统计地震学的基本问题
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摘要
"统计地震学"决不仅仅是统计学在地震研究中的简单应用。对这一点的忽视常常导致对"统计地震学"意义的低估。经过几十年的发展,现在是系统讨论"统计地震学"基本问题的时候了。这种讨论不仅对"统计地震学"自身的发展,而且对与地震预测预报相关的交叉学科的研究都是有益的。本文的注意力集中于"狭义的""统计地震学",即以地震预测预报为目标的、针对地震现象(主要是地震活动性)的统计研究。我们把"统计地震学"基本问题归纳为7个方面:①地震活动的统计规律及其独立性问题;②长期地震预测的统计方法的有效性问题;③中期时间尺度地震活动的"异常"问题;④可能的地震前兆和地震预测预报方法的统计显著性问题;⑤地震的物理可预报性问题;⑥地震预测预报的地震活动性方法的能力和限度问题;⑦地震活动的物理模型的"真实性"问题。本文的目的不是对"统计地震学"提出一个"希尔伯特问题"的框架,而是试图引起更多的讨论,特别是引起人们对超越争论、超越算法的基本问题的关注。
It has been more and more clear that statistical seismology as an independent subject is much more complicated than the simple application of statistical tools to seismological problems. Misunderstanding of this point often leads to the underestimation of the significance of statistical seismology. With the development of models and concepts over the past decades, especially in recent years, it is time to outline the framework of statistical seismology both for the interdisciplinary communications and for the further development of this research field. For this purpose we try to discuss the fundamental problems of statistical seismology. Our attention is focused on "special statistical seismology", that is, statistical studies of earthquake phenomenology, especially seismicity, for earthquake forecast/prediction. We try to discuss the fundamental problems of statistical seismology in the following seven aspects: (1) independence of statistical distributions of seismicity parameters; (2) effectiveness of probabilistic forecast of long-term seismic hazard; (3) "normal" versus "abnormal" seismicity at intermediate-term time scale; (4) statistical significance of candidate earthquake precursors and schemes for earthquake forecast; (5) physical predictability of earthquakes and its observational evidences; (6) capability and limit of analysis of seismicity in earthquake forecast; and (7) validity of physical models in understanding the characteristics of seismicity. The aim is not to propose a set of Hilbert problems——Rather, the aim is to invoke further discussions on the more fundamental problems in statistical seismology beyond the controversies and the technique issues.
It has been more and more clear that statistical seismology as an independent subject is much more complicated than the simple application of statistical tools to seismological problems. Misunderstanding of this point often leads to the underestimation of the significance of statistical seismology. With the development of models and concepts over the past decades, especially in recent years, it is time to outline the framework of statistical seismology both for the interdisciplinary communications and for the further development of this research field. For this purpose we try to discuss the fundamental problems of statistical seismology. Our attention is focused on "special statistical seismology", that is, statistical studies of earthquake phenomenology, especially seismicity, for earthquake forecast/prediction. We try to discuss the fundamental problems of statistical seismology in the following seven aspects: (1) independence of statistical distributions of seismicity parameters; (2) effectiveness of probabilistic forecast of long-term seismic hazard; (3) "normal" versus "abnormal" seismicity at intermediate-term time scale; (4) statistical significance of candidate earthquake precursors and schemes for earthquake forecast; (5) physical predictability of earthquakes and its observational evidences; (6) capability and limit of analysis of seismicity in earthquake forecast; and (7) validity of physical models in understanding the characteristics of seismicity. The aim is not to propose a set of Hilbert problems——Rather, the aim is to invoke further discussions on the more fundamental problems in statistical seismology beyond the controversies and the technique issues.
引文
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Albeverio S.,Jentsch V.and Kantz H.(eds.),2005,Extreme Events in Nature and Society.Amsterdam:Springer.
Ben-Zion Y.,Dahmen K.,Lyakhovsky V.,Ertas D.and Agnon A.,1999,Self-driven mode switchingof earthquake activityonafaultsystem.EPSL,172,11~21.
