Stiffness effect for sites in CENA, starting with fpeak · 2016-11-11 · Hassani and Atkinson...
Transcript of Stiffness effect for sites in CENA, starting with fpeak · 2016-11-11 · Hassani and Atkinson...
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Stiffness effect for sites in CENA, starting with fpeak
BehzadHassaniandGailAtkinson
November,2016
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fpeak from Microtremor survey vs. Earthquake H/V
MicrotremorsurveyinsouthernOntariofor8seismicstaCons.
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Hassani and Atkinson (2016) presented an fpeak -based site-amplification model • nosCffnessscalingterminour2016model• HerewelookatthesCffnesseffectontheamplificaConofsitesinCENA.
• Inthefirststep,wefirstremovethefpeak-basedamplificaConmodelfromtheobservedata,andthenlookattheresidualsitetermswithrespecttoVS30.
• Inordertodothat,wefirstcalculatetheresidualswithrespecttoSOSNGMPEmodel(Atkinsonetal.,2015)usingthesite-effectsmodeldevelopedwrthard-rocksitecondiCons,andthendefinethesitetermswithrespecttohard-rocksitecondiCon.
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Finding Residual Site terms
WealsoincludesiteswithVS30>1500m/sandnoobservedfpeakvalues.Forthesesites,weassumethatthe
fpeakvalueishigherthan20Hz.
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VS30ScalingtermWeuseParkeretal.(2016)updatedVS30valuesforoursites.
Glaciated
ThesearetheapparenttrendsifweneglectuncertaintyinVS30esCmates(VS30variance)
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VS30Scalingterm,applyingMonteCarlosimulaCon
• InordertoderivetherightVS30-scalingmodel,it’scorrespondingstandarddeviaConandalsothestandarderrorofthecoefficients,weneedtosomehowtakeaccountforthedifferentvarianceinourVS30esCmates(e.g.differentproxieshavedifferentesCmatestandarddeviaCon).
• Moreover,eachoftheaverageresidualsitetermscomeswithastandarddeviaContoo(e.g.weaveragedresidualsitetermsateachstaConwiththreeormorerecords).WealsoneedtotakeaccountforthisvariabilityinourVS30-Scalingmodel.
• ThesoluConthatwepresenthereistouseMonteCarlosimulaContopopulateourdata.Foreachofthedatapoints,wehaveaVs30esCmatewithanassignedstandarddeviaCon(e.g.logofVs30),andalsowehaveastandarddeviaConforeachoftheaverageresidualsiteterms.Werandomlygenerate50pointsforeachofourdatapointsassuminganormaldistribuConforlogofVS30andaverageresidualsiteterm(SSOSN,j).
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VS30Scalingterm,applyingMonteCarlosimulaConGlaciated
ThistrendaccommodatestheuncertaintyforVS30esCmatesandalsoforaverageresidualsiteterms(normaldistribuCon)
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VS30Scalingterm
Non-Glaciated
ApparenttrendneglecCnguncertaintyinVS30esCmates(VS30variance)
WeuseParkeretal.(2016)updatedVS30valuesforoursites.
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VS30Scalingterm,applyingMonteCarlosimulaConNon-Glaciated
ApparenttrendconsideringuncertaintyinVS30esCmatesandalsoinaverageresidualsiteterms
NoobviousVS30-dependenttrendduetolargeVS30uncertainCes!
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A consequence of large variance in VS30 estimates
ConsideringthevariabilityofVS30esCmatescansignificantlychangetheaverageVS30-scalingmodelfornonaciatedsites.TheproblemisthatforsomeofthesitesthevarianceontheVS30esCmatesareveryhigh(e.g.0.85inlnunits),whichcanaffecttheaverageVS30scalingmodel.
Here,weconstrainournon-glaciatedmodelbasedonthemodelthatwedevelopedforglaciatedsitesandwescaleittomatchthefewnon-glaciateddatapointswithsmallVS30standarddeviaCon(<=0.3).WeassumethatthescalingtermforsiteswithVS30>1500m/sisthesameastheglaciatedmodel,andwefixthescalingtermforsiteswithVS30<250m/susingthenon-glaciateddatapointswithVS30~300m/s.
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VS30Scalingterm,applyingMonteCarlosimulaCon(0.3sigma) Non-Glaciated
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VS30 Scaling term, non-glaciated
Non-GlaciatedscalingmodelderivedbasedontheglaciatedmodelandalsodatapointswithlowVS30variance.
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C4,VS30Scalingslope,Glaciatedandnon-glaciated
ToderivetherightstandarderrorfortheC4term,wemulCplytheesCmatedstandarderrorbasedonthepopulateddatabasebyafactorof7(squarerootof50(numberoftherandomdatapointsgenerated)),tocorrectitfortheactualnumberofobservaConswehave.
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VS30ScalingtermBasedontheobservedVS30-dependenttrends,wederivetwoseparatemodelsforglaciatedandnon-glaciatedsites.
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Fpeak and VS30 based amplification model
C1,C2andC3arecoefficientsfromHassaniandAtkinson(2016)obtainedforhard-rockreferencesitecondiCon.
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Fpeak and VS30 based amplification model, examples
Glaciated
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Fpeak and VS30 based amplification model, examples
Glaciated
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Fpeak and VS30 based amplification model, examples
Glaciated
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Fpeak and VS30 based amplification model, examples
Non-Glaciated
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Fpeak and VS30 based amplification model, examples
Non-Glaciated
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Fpeak and VS30 based amplification model, examples
Non-Glaciated
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Atkinson’s group Recipe for Site Response in CENA • Ifweonlyhavefpeak:
WherethecoefficientswerederivedinHassaniandAtkinson(2016).
• IfwehavebothfpeakandVS30:
WherethecoefficientsoftheV30-dependantpartofthemodelwerediscussedinpreviousslides.
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Atkinson’s group Recipe for Site Response in CENA IfweonlyhaveVS30:OnealternaCveisthatweusethecorrelaConbetweenVS30andfpeaktofindthefpeakvaluecorrespondingtotheselectedVS30value(HassaniandAtkinson2016).ThenweusetheHassaniandAtkinson(2016)fpeak-basedamplificaConmodel.