序列衰减与余震激发研究进展及应用成果
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摘要
着重于序列衰减与余震激发,系统介绍了修改的大森公式、ETAS模型及BASS模型的最新理论研究进展及应用成果。修改的大森公式是迄今为止对序列衰减的最好描述,据此可对序列衰减特征进行定量表述。大森公式本质上是一种典型的现象统计模型,但由于其参数少、计算简单,并且确实能够反映序列衰减的总体特征,因而在实际中应用广泛。ETAS模型考虑了具有统计自相似特征的次级余震激发问题,次级余震激发强度与父地震强度有关,这在物理过程方面对大森公式进行了大大的拓展。由于考虑了次级余震的激发问题,ETAS模型不但在余震序列研究方面比修改的大森公式有了明显的进展,而且在诸如平静检测、余震群集剔除、背景地震活动评估、外因触发地震活动检测等方面也有诸多应用。BASS模型遵循修改的Bath定律,而ETAS模型遵循的是与父地震震级有关的相似率,这是BASS模型与ETAS模型的最大区别,因而相对ETAS模型而言,BASS模型是一种完全自相似的理想化模型,但目前基于BASS模型的应用研究尚不多见。
Focusing on decay and generation of the aftershock activity,the latest theoretical advancements and applications on the modified Omori law,the ETAS model and the BASS model have been introduced in this paper. Up to now,the modified Omori law is the best formula for fitting the temporal decay of aftershock activity,which has been used to describe the decay characteristics of aftershock sequences quantitatively. Essentially,the modified Omori law is a typical statistical model on observing phenomena,but it has been used widely in practice owing to its less parameters,simple calculation,and higher capability of describing the general features of sequence decay. ETAS model,which takes into account the generation of the high order aftershocks with statistical self-similar characteristics,is a physical expansion of the modified Omori law,and the generation intensity of high order aftershocks is concerned to be related to the magnitude of the father earthquake. Since considering the problems of high order aftershock generation,ETAS model not only has a large improvement in study field of aftershock sequences,but also has many other applications,such as detection of relative quiescence,removing of the cluster aftershock activity,assessment of background seismicity,detection of seismic activity triggered by external factors and so on. BASS model follows the modified Bath's law,while the ETAS model follows the similar rate with the magnitude of the father earthquake,this is the largest difference between ETAS model and BASS model. So,the BASS model is a completely self-similar theoretical model compared with the ETAS,but only few papers concerning its application.
Focusing on decay and generation of the aftershock activity,the latest theoretical advancements and applications on the modified Omori law,the ETAS model and the BASS model have been introduced in this paper. Up to now,the modified Omori law is the best formula for fitting the temporal decay of aftershock activity,which has been used to describe the decay characteristics of aftershock sequences quantitatively. Essentially,the modified Omori law is a typical statistical model on observing phenomena,but it has been used widely in practice owing to its less parameters,simple calculation,and higher capability of describing the general features of sequence decay. ETAS model,which takes into account the generation of the high order aftershocks with statistical self-similar characteristics,is a physical expansion of the modified Omori law,and the generation intensity of high order aftershocks is concerned to be related to the magnitude of the father earthquake. Since considering the problems of high order aftershock generation,ETAS model not only has a large improvement in study field of aftershock sequences,but also has many other applications,such as detection of relative quiescence,removing of the cluster aftershock activity,assessment of background seismicity,detection of seismic activity triggered by external factors and so on. BASS model follows the modified Bath's law,while the ETAS model follows the similar rate with the magnitude of the father earthquake,this is the largest difference between ETAS model and BASS model. So,the BASS model is a completely self-similar theoretical model compared with the ETAS,but only few papers concerning its application.
引文
蒋海昆,李永莉,曲延军,等.2006.中国大陆中强地震序列类型空间分布特征[J].地震学报,28(4):417—427.JIANG Hai-kun,LI Yong-li,QU Yan-jun,et al.2006.Spatial distribution features of sequence types of moderate andlarge earthquake in Chinese mainland[J].Acta Seismologica Sinica,28(4):417—427(in Chinese).