Ben-Zion Y.,Eneva M.and Liu Y.-F.,2003,Large earthquake cycles and intermittent criticality on heterogeneous faults due to evolving stress and seismicity.J.Geophys.Res.,108(B6),doi:10.1029/2002JB002121.
Bowman D.D.and King G.C.P.,2001,Accelerating seismicity and stress accumulation before large earthquakes.Geophys.Res.Lett.,28,4039~4042.
Campbell K.W.,1982,Bayesian analysis of extreme earthquake occurrences.Part I.Probabilistic hazard model,Bull.Seism.Soc.Amer.,72,1689~1705.
Cornell C.A.,1968,Engineering seismic risk analysis.Bull.Seism.Soc.Amer.,58,1583~1606.
Dietrich J.,1994,Aconstitutive lawfor rate of earthquake production andits applicationto earthquake clustering,J.Geophys.Res.,99,2601~2618.
Evans R.(eds.),1997,Special Section-Assessment of Schemes for Earthquake Prediction.Geophys.J.Int.,131,413~533.
Field E.D.(eds.),2007,Special Issue-Regional Earthquake Likelihood Models.Seism.Res.Lett.,78,1~140.
Gardner J.K.and Knopoff L.,1974,Is the sequence of earthquakes in Southern California,with aftershocks removed,Poissonian?Bull.Seism.Soc.Amer.,64,1363~1367.
Geller R.J.(eds.),1996,Special Section-Debate on Evaluation of the VAN Method.Geophys.Res.Lett.,23,1291~1452.
Geller R.J.,Jackson D.D.,Kagan Y.Y.and Mulargia F.,1997,Earthquakes cannot be predicted.Science,275,1616~1617.
Harris R.A.(eds.),1998,Special Section-Stress Triggers,Stress Shadows,andImplicationfor Seismic Hazard.J.Geophys.Res.,103,24347~24572.
Harris R.A.,2003,Stress triggers,stress shadows,and seismic hazard.In:Lee,W.H.K.,Kanamori,H.,Jennings,P.C.andKisslinger,C.(eds.),International Handbook of Earthquake and Engineering Seismology,Amsterdam:Academic Press,1217~1232.
Helmstetter A.and Sornette D.,2003,Bath s lawderived fromthe Gutenberg-Richter lawand fromaftershock properties.Geophys.Res.Lett.,30,2069,doi:10.1029/2003GL018186.
Huang Q.,2006,Search for reliable precursors:A case study of the seismic quiescence of the2000western Tottori prefectureearthquake.J.Geophys.Res.,111(4),B04301,doi:10.1029/2005JB003982.
Jackson D.D.,2004,Earthquake prediction and forecasting.In:IUGG(eds.),State of the Planet:Frontiers and Challenges,Washington DC:AGU,225~348.
Jiang C.S.and Wu Z.L.,2006,Benioff strainrelease before earthquakesin China:Accelerating or not?Pure appl.Geophys.,163,1965~1976.
JohnsonS.M.and Sheridan J.M.,1997,Distinguishing between random and nonrandom patterns in the energy release of greatearthquakes.J.Geophys.Res.,102,2853~2855.
Keilis-Borok V.I.,Knopoff L.and Rotvain I.M.,1980,Bursts of aftershocks,long-termprecursors of strong earthquakes.Nature,283,259~263.
Keilis-Borok V.I.and Shebalin P.N.(eds.),1999,Special Issue-Dynamics of Lithosphere and Earthquake Prediction.Phys.EarthPlanet.Interi.,111,179~327.
Keilis-Borok V.I.,1990,The lithosphere of the Earth as a nonlinear system with implications for earthquake prediction.Rev.Geophys.,28,19~34.
Keilis-Borok V.,Shebalin P.,Gabrielov A.and Turcotte D.,2004,Reverse tracing of short-termearthquake precursors.Phys.EarthPlanet.Interi.,145,75~85.
Knopoff L.,2000,The magnitude distribution of declustered earthquakesin Southern California.Proc.Nat.Acad.Sci.U.S.A.,97,11880~11884.
