of aftershock shortage,and since the Limited Power Law (LPL) formula performs better than the Omori law for the earliest aftershocks,this paper modifies the Epidemic Type Aftershock Sequence (ETAS) model for the aftershock rate by using the LPL formula in place of the modified Omori law. The parameters are estimated by the maximum likelihood method. The model is then applied to the Chi-Chi sequence and the resulting AIC values show that the new model performs better than the original ETAS model for the earliest aftershocks.
引文
刘文兵、马丽,2004,台湾集集和华北大同地震序列的定量模型分析,地震,24(1),155～162。
庄建仓、马丽,2000,从大森公式到ETAS模型,国际地震动态,15,12～18。
Akaike H,1974,ANewLook at the Statistical Model Identification.IEEE Trans on Automatic Control,19,716～723.
Akaike H,1977,On entropy maximization principle.In P.R.Krishnaish,(ed.),Applications of Statistics,Amsterdam:North-Holland,27～41.
Harte D,1998,Documentationfor the statistical seismologylibrary.School of Mathematical and Computing Sciences,VUW,Research Report,10.
Healy J.H.,Keilis-Borok V.I.Lee W.H.K,1997,IASPEI Software Library,6.
Ma L.,Vere-Jones D,1997,Application of M8and Lin-Lin Algorithms to NewZealand Earthquake Data,NewZealand J.Geology.And Geophys,40,77～89.
Narteau C.,Shebalin P.,Holschneider M,2002,Temporal Limits of the Power Law Aftershock Decay Rate.J.Geophys.Res.,107(B12),2359.
Narteau C.,Shebalin P.,Hainzl S.,et al,2003,Emergence of a Band-limited Power Lawinthe Aftershock Decay Rate of a Slider-block Model.Geophys.Res.Letters,30(11),1568.
Ogata Y,1983,Estimation of the Parameters in the Modified Omori Formula for Aftershock Frequencies by the Maximum Likelihood Procedure.J.Phys.Earth,31,115～124.
Ogata,Y,1988,Statistical models for earthquake occurrences and residual analysis for point processes.J.Amer.Statist.Assoc.,83,9～27.
Omori F,1894,On Aftershocks of Earthquakes,J.Coll.Sci.Imp.Univ,Tokyo,7,11～200.
Shebalin P.N,2004,Aftershocks as Indicators of the State of Stress in a Fault System,Doklady Earth Sciences,398(7),978～982.
Ustu,T.,Seki,A,1955,Relation betweenthe area of aftershockregion andthe energy of the mainshock.Zisin2nd Ser,7,1～13.
Ustu,T,1961,Statistical Study onthe Occurrence of Aftershocks.Geophys.Mag.,30,521～605.
庄建仓、马丽,2000,从大森公式到ETAS模型,国际地震动态,15,12～18。
Akaike H,1974,ANewLook at the Statistical Model Identification.IEEE Trans on Automatic Control,19,716～723.
Akaike H,1977,On entropy maximization principle.In P.R.Krishnaish,(ed.),Applications of Statistics,Amsterdam:North-Holland,27～41.
Harte D,1998,Documentationfor the statistical seismologylibrary.School of Mathematical and Computing Sciences,VUW,Research Report,10.
Healy J.H.,Keilis-Borok V.I.Lee W.H.K,1997,IASPEI Software Library,6.
Ma L.,Vere-Jones D,1997,Application of M8and Lin-Lin Algorithms to NewZealand Earthquake Data,NewZealand J.Geology.And Geophys,40,77～89.
Narteau C.,Shebalin P.,Holschneider M,2002,Temporal Limits of the Power Law Aftershock Decay Rate.J.Geophys.Res.,107(B12),2359.
Narteau C.,Shebalin P.,Hainzl S.,et al,2003,Emergence of a Band-limited Power Lawinthe Aftershock Decay Rate of a Slider-block Model.Geophys.Res.Letters,30(11),1568.
Ogata Y,1983,Estimation of the Parameters in the Modified Omori Formula for Aftershock Frequencies by the Maximum Likelihood Procedure.J.Phys.Earth,31,115～124.
Ogata,Y,1988,Statistical models for earthquake occurrences and residual analysis for point processes.J.Amer.Statist.Assoc.,83,9～27.
Omori F,1894,On Aftershocks of Earthquakes,J.Coll.Sci.Imp.Univ,Tokyo,7,11～200.
Shebalin P.N,2004,Aftershocks as Indicators of the State of Stress in a Fault System,Doklady Earth Sciences,398(7),978～982.
Ustu,T.,Seki,A,1955,Relation betweenthe area of aftershockregion andthe energy of the mainshock.Zisin2nd Ser,7,1～13.
Ustu,T,1961,Statistical Study onthe Occurrence of Aftershocks.Geophys.Mag.,30,521～605.
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