蒋海昆,傅征祥,刘杰,等.2007a.中国大陆地震序列研究[M].北京:地震出版社.1—2.JIANG Hai-kun,FUZheng-xiang,LIUJie,et al.2007a.Research of earthquake sequences in China[M].Seismologi-cal Press,Beijing.1—2.
蒋海昆,郑建常,吴琼,等.2007b.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.JIANG Hai-kun,ZHENG Jian-chang,WU Qiong,et al.2007b.Earlier statistical features of ETAS model parametersand their seismological meanings[J].Chinese J Geophys,50(6):1778—1786(in Chinese).
刘正荣,钱兆霞,王维清,等.1979.前震的一个标志:地震频度的衰减[J].地震研究,2(4):1—9.LIU Zheng-rong,QIAN Zhao-xia,WANG Wei-qing,et al.1979.An indication of the fore-shock:The attenuation tothe earthquake frequency[J].Journal of Seismological Research,2(4):1—9(in Chinese).
刘正荣.1984.根据地震频度衰减预报地震的工作细则[J].地震,1:32—37.LIU Zheng-rong.1984.A code of practice for earthquake prediction using frequency attenuation of earthquakes[J].Earthquake,1:32—37(in Chinese).
刘正荣,孔绍麟.1986.地震频度衰减与地震预报[J].地震研究,9(1):6—8.LIU Zheng-rong,KONG Shao-lin.1986.Earthquake frequency attenuation and earthquake prediction[J].Journal ofSeismological Research,9(1):6—8(in Chinese).
王碧泉,王春珍.1983.余震序列的时空特征[J].地震学报,5(4):383—396.WANG Bi-quan,WANG Chun-zhen.1983.Temporal and spatial features of aftershock sequences[J].Acta Seis-mologica Sinica,5(4):383—396(in Chinese).
许绍燮主编.1990.地震学分析预报方法程式指南[Z].北京:地震出版社.72—77.XU Shao-xie(chief editor).1990.Guide of Seismological Analysis and Prediction Method[M].Seismological Press,Beijing.72—77.
赵志新,尾池和夫,松村一男,等.1992.中国大陆性地震的余震活动的p值[J].地震学报,14(1):9—16.ZHAO Zhi-xin,Oike Kazuo,Matsumura Kazuo,et al.1992.Pvalues of continental aftershock activity in China[J].Acta Seismologica Sinica,14(1):9—16(in Chinese).
Akaike H.1974.A new look at the statistical model identification[J].IEEE Trans Autom Control,19:716—723.
Akaike H.1977.On entropy maximization principle[A].In:Krishnaiah P R(ed).Applications of Statistics.pp.27—41.
Creamer F H,C Kisslinger.1993.The relation between temperature and the Omori decay parameter for aftershock se-quences near Japan[J].EOS74,43(Suppl):417.
Drakatos George.2000.Relative seismic quiescence before large aftershocks[J].Pure and Applied Geophysics,157:1407—1421.
Felzer K R and Brodsky E E.2006.Decay of aftershock density with distance indicates triggering by dynamic stress[J].Nature,441:735—738.
GallovicˇFranti ek,Johana Broke ová.2008.Probabilistic aftershock hazard assessmentⅠ:Numerical testing of meth-odological features[J].J Seismol,12:53—64.
Gardner J,Knopoff L.1974.“Is the sequence of earthquakes in Southern California,with aftershock removed,Possion-ian?”[J].Bull Seism Soc Am,64:1363—1367.
Gentili S,Bressan G.2008.The partitioning of radiated energy and the largest aftershock of seismic sequences occurredin the northeastern Italy and western Slovenia[J].J Seismol,12:343—354.
Guo Z,Ogata Y.1997.Statistical relations between the parameters of aftershocks in time,space and magnitude[J].JGeophys Res,102(B2):2857—2873.