Kossobokov V.G.,2006,Testing earthquake prediction methods:《The West Pacific short-termforecast of earthquakes with magnitudeMwHRV≥5.8》.Tectonophysics,413,25~31.
Main I.G.and Al-Kindy F.H.,2002,Entropy,energy,and proximityto criticalityin global earthquake populations.Geophys.Res.Lett.,29(7),doi:10.1029/2001GL014078.
MainI.G.,1995,Earthquakes as critical phenomena:implicationsfor probabilistic seismic hazard analysis.Bull.Seism.Soc.Amer.,85,1299~1308.
Main I.,1996,Statitical physics,seismogenesis,and seismic hazard.Rev.Geophys.,34,433~462.
Michael A.J.,1997,Testing prediction methods:earthquake clustering versus a Poisson model.Geophys.Res.Lett.,24,1891~1894.
Mulargia F.,1997,Retrospective validation of the time association of precursors.Geophys.J.Int.,131,500~504.
Mulargia F.,2001,Retrospective selection bias(or the benefit of hindsight).Geophys.J.Int.,146,489~496.
Ogata Y.,1989,Statistical models for standard seismicity and detection of anomalies by residual analysis for point processes.Tectonophysics,83,9~27.
Ogata Y.,2004,Space-time model for regional seismicity and detection of crustal stress changes.J.Geophys.Res.,109,B03308,doi:10.1029/2003JB002621.
Panza G.F.,Romaneli F.,Vaccari F.,Decanini L.and Mollaioli F.,2004,Seismic ground motion modeling and damage earthquakescenarios:Apossible bridge betweenseismologists andseismic engineers.In:Chen,Y.T.,Panza,G.F.and Wu,Z.L.(eds.),Earthquake:Hazard,Risk,and Strong Ground Motion.Beijing:Seismological Press,323~349.
Pepke S.L.,Carlson J.M.and ShawB.E.,1994,Prediction of large events on a dynamical model of a fault.J.Geophys.Res.,99,6769~6788.
Rhoades D.A.and Evison F.F.,2004,Long-range earthquake forecasting with every earthquake a precursor accordingto scale.Pureappl.Geophys.,161,47~72.
Rhoades D.A.and Evison F.F.,2005,Test of the EEPAS forecasting model on the Japan earthquake catalogue.Pure appl.Geophys.,162,1271~1290.
Rundle J.B.,Gross S.,Klein W.,Ferguson C.and Turcotte D.L.,1997,The statistical mechanics of earthquakes.Tectonophysics,277,147~164.
Rundle J.B.,Turcotte D.L.,Shcherbakov R.,Klein W.and Sammis C.,2003,Statistical physics approach to understanding themultiscale dynamics of earthquake fault systems.Rev.Geophys.,41(4),doi:10.1029/2003RG000135.
Saichev A.and Sornette D.,2007,Theory of earthquake recurrence times.J.Geophys.Res.,112,B04313,doi:10.1029/2006JB004536.
Seher T.and Main I.G.,2004,Astatistical evaluation of a“stress-forecast”earthquake.Geophys.J.Int.,157,187~193.
Shebalin P.,Zaliapin I.and Keilis-Borok V.,2000,Premonitory raise of the earthquakes correlation range:Lesser Antilles.Phys.Earth Planet.Interi.,122,241~249.
Sornette A.and Sornette D.,1990,Earthquake rupture as a critical point:consequences for telluric precursors.Tectonophysics,179,327~334.
Stark P.B.,1997,Earthquake prediction:the null hypothesis.Geophys.J.Int.,131,495~499.
Turcotte D.L.,1992,Fractals and Chaos in Geology and Geophysics.Cambridge:Cambridge University Press,35~51
Turcotte D.L.,HollidayJ.R.and Rundle J.B.,2007,BASS,analternativeto ETAS.Geophys.Res.Lett.,34,L12303,doi:10.1029/2007GL029696.
