Stiffness effect for sites in CENA, starting with fpeak

BehzadHassaniandGailAtkinson

November,2016

fpeak from Microtremor survey vs. Earthquake H/V

MicrotremorsurveyinsouthernOntariofor8seismicstaCons.

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.

Finding Residual Site terms

WealsoincludesiteswithVS30>1500m/sandnoobservedfpeakvalues.Forthesesites,weassumethatthe

fpeakvalueishigherthan20Hz.

VS30ScalingtermWeuseParkeretal.(2016)updatedVS30valuesforoursites.

Glaciated

ThesearetheapparenttrendsifweneglectuncertaintyinVS30esCmates(VS30variance)

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).

VS30Scalingterm,applyingMonteCarlosimulaConGlaciated

ThistrendaccommodatestheuncertaintyforVS30esCmatesandalsoforaverageresidualsiteterms(normaldistribuCon)

VS30Scalingterm

Non-Glaciated

ApparenttrendneglecCnguncertaintyinVS30esCmates(VS30variance)

WeuseParkeretal.(2016)updatedVS30valuesforoursites.

VS30Scalingterm,applyingMonteCarlosimulaConNon-Glaciated

ApparenttrendconsideringuncertaintyinVS30esCmatesandalsoinaverageresidualsiteterms

NoobviousVS30-dependenttrendduetolargeVS30uncertainCes!

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.

VS30Scalingterm,applyingMonteCarlosimulaCon(0.3sigma) Non-Glaciated

VS30 Scaling term, non-glaciated

Non-GlaciatedscalingmodelderivedbasedontheglaciatedmodelandalsodatapointswithlowVS30variance.

C4,VS30Scalingslope,Glaciatedandnon-glaciated

ToderivetherightstandarderrorfortheC4term,wemulCplytheesCmatedstandarderrorbasedonthepopulateddatabasebyafactorof7(squarerootof50(numberoftherandomdatapointsgenerated)),tocorrectitfortheactualnumberofobservaConswehave.

VS30ScalingtermBasedontheobservedVS30-dependenttrends,wederivetwoseparatemodelsforglaciatedandnon-glaciatedsites.

Fpeak and VS30 based amplification model

C1,C2andC3arecoefficientsfromHassaniandAtkinson(2016)obtainedforhard-rockreferencesitecondiCon.

Fpeak and VS30 based amplification model, examples

Glaciated

Fpeak and VS30 based amplification model, examples

Glaciated

Fpeak and VS30 based amplification model, examples

Glaciated

Fpeak and VS30 based amplification model, examples

Non-Glaciated

Fpeak and VS30 based amplification model, examples

Non-Glaciated

Fpeak and VS30 based amplification model, examples

Non-Glaciated

Atkinson’s group Recipe for Site Response in CENA •  Ifweonlyhavefpeak:

WherethecoefficientswerederivedinHassaniandAtkinson(2016).

•  IfwehavebothfpeakandVS30:

WherethecoefficientsoftheV30-dependantpartofthemodelwerediscussedinpreviousslides.

Atkinson’s group Recipe for Site Response in CENA IfweonlyhaveVS30:OnealternaCveisthatweusethecorrelaConbetweenVS30andfpeaktofindthefpeakvaluecorrespondingtotheselectedVS30value(HassaniandAtkinson2016).ThenweusetheHassaniandAtkinson(2016)fpeak-basedamplificaConmodel.