Gutenberg B,Richter C F.1954.Seismicity of the Earth and Associated Phenomena[M].Princeton Univ Press,Prin-ceton N J.
Hainzl S,Marsan D.2008.Dependence of the Omori-Utsu lawparameters on main shock magnitude:Observations andmodeling[J].J Geophys Res,113:B10309.
Hainzl S,Ogata Y.2005.Detecting fluid signals in seismicity data through statistical earthquake modeling[J].J Geo-phys Res,110:B05S07.
Helmstetter A,Kagan Y Y,Jackson D D.2005.Importance of small earthquakes for stress transfers and earthquaketriggering[J].J Geophys Res,110:B05S08.
Helmstetter A,Sornette D.2003.Foreshocks explained by cascades of triggered seismicity[J].J Geophys Res,108(B10):2457.
Hirano R.1924.Investigation of aftershocks of the great Kanto earthquake at Kumagaya[J].Kishoshushi(Ser2),2:77—83(in Japanese).
Holliday James R,Turcotte Donald L,Rundle John B.2008.A review of earthquake statistics:fault and seismicity-based models,ETAS and BASS[J].Pure Appl Geophys,165:1003—1024.
Husen Stephan,Wiemer Stefan,Smith Robert B.2004.Remotely triggered seismicity in the Yellowstone National Parkregion by the2002MW7.9Denali Fault earthquake,Alaska[J].Bull Seism Soc Amv,94(6B):S317—S331.
Jeffreys H.1938.Aftershocks and periodicity in earthquakes[J].Gerlands Beitr Geophys,56:114—139.
Kellis-Borok VⅠ,Kossobokov VⅠ.1986.Time of increased probability for the great earthquakes of the world[J].Computational Seismology,19:45—58.
Latoussakis J,Drakatos G.1994.A quantitative study of some aftershock sequences in Greece[J].Pure and AppliedGeophysics,143(4):603—616.
Lei Xing-lin,Yu Guo-zheng,Ma Sheng-li,et al.2008.Earthquakes induced by water injection at～3km depth withinthe Rongchang gas field,Chongqing,China[J].J Geophys Res,113:B10310.
Lolli B,Gasperini P.2003.Aftershocks hazard in Italy PartⅠ:Estimation of time-magnitude distribution model param-eters and computation of probabilities of occurrence[J].J Seismol,7:235—257.
Mogi K.1962.On the time distribution of aftershocks accompanying the recent major earthquakes in and near Japan[J].Bull Earthquake Res Inst Univ Tokyo,40:175—185.
Nyffenegger P,Frohlich C.2000.Aftershock occurrence rate decay properties for intermediate and deep earthquake se-quences[J].Geophys Res Lett,27(8):1215—1218.
Ogata Y.1988.Statistical models for earthquake occurrences and residual analysis for point processes[J].J Am StatAssoc,83:9—27.
Ogata Y.1992.Detection of precursory relative quiescence before great earthquakes through a statistical model[J].JGeophys Res,97:19845—19871.
Ogata Y.1998.Space-time point-process models for earthquake occurrences[J].Ann Inst Stat Math,50:379—402.
Ogata Y.2001.Increased probability of large earthquakes near aftershock regions with relative quiescence[J].J Geo-phys Res,106(B5):8729—8744.
Ogata Y.2003.When and where the aftershock activity was depressed:Contrasting decay patterns of the proximate largeearthquakes in southern California[J].J Geophys Res,108(B6):2318.
Ogata Y.2005.Detection of anomalous seismicity as a stress change sensor[J].J Geophys Res,110:B05S06.
Ogata Y.2007.Seismicity and geodetic anomalies in a wide area preceding the Niigata-Ken-Chuetsu earthquake of23October2004,central Japan[J].J Geophys Res,112:B10301.