Vere-Jones D.and Ogata Y.,2003,Statistical principlesfor seismologists.In:Lee,W.H.K.,Kanamori,H.,Jennings,P.C.andKisslinger,C.(eds.),International Handbook of Earthquake and Engineering Seismology,Amsterdam:Academic Press,1573~1586.
Vere-Jones D.,2007,Foundations of statistical seismology.In:Cocco,M.,Console,R.and Wiemer,S.(eds.),StatisticalSeismology:Physical and Stochastic Modelling of Earthquake Occurrence and Forecasting-Proceedings/Abstracts of the28th Workshopof the International School of Geophysics,May31-June6,2007,Erice,Sicily,Italy,23~30.
Wyss M.and Dmowska R.(eds.),1997,Special Issue-Earthquake Prediction,State-of-the-art.Pure appl.Geophys.,149,1~264.
Wu Z.L.,Wan Y.G.and Zhou G.W.,2004,Focal mechanismdependence of a fewseismic phenomena anditsimplicationsfor thephysics of earthquakes.Pure appl.Geophys.,161,1969~1978.
Wu Z.L.,Liu J.,Zhu C.Z.,Jiang C.S.and Huang F.Q.,2007,Annual consultation on the likelihood of earthquakes incontinental China:Its scientific and practical merits.Earthquake Researchin China,21,365~371.
Xu H.J.and Knopoff L.,1994,Periodicity and chaosin a one-dimensional dynamical model of earthquakes.Phys.Rev.,E50,3577~3581.
Zhuang J.,Ogata Y.and Vere-Jones D.,2002,Stochastic declusteringof space-time earthquake occurrences.J.Amer.Stat.Assoc.,97,369~380.
Zoeller G.,Hainzl S.and Kurths J.,2001,Observation of growing correlationlength as anindicator for critical point behavior prior tolarge earthquakes.J.Geophys.Res.,106,2167~2175.
Albeverio S.,Jentsch V.and Kantz H.(eds.),2005,Extreme Events in Nature and Society.Amsterdam:Springer.
Ben-Zion Y.,Dahmen K.,Lyakhovsky V.,Ertas D.and Agnon A.,1999,Self-driven mode switchingof earthquake activityonafaultsystem.EPSL,172,11~21.
Ben-Zion Y.,Eneva M.and Liu Y.-F.,2003,Large earthquake cycles and intermittent criticality on heterogeneous faults due to evolving stress and seismicity.J.Geophys.Res.,108(B6),doi:10.1029/2002JB002121.
Bowman D.D.and King G.C.P.,2001,Accelerating seismicity and stress accumulation before large earthquakes.Geophys.Res.Lett.,28,4039~4042.
Campbell K.W.,1982,Bayesian analysis of extreme earthquake occurrences.Part I.Probabilistic hazard model,Bull.Seism.Soc.Amer.,72,1689~1705.
Cornell C.A.,1968,Engineering seismic risk analysis.Bull.Seism.Soc.Amer.,58,1583~1606.
Dietrich J.,1994,Aconstitutive lawfor rate of earthquake production andits applicationto earthquake clustering,J.Geophys.Res.,99,2601~2618.
Evans R.(eds.),1997,Special Section-Assessment of Schemes for Earthquake Prediction.Geophys.J.Int.,131,413~533.
Field E.D.(eds.),2007,Special Issue-Regional Earthquake Likelihood Models.Seism.Res.Lett.,78,1~140.
Gardner J.K.and Knopoff L.,1974,Is the sequence of earthquakes in Southern California,with aftershocks removed,Poissonian?Bull.Seism.Soc.Amer.,64,1363~1367.
Geller R.J.(eds.),1996,Special Section-Debate on Evaluation of the VAN Method.Geophys.Res.Lett.,23,1291~1452.
Geller R.J.,Jackson D.D.,Kagan Y.Y.and Mulargia F.,1997,Earthquakes cannot be predicted.Science,275,1616~1617.
Harris R.A.(eds.),1998,Special Section-Stress Triggers,Stress Shadows,andImplicationfor Seismic Hazard.J.Geophys.Res.,103,24347~24572.
