2013年芦山M_S7.0地震序列参数的早期特征:传染型余震序列模型计算结果
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摘要
为考察2013年4月20日芦山MS7.0地震震后序列参数的早期特征,利用"传染型余震序列"(ETAS)模型和最大似然法进行了参数估计.设定截止震级Mc=ML2.0,拟合时段为震后0.31—24.12天,计算获得α=1.89,p=1.22,同时利用最大似然法估计获得b=0.72.与中国大陆地区其它中强震的余震序列参数的比较表明,芦山MS7.0地震序列参数表现为触发次级余震的能力较弱和序列衰减速率较快的特征,反映出余震区相对较高的应力水平.为检测结果的稳定性,设定不同的截止震级Mc以及不同的拟合截止时间,分别进行参数拟合和参数标准差估计.结果表明,Mc的选取对α值影响明显,对p值影响则较小.此外,震后10天内获得的参数拟合结果随时间变化较为明显,而其后各参数变化总体较为平稳.
The epidemic-type aftershock sequence(ETAS)model was fitted to the aftershock sequence of the April 20,2013 Lushan MS7.0 earthquake with cutoff magnitude Mc=ML2.0 and a fitting time interval from 0.31 days to 24.12 days after the earthquake.The maximum likelihood estimates of the model parameters areα=1.89,p=1.22 and b=0.72.Comparing to other earthquakesequences in China continent,the Lushan MS7.0 earthquake sequence is characterized by a weak triggering ability in generating secondary aftershocks,aquick decay rate of aftershocks,indicating a high stress level in the aftershock region.To examine the stability of parameters,the ETAS parameters and their standard errors are estimated with different cutoff magnitudes Mc and different ending times of the fitting interval.It is observed that Mc affects the value ofαsignificantly but has less influence on p.Furthermore,the temporal variation of the ETAS parameters changed obviously within 10 days after the main shock,but became more stable beyond this time interval.
The epidemic-type aftershock sequence(ETAS)model was fitted to the aftershock sequence of the April 20,2013 Lushan MS7.0 earthquake with cutoff magnitude Mc=ML2.0 and a fitting time interval from 0.31 days to 24.12 days after the earthquake.The maximum likelihood estimates of the model parameters areα=1.89,p=1.22 and b=0.72.Comparing to other earthquakesequences in China continent,the Lushan MS7.0 earthquake sequence is characterized by a weak triggering ability in generating secondary aftershocks,aquick decay rate of aftershocks,indicating a high stress level in the aftershock region.To examine the stability of parameters,the ETAS parameters and their standard errors are estimated with different cutoff magnitudes Mc and different ending times of the fitting interval.It is observed that Mc affects the value ofαsignificantly but has less influence on p.Furthermore,the temporal variation of the ETAS parameters changed obviously within 10 days after the main shock,but became more stable beyond this time interval.
引文
陈运泰,杨智娴,张勇,刘超.2013.从汶川地震到芦山地震[J].中国科学:地球科学,43(6):1064--1072.
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蒋海昆,郑建常,吴琼,曲延军,李永莉.2007.传染型余震序列模型震后早期参数特征及其地震学意义[J].地球物理学报,50(6):1778--1786.
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中华人民共和国中央人民政府.2013.民政部:芦山地震已造成193人死亡,25人失踪[EB/OL].[2013-04-23].http:∥www.gov.cn/jrzg/2013-04/23/content_2386791.htm.
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Ogata Y.1992.Detection of precursory relative quiescence before great earthquakes through a statistical model[J].J Geophys Res,97(B13):19845--19871.
Ogata Y.1998.Space-time point-process models for earthquake occurrences[J].Ann Inst Statist Math,50(2):379--402.
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Schoenberg F P,Chu A,Veen A.2010.On the relationship between lower magnitude thresholds and bias in ETAS parameter estimates[J].J Geophys Res,115(B4):B04309,doi:10.1029/2009JB006387.
Shi Y,Bolt B A.1982.The standard error of the magnitude frequency b-value[J].Bull Seismol Soc Am,72(5):1677--1687.
Sornette D,Werner M J.2005.Apparent clustering and apparent background earthquakes biased by undetected seismicity[J].J Geophys Res,110(B9):B09303,doi:10.1029/2005JB003621.
Stein S,Liu M.2009.Long aftershock sequences within continents and implications for earthquake hazard assessment[J].Nature,462:87--89.
Utsu T.1961.A statistical study on the occurrence of aftershocks[J].Geophys Mag,30:521--605.
Utsu T.1965.A method for determining the value of bin a formula logn=a-bmshowing the magnitude frequency for earthquakes[J].Geophys Bull Hokkaido Univ,13:99--103.
Wang Q,Jackson D D,Zhuang J C.2010a.Missing links in earthquake clustering models[J].Geophys Res Lett,37(21):L21307,doi:10.1029/2010GL044858.
Wang Q,Schoenberg F P,Jackson D D.2010b.Standard errors of parameter estimates in the ETAS model[J].Bull Seismol Soc Am,100(5A):1989--2001.
Zhuang J C.2000.Statistical modeling of seismicity patterns before and after the 1990Oct 5Cape Palliser earthquake,New Zealand[J].NZJ Geol Geophys,43(3):447--460.
Zhuang J,Harte D,Werner M J,Hainzl S,Zhou S.2012.Basic Models of Seismicity:Temporal Models[M/OL].Community Online Resource for Statistical Seismicity Analysis.doi:10.5078/corssa-79905851.http:∥www.corssa.org.
Zhuang J,Ogata Y.2006.Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks[J].Physical Review E,73(4):046134,doi:10.1103/PhysRevE.73.046134.