Ojala Ira O,Main Ian G,Ngwenya Bryne T.2004.Strain rate and temperature dependence of Omori law scaling con-stants of AE data:Implications for earthquake foreshock-aftershock sequences[J].Geophys Res Lett,31:L24617.
Omori F.1894a.On after-shocks[J].Rep Imp Earthq Inv Com,2:103—138(in Japanese).
Omori F.1894b.On after-shocks of earthquakes[J].J Coll Sci Imp Univ,7:111—200.
Ouillon G,Sornette D.2005.Magnitude-dependent Omori law:Theory and empirical study[J].J Geophys Res,110:B04306.
ztrk S,Cinar H,Bayrak Y,et al.2008.Properties of the aftershock sequences of the2003Bingol,MD=6.4,(Tur-key)earthquake[J].Pure appl Geophys,165:349—371.
Rabinowitz Nitzan,Steinberg David M.1998.Aftershock decay of three recent strong earthquakes in the Levant[J].Bull Seism Soc Am,88(6):1580—1587.
Shcherbakov Robert,Turcotte Donald L.2004a.A modified form of Bath s Law[J].Bull Seism Soc Am,94:1968—1975.
Shcherbakov R,Turcotte D L,Rundle J B.2004b.A generalized Omori s law for earthquake aftershock decay[J].Geophys Res Lett31:L11613,5pp.
Turcotte D L,Holliday J R,Rundle J B.2007.BASS,an alternative to ETAS[J].J Geophys Res,34:L12303.
Utsu T.1957.Magnitudes of earthquakes and occurrence of their aftershocks[J].ZiSin(Ser),2(10):35—45(inJapanese).
Utsu T.1961.A statistical study on the occurrence of aftershocks[J].Geophys Mag,30:521—605.
Ustu T.1969.Aftershocks and earthquake statistics(Ⅰ):Some parameters which characterize an aftershock sequenceand their interaction[J].J Faculty Sci,Hokkaido Univ,(SerⅦ)3:129—195.
Utsu T,Ogata Y,Matsuura R S.1995.The centenary of the Omori formula for a decay lawof aftershock activity[J].J Phys Earth,43(1):1—33.
蒋海昆,傅征祥,刘杰,等.2007a.中国大陆地震序列研究[M].北京:地震出版社.1—2.JIANG Hai-kun,FUZheng-xiang,LIUJie,et al.2007a.Research of earthquake sequences in China[M].Seismologi-cal Press,Beijing.1—2.
蒋海昆,郑建常,吴琼,等.2007b.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.JIANG Hai-kun,ZHENG Jian-chang,WU Qiong,et al.2007b.Earlier statistical features of ETAS model parametersand their seismological meanings[J].Chinese J Geophys,50(6):1778—1786(in Chinese).
刘正荣,钱兆霞,王维清,等.1979.前震的一个标志:地震频度的衰减[J].地震研究,2(4):1—9.LIU Zheng-rong,QIAN Zhao-xia,WANG Wei-qing,et al.1979.An indication of the fore-shock:The attenuation tothe earthquake frequency[J].Journal of Seismological Research,2(4):1—9(in Chinese).
刘正荣.1984.根据地震频度衰减预报地震的工作细则[J].地震,1:32—37.LIU Zheng-rong.1984.A code of practice for earthquake prediction using frequency attenuation of earthquakes[J].Earthquake,1:32—37(in Chinese).
刘正荣,孔绍麟.1986.地震频度衰减与地震预报[J].地震研究,9(1):6—8.LIU Zheng-rong,KONG Shao-lin.1986.Earthquake frequency attenuation and earthquake prediction[J].Journal ofSeismological Research,9(1):6—8(in Chinese).
王碧泉,王春珍.1983.余震序列的时空特征[J].地震学报,5(4):383—396.WANG Bi-quan,WANG Chun-zhen.1983.Temporal and spatial features of aftershock sequences[J].Acta Seis-mologica Sinica,5(4):383—396(in Chinese).