Harris R.A.,2003,Stress triggers,stress shadows,and seismic hazard.In:Lee,W.H.K.,Kanamori,H.,Jennings,P.C.andKisslinger,C.(eds.),International Handbook of Earthquake and Engineering Seismology,Amsterdam:Academic Press,1217~1232.
Helmstetter A.and Sornette D.,2003,Bath s lawderived fromthe Gutenberg-Richter lawand fromaftershock properties.Geophys.Res.Lett.,30,2069,doi:10.1029/2003GL018186.
Huang Q.,2006,Search for reliable precursors:A case study of the seismic quiescence of the2000western Tottori prefectureearthquake.J.Geophys.Res.,111(4),B04301,doi:10.1029/2005JB003982.
Jackson D.D.,2004,Earthquake prediction and forecasting.In:IUGG(eds.),State of the Planet:Frontiers and Challenges,Washington DC:AGU,225~348.
Jiang C.S.and Wu Z.L.,2006,Benioff strainrelease before earthquakesin China:Accelerating or not?Pure appl.Geophys.,163,1965~1976.
JohnsonS.M.and Sheridan J.M.,1997,Distinguishing between random and nonrandom patterns in the energy release of greatearthquakes.J.Geophys.Res.,102,2853~2855.
Keilis-Borok V.I.,Knopoff L.and Rotvain I.M.,1980,Bursts of aftershocks,long-termprecursors of strong earthquakes.Nature,283,259~263.
Keilis-Borok V.I.and Shebalin P.N.(eds.),1999,Special Issue-Dynamics of Lithosphere and Earthquake Prediction.Phys.EarthPlanet.Interi.,111,179~327.
Keilis-Borok V.I.,1990,The lithosphere of the Earth as a nonlinear system with implications for earthquake prediction.Rev.Geophys.,28,19~34.
Keilis-Borok V.,Shebalin P.,Gabrielov A.and Turcotte D.,2004,Reverse tracing of short-termearthquake precursors.Phys.EarthPlanet.Interi.,145,75~85.
Knopoff L.,2000,The magnitude distribution of declustered earthquakesin Southern California.Proc.Nat.Acad.Sci.U.S.A.,97,11880~11884.
Kossobokov V.G.,2006,Testing earthquake prediction methods:《The West Pacific short-termforecast of earthquakes with magnitudeMwHRV≥5.8》.Tectonophysics,413,25~31.
Main I.G.and Al-Kindy F.H.,2002,Entropy,energy,and proximityto criticalityin global earthquake populations.Geophys.Res.Lett.,29(7),doi:10.1029/2001GL014078.
MainI.G.,1995,Earthquakes as critical phenomena:implicationsfor probabilistic seismic hazard analysis.Bull.Seism.Soc.Amer.,85,1299~1308.
Main I.,1996,Statitical physics,seismogenesis,and seismic hazard.Rev.Geophys.,34,433~462.
Michael A.J.,1997,Testing prediction methods:earthquake clustering versus a Poisson model.Geophys.Res.Lett.,24,1891~1894.
Mulargia F.,1997,Retrospective validation of the time association of precursors.Geophys.J.Int.,131,500~504.
Mulargia F.,2001,Retrospective selection bias(or the benefit of hindsight).Geophys.J.Int.,146,489~496.
Ogata Y.,1989,Statistical models for standard seismicity and detection of anomalies by residual analysis for point processes.Tectonophysics,83,9~27.
Ogata Y.,2004,Space-time model for regional seismicity and detection of crustal stress changes.J.Geophys.Res.,109,B03308,doi:10.1029/2003JB002621.
Panza G.F.,Romaneli F.,Vaccari F.,Decanini L.and Mollaioli F.,2004,Seismic ground motion modeling and damage earthquakescenarios:Apossible bridge betweenseismologists andseismic engineers.In:Chen,Y.T.,Panza,G.F.and Wu,Z.L.(eds.),Earthquake:Hazard,Risk,and Strong Ground Motion.Beijing:Seismological Press,323~349.
