Aftershock Relaxation for Japanese and Sumatra Earthquakes：日本和苏门答腊的地震余震松弛.ppt

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1、AftershockRelaxationforJapaneseandSumatraEarthquakesKazuZ.Nanjo1,B.Enescu2,R.Shcherbakov3,D.L.Turcotte3,T.Iwata1,&Y.Ogata11,ISM,Tokyo,Japan2,KyotoUniv.,Kyoto,Japan3,UCDavis,CA,USAObjective:AnalyzethedecayoftheaftershockactivityforJapaneseandSumatraearthquakes,usingcatalogsmaintaine

2、dbyJapanMeteorologicalAgencyandAdvancedNationalSeismicSystem.Approach:GeneralizedOmori’slawproposedbyShcherbakovetal.(2004,2005).TheGutenberg-Richter(GR)law(GutenbergandRichter,1954)N:#ofearthq.withmag.≥mAandb:constantsThemodifiedBath’slaw(ShcherbakovandTurcotte,2004)Δm*=mms-m*m*:m

3、ag.oftheinferredlargestaftershock(m*=A/b)ormag.attheinterceptbetweenanextrapolationoftheapplicableGRlawandN=1mms:mainshockmag.TheGRlawcanberewrittenforaftershocksasThemodifiedOmori’slaw(Utsu,1962)dN/dt:rateofoccurrenceofaftershockswithmag.≥mt:timesincethemainshockcandτ:characterist

4、ictimesp:exponentRequirementamongtheparametersAssume:pisaconstantindependentofmandmms(Utsu,1962)b,mms,andΔm*areknownparametersThreepossiblehypotheses:cisaconstantc=c0andτisdependentonmτisaconstantτ=τ0andcisdependentonmcandτaredependentonm(Shcherbakovetal.,2004,2005)Hypoth.I,c=c0Hyp

5、oth.II,τ=τ0Hypoth.III,candτaredependentofmc(m*):thecharacteristictime;β:aconstantHypoth.IIIHypoth.Iifc(m*)=c0andβ=bHypoth.IIifc(m*)=τ0(p-1)andβ=bpThelistofmainshocksSpatialdistributionandGRlawforKobeMag.≥2t(days)<1000(Δm*=1.1m*=A/b=6.2mms=7.3t(days)<1000A=4.85,b=0.78L(km)=0.02X10

6、0.5m_ms[Kagan,2002]AftershockrelaxationforKobeandsmallaftershocksintheearlyperiods0.1≤t<1.00.01≤t<0.1t(days)<1000HowtofindthebesthypothesisTofindtheoptimalfittingofthepredictiontothedataforindividualhypothesesPointprocessmodelingwithmax.likelihood(e.g.,Ogata,1983).AIC(Akaike,1974)t

7、ofindthebesthypothesis.AIC=-2(max.log-likelihood)+2(#ofparameters)#ofparametersHypoth.I:two(c0andp)Hypoth.II:two(τ0andp)Hypoth.III:three(c(m*),β,andp)TestofthegeneralizedOmori’slawforKobeHypoth.I,c=c0Hypoth.II,τ=τ0Hypoth.III,candτaredependentonmAIC=-3376.95AIC=-3405.00AIC=-3403.00A

8、ftershocksofSumatraearthq.