许绍燮主编.1990.地震学分析预报方法程式指南[Z].北京:地震出版社.72—77.XU Shao-xie(chief editor).1990.Guide of Seismological Analysis and Prediction Method[M].Seismological Press,Beijing.72—77.
赵志新,尾池和夫,松村一男,等.1992.中国大陆性地震的余震活动的p值[J].地震学报,14(1):9—16.ZHAO Zhi-xin,Oike Kazuo,Matsumura Kazuo,et al.1992.Pvalues of continental aftershock activity in China[J].Acta Seismologica Sinica,14(1):9—16(in Chinese).
Akaike H.1974.A new look at the statistical model identification[J].IEEE Trans Autom Control,19:716—723.
Akaike H.1977.On entropy maximization principle[A].In:Krishnaiah P R(ed).Applications of Statistics.pp.27—41.
Creamer F H,C Kisslinger.1993.The relation between temperature and the Omori decay parameter for aftershock se-quences near Japan[J].EOS74,43(Suppl):417.
Drakatos George.2000.Relative seismic quiescence before large aftershocks[J].Pure and Applied Geophysics,157:1407—1421.
Felzer K R and Brodsky E E.2006.Decay of aftershock density with distance indicates triggering by dynamic stress[J].Nature,441:735—738.
GallovicˇFranti ek,Johana Broke ová.2008.Probabilistic aftershock hazard assessmentⅠ:Numerical testing of meth-odological features[J].J Seismol,12:53—64.
Gardner J,Knopoff L.1974.“Is the sequence of earthquakes in Southern California,with aftershock removed,Possion-ian?”[J].Bull Seism Soc Am,64:1363—1367.
Gentili S,Bressan G.2008.The partitioning of radiated energy and the largest aftershock of seismic sequences occurredin the northeastern Italy and western Slovenia[J].J Seismol,12:343—354.
Guo Z,Ogata Y.1997.Statistical relations between the parameters of aftershocks in time,space and magnitude[J].JGeophys Res,102(B2):2857—2873.
Gutenberg B,Richter C F.1954.Seismicity of the Earth and Associated Phenomena[M].Princeton Univ Press,Prin-ceton N J.
Hainzl S,Marsan D.2008.Dependence of the Omori-Utsu lawparameters on main shock magnitude:Observations andmodeling[J].J Geophys Res,113:B10309.
Hainzl S,Ogata Y.2005.Detecting fluid signals in seismicity data through statistical earthquake modeling[J].J Geo-phys Res,110:B05S07.
Helmstetter A,Kagan Y Y,Jackson D D.2005.Importance of small earthquakes for stress transfers and earthquaketriggering[J].J Geophys Res,110:B05S08.
Helmstetter A,Sornette D.2003.Foreshocks explained by cascades of triggered seismicity[J].J Geophys Res,108(B10):2457.
Hirano R.1924.Investigation of aftershocks of the great Kanto earthquake at Kumagaya[J].Kishoshushi(Ser2),2:77—83(in Japanese).
Holliday James R,Turcotte Donald L,Rundle John B.2008.A review of earthquake statistics:fault and seismicity-based models,ETAS and BASS[J].Pure Appl Geophys,165:1003—1024.
Husen Stephan,Wiemer Stefan,Smith Robert B.2004.Remotely triggered seismicity in the Yellowstone National Parkregion by the2002MW7.9Denali Fault earthquake,Alaska[J].Bull Seism Soc Amv,94(6B):S317—S331.
Jeffreys H.1938.Aftershocks and periodicity in earthquakes[J].Gerlands Beitr Geophys,56:114—139.
Kellis-Borok VⅠ,Kossobokov VⅠ.1986.Time of increased probability for the great earthquakes of the world[J].Computational Seismology,19:45—58.
Latoussakis J,Drakatos G.1994.A quantitative study of some aftershock sequences in Greece[J].Pure and AppliedGeophysics,143(4):603—616.