Pepke S.L.,Carlson J.M.and ShawB.E.,1994,Prediction of large events on a dynamical model of a fault.J.Geophys.Res.,99,6769~6788.
Rhoades D.A.and Evison F.F.,2004,Long-range earthquake forecasting with every earthquake a precursor accordingto scale.Pureappl.Geophys.,161,47~72.
Rhoades D.A.and Evison F.F.,2005,Test of the EEPAS forecasting model on the Japan earthquake catalogue.Pure appl.Geophys.,162,1271~1290.
Rundle J.B.,Gross S.,Klein W.,Ferguson C.and Turcotte D.L.,1997,The statistical mechanics of earthquakes.Tectonophysics,277,147~164.
Rundle J.B.,Turcotte D.L.,Shcherbakov R.,Klein W.and Sammis C.,2003,Statistical physics approach to understanding themultiscale dynamics of earthquake fault systems.Rev.Geophys.,41(4),doi:10.1029/2003RG000135.
Saichev A.and Sornette D.,2007,Theory of earthquake recurrence times.J.Geophys.Res.,112,B04313,doi:10.1029/2006JB004536.
Seher T.and Main I.G.,2004,Astatistical evaluation of a“stress-forecast”earthquake.Geophys.J.Int.,157,187~193.
Shebalin P.,Zaliapin I.and Keilis-Borok V.,2000,Premonitory raise of the earthquakes correlation range:Lesser Antilles.Phys.Earth Planet.Interi.,122,241~249.
Sornette A.and Sornette D.,1990,Earthquake rupture as a critical point:consequences for telluric precursors.Tectonophysics,179,327~334.
Stark P.B.,1997,Earthquake prediction:the null hypothesis.Geophys.J.Int.,131,495~499.
Turcotte D.L.,1992,Fractals and Chaos in Geology and Geophysics.Cambridge:Cambridge University Press,35~51
Turcotte D.L.,HollidayJ.R.and Rundle J.B.,2007,BASS,analternativeto ETAS.Geophys.Res.Lett.,34,L12303,doi:10.1029/2007GL029696.
Vere-Jones D.and Ogata Y.,2003,Statistical principlesfor seismologists.In:Lee,W.H.K.,Kanamori,H.,Jennings,P.C.andKisslinger,C.(eds.),International Handbook of Earthquake and Engineering Seismology,Amsterdam:Academic Press,1573~1586.
Vere-Jones D.,2007,Foundations of statistical seismology.In:Cocco,M.,Console,R.and Wiemer,S.(eds.),StatisticalSeismology:Physical and Stochastic Modelling of Earthquake Occurrence and Forecasting-Proceedings/Abstracts of the28th Workshopof the International School of Geophysics,May31-June6,2007,Erice,Sicily,Italy,23~30.
Wyss M.and Dmowska R.(eds.),1997,Special Issue-Earthquake Prediction,State-of-the-art.Pure appl.Geophys.,149,1~264.
Wu Z.L.,Wan Y.G.and Zhou G.W.,2004,Focal mechanismdependence of a fewseismic phenomena anditsimplicationsfor thephysics of earthquakes.Pure appl.Geophys.,161,1969~1978.
Wu Z.L.,Liu J.,Zhu C.Z.,Jiang C.S.and Huang F.Q.,2007,Annual consultation on the likelihood of earthquakes incontinental China:Its scientific and practical merits.Earthquake Researchin China,21,365~371.
Xu H.J.and Knopoff L.,1994,Periodicity and chaosin a one-dimensional dynamical model of earthquakes.Phys.Rev.,E50,3577~3581.
Zhuang J.,Ogata Y.and Vere-Jones D.,2002,Stochastic declusteringof space-time earthquake occurrences.J.Amer.Stat.Assoc.,97,369~380.
Zoeller G.,Hainzl S.and Kurths J.,2001,Observation of growing correlationlength as anindicator for critical point behavior prior tolarge earthquakes.J.Geophys.Res.,106,2167~2175.
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