Zhuang J,Ogata Y,Vere-Jones D.2002.Stochastic declustering of space-time earthquake occurrences[J].J Amer Stat Assoc,97(458):369--380.
①全国地震编目系统.http:∥10.5.202.22/bianmu/index.jsp.查阅日期:2013年5月15日.
蒋长胜,吴忠良.2011.玉树MS7.1地震前的中长期加速矩释放(AMR)[J].地球物理学报,54(6):1501--1510.
蒋海昆,郑建常,吴琼,曲延军,李永莉.2007.传染型余震序列模型震后早期参数特征及其地震学意义[J].地球物理学报,50(6):1778--1786.
刘杰,易桂喜,张致伟,官致军,阮祥,龙锋,杜方.2013.2013年4月20日四川芦山MS7.0级地震介绍[J].地球物理学报,56(4):1404--1407.
中华人民共和国中央人民政府.2013.民政部:芦山地震已造成193人死亡,25人失踪[EB/OL].[2013-04-23].http:∥www.gov.cn/jrzg/2013-04/23/content_2386791.htm.
Akaike H.1974.A new look at the statistical model identification[J].IEEE Trans Automat Control,19(6):716--723.
Aki K.1965.Maximum likelihood estimate of bin the formula logn=a-bmand its confidence limits[J].Bull Earthquake Re Inst,43(2):237--239.
Daley D D,Vere-Jones D.2003.An Introduction to Theory of Point Processes——Volume 1:Elementary Theory and Methods[M].Second Edition.Springer:New York:17--33.
Guo Z,Ogata Y.1997.Statistical relations between the parameters of aftershocks in time,space and magnitude[J].J Geophys Res,102(B2):2857--2873.
Huang Q.2006.Search for reliable precursors:A case study of the seismic quiescence of the 2000Western Tottori prefecture earthquake[J].J Geophys Res,111(B4):B04301,doi:10.1029/2005JB003982.
Jiang C S,Wu Z L.2012.Testing the forecast of aftershocks:A simple method with an example of application[J].Research in Geophysics,2(1):29--33.
Kagan Y Y,Bird P,Jackson D D.2010.Earthquake patterns in diverse tectonic zones of the globe[J].Pure Appl Geophys,167(6/7):721--741.
Ogata Y.1978.The asymptotic behavior of maximum likelihood estimators for stationary point processes[J].Ann Inst Statist Math,30(2):243--261.
Ogata Y.1988.Statistical models for earthquake occurrences and residual analysis for point processes[J].J Amer Statist Assoc,83(401):9--27.
Ogata Y.1989.Statistical model for standard seismicity and detection of anomalies by residual analysis[J].Tectonophysics,169(1/3):159--174.
Ogata Y.1992.Detection of precursory relative quiescence before great earthquakes through a statistical model[J].J Geophys Res,97(B13):19845--19871.
Ogata Y.1998.Space-time point-process models for earthquake occurrences[J].Ann Inst Statist Math,50(2):379--402.
Ogata Y.2001.Increased probability of large earthquakes near aftershock regions with relative quiescence[J].J Geophys Res,106(B5):8729--8744.
Omori F.1894.On aftershocks of earthquakes[J].J Coll Sci Imp Univ Tokyo,7:111--200.
Peng Y J,Zhou S Y,Zhuang J C.2012.An approach to detect the abnormal seismicity increase in Southwestern China triggered co-seismically by 2004Sumatra MW9.2earthquake[J].Geophys J Int,189(3):1734--1740.
Schoenberg F P,Chu A,Veen A.2010.On the relationship between lower magnitude thresholds and bias in ETAS parameter estimates[J].J Geophys Res,115(B4):B04309,doi:10.1029/2009JB006387.
Shi Y,Bolt B A.1982.The standard error of the magnitude frequency b-value[J].Bull Seismol Soc Am,72(5):1677--1687.
Sornette D,Werner M J.2005.Apparent clustering and apparent background earthquakes biased by undetected seismicity[J].J Geophys Res,110(B9):B09303,doi:10.1029/2005JB003621.
Stein S,Liu M.2009.Long aftershock sequences within continents and implications for earthquake hazard assessment[J].Nature,462:87--89.
Utsu T.1961.A statistical study on the occurrence of aftershocks[J].Geophys Mag,30:521--605.
Utsu T.1965.A method for determining the value of bin a formula logn=a-bmshowing the magnitude frequency for earthquakes[J].Geophys Bull Hokkaido Univ,13:99--103.
Wang Q,Jackson D D,Zhuang J C.2010a.Missing links in earthquake clustering models[J].Geophys Res Lett,37(21):L21307,doi:10.1029/2010GL044858.
Wang Q,Schoenberg F P,Jackson D D.2010b.Standard errors of parameter estimates in the ETAS model[J].Bull Seismol Soc Am,100(5A):1989--2001.
Zhuang J C.2000.Statistical modeling of seismicity patterns before and after the 1990Oct 5Cape Palliser earthquake,New Zealand[J].NZJ Geol Geophys,43(3):447--460.
Zhuang J,Harte D,Werner M J,Hainzl S,Zhou S.2012.Basic Models of Seismicity:Temporal Models[M/OL].Community Online Resource for Statistical Seismicity Analysis.doi:10.5078/corssa-79905851.http:∥www.corssa.org.
Zhuang J,Ogata Y.2006.Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks[J].Physical Review E,73(4):046134,doi:10.1103/PhysRevE.73.046134.
Zhuang J,Ogata Y,Vere-Jones D.2002.Stochastic declustering of space-time earthquake occurrences[J].J Amer Stat Assoc,97(458):369--380.
①全国地震编目系统.http:∥10.5.202.22/bianmu/index.jsp.查阅日期:2013年5月15日.
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