Lei Xing-lin,Yu Guo-zheng,Ma Sheng-li,et al.2008.Earthquakes induced by water injection at～3km depth withinthe Rongchang gas field,Chongqing,China[J].J Geophys Res,113:B10310.
Lolli B,Gasperini P.2003.Aftershocks hazard in Italy PartⅠ:Estimation of time-magnitude distribution model param-eters and computation of probabilities of occurrence[J].J Seismol,7:235—257.
Mogi K.1962.On the time distribution of aftershocks accompanying the recent major earthquakes in and near Japan[J].Bull Earthquake Res Inst Univ Tokyo,40:175—185.
Nyffenegger P,Frohlich C.2000.Aftershock occurrence rate decay properties for intermediate and deep earthquake se-quences[J].Geophys Res Lett,27(8):1215—1218.
Ogata Y.1988.Statistical models for earthquake occurrences and residual analysis for point processes[J].J Am StatAssoc,83:9—27.
Ogata Y.1992.Detection of precursory relative quiescence before great earthquakes through a statistical model[J].JGeophys Res,97:19845—19871.
Ogata Y.1998.Space-time point-process models for earthquake occurrences[J].Ann Inst Stat Math,50:379—402.
Ogata Y.2001.Increased probability of large earthquakes near aftershock regions with relative quiescence[J].J Geo-phys Res,106(B5):8729—8744.
Ogata Y.2003.When and where the aftershock activity was depressed:Contrasting decay patterns of the proximate largeearthquakes in southern California[J].J Geophys Res,108(B6):2318.
Ogata Y.2005.Detection of anomalous seismicity as a stress change sensor[J].J Geophys Res,110:B05S06.
Ogata Y.2007.Seismicity and geodetic anomalies in a wide area preceding the Niigata-Ken-Chuetsu earthquake of23October2004,central Japan[J].J Geophys Res,112:B10301.
Ojala Ira O,Main Ian G,Ngwenya Bryne T.2004.Strain rate and temperature dependence of Omori law scaling con-stants of AE data:Implications for earthquake foreshock-aftershock sequences[J].Geophys Res Lett,31:L24617.
Omori F.1894a.On after-shocks[J].Rep Imp Earthq Inv Com,2:103—138(in Japanese).
Omori F.1894b.On after-shocks of earthquakes[J].J Coll Sci Imp Univ,7:111—200.
Ouillon G,Sornette D.2005.Magnitude-dependent Omori law:Theory and empirical study[J].J Geophys Res,110:B04306.
ztrk S,Cinar H,Bayrak Y,et al.2008.Properties of the aftershock sequences of the2003Bingol,MD=6.4,(Tur-key)earthquake[J].Pure appl Geophys,165:349—371.
Rabinowitz Nitzan,Steinberg David M.1998.Aftershock decay of three recent strong earthquakes in the Levant[J].Bull Seism Soc Am,88(6):1580—1587.
Shcherbakov Robert,Turcotte Donald L.2004a.A modified form of Bath s Law[J].Bull Seism Soc Am,94:1968—1975.
Shcherbakov R,Turcotte D L,Rundle J B.2004b.A generalized Omori s law for earthquake aftershock decay[J].Geophys Res Lett31:L11613,5pp.
Turcotte D L,Holliday J R,Rundle J B.2007.BASS,an alternative to ETAS[J].J Geophys Res,34:L12303.
Utsu T.1957.Magnitudes of earthquakes and occurrence of their aftershocks[J].ZiSin(Ser),2(10):35—45(inJapanese).
Utsu T.1961.A statistical study on the occurrence of aftershocks[J].Geophys Mag,30:521—605.
Ustu T.1969.Aftershocks and earthquake statistics(Ⅰ):Some parameters which characterize an aftershock sequenceand their interaction[J].J Faculty Sci,Hokkaido Univ,(SerⅦ)3:129—195.
Utsu T,Ogata Y,Matsuura R S.1995.The centenary of the Omori formula for a decay lawof aftershock activity[J].J Phys Earth,43(1):1—33.
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