Monitoring a Building Using Deconvolutionl

MonitoringaBuildingUsingDeconvolution

Interferometry.I:Earthquake-DataAnalysis

byNoriNakata,RoelSnieder,SeiichiroKuroda,ShunichiroIto,

TakaoAizawa,andTakashiKunimi

AbstractForhealthmonitoringofabuilding,weneedtoseparatetheresponseof

thebuildingtoanearthquakefromtheimprintofsoil-structurecouplingandfrom

wavepropagationbelowthebaseofthebuilding.Seismicinterferometrybasedon

deconvolution,wherewedeconvolvethewavefieldsrecordedatdifferentfloors,

isatechniquetoextractthisbuildingresponseandthusestimatevelocityofthewave

thatpropagatesinsidethebuilding.Deconvolutioninterferometryalsoallowsusto

estimatethedampingfactorofthebuilding.Comparedwithotherinterferometrytech-

niques,suchascross-correlationandcross-coherenceinterferometry,deconvolution

interferometryisthemostsuitabletechniquetomonitorabuildingusingearthquake

records.Fordeconvolutioninterferometry,wedeconvolvethewavefieldsrecordedat

alllevelswiththewavesrecordedatatargetreceiverinsidethebuilding.Thisreceiver

behavesasavirtualsource,andweretrievetheresponseofacut-offbuilding,ashort

buildingthatiscutoffatthevirtualsource.Becausethecut-offbuildingisindepen-

dentfromthestructurebelowthevirtualsource,thetechniquemightbeusefulfor

estimatinglocalstructureandlocaldamage.Weapplydeconvolutioninterferometry

to17earthquakesrecordedduringtwoweeksatabuildinginFukushima,Japan,and

estimatetime-lapsechangesinvelocityandnormal-modefrequency.Asshownina

previousstudy,thechangeinvelocitycorrelateswiththechangeinnormal-modefre-

quency.Wecomputethevelocitiesfrombothtravelingwavesandthefundamental

modeusingcoda-waveinterferometry.Thesevelocitieshaveanegativecorrelation

withthemaximumaccelerationoftheobservedearthquakerecords.

Introduction

Theresponseofabuildingtoanearthquakehasbeen

studiedsincetheearly1900s(e.g.,Biot,1933;Sezawa

andKanai,1935;Carder,1936).Wecanestimatethefre-

quenciesofthefundamentalandhighermodesofbuildings

usingambientandforcedvibrationexperiments(Trifunac,

1972;Ivanovićetal.,2000;Kohleretal.,2005;Clintonetal.,

2006;Micheletal.,2008).Becauseoftheshakingcausedby

majorearthquakes,thefrequenciesofnormalmodesde-

crease(Trifunacetal.,2001a;Kohleretal.,2005);thereduc-

tionismostlytemporary(afewminutes)andhealingoccurs

withtime,butsomereductionispermanent.Clintonetal.,

2006foundmorethan20%temporalreductionand4%per-

manentreductioninthefundamentalfrequencyofthemotion

oftheMillikanLibrarylocatedattheCaliforniaInstituteof

Technologyafterthe1987ML5.9WhittierNarrowsearth-

quake.Thereductioninthefrequencylogarithmicallycorre-

lateswiththemaximumaccelerationofobservedrecords

(Clintonetal.,2006).Precipitation,strongwind,tempera-

ture,reinforcement,andheavyweightloadedinabuilding

alsochangethefrequenciesofnormalmodes(Kohleretal.,2005;Clintonetal.,2006).Becausethesefrequenciesare

relatedtoboththebuildingitselfandthesoil-structurecou-

pling,wehavetoconsidersoil-structureinteractions(Şafak,

1995)andnonlinearitiesintheresponseofthefoundation

soil(Trifunacetal.,2001a,b).Normal-modefrequencieses-

timatedfromobservedrecordsare,therefore,notsuitablefor

healthmonitoringofabuildinginisolationofitsenviron-

ment(TodorovskaandTrifunac,2008b).

SniederandŞafak(2006)showthatonecanestimatean

impulseresponseindependentfromthesoil-structurecoupling

andthecomplicatedwavepropagation(e.g.,attenuationand

scattering)belowthebottomreceiverbyusingseismicinter-

ferometrybasedondeconvolution.Seismicinterferometryisa

techniquetoextracttheGreen’sfunction,whichaccountsfor

thewavepropagationbetweenreceivers(LobkisandWeaver

2001;Derodeetal.,2003;Snieder,2004;Pauletal.,2005;

Snieder,Wapenaar,etal.,2006;WapenaarandFokkema,

2006).Seismicinterferometrycanbebasedoncrosscorrela-

tion,deconvolution,andcrosscoherence(Sniederetal.,2009;

Wapenaaretal.,2010).Deconvolutioninterferometryisa

1662BulletinoftheSeismologicalSocietyofAmerica,Vol.103,No.3,pp.1662–1678,June2013,doi:10.1785/0120120291usefultechniqueformonitoringstructures,especiallyinone

dimension(NakataandSnieder,2011,2012a,b).Becausede-

convolutioninterferometrychangestheboundaryconditionat

thebaseofthebuilding,weareabletoextractthepurere-

sponseofthebuildingregardlessofitscouplingtothesubsur-

face(SniederandŞafak,2006;Snieder,Sheiman,etal.,2006).

Deconvolutioninterferometryhasbeenappliedtoearth-

quakerecordsobservedinabuildingtoretrievethevelocityof

travelingwavesandattenuationofthebuilding(Oyunchimeg

andKawakami,2003;SniederandŞafak,2006;Kohleretal.,

2007;TodorovskaandTrifunac,2008a,b;somestudiescall

themethodimpulseresponsefunctionornormalizedinput–

outputminimization).TodorovskaandTrifunac(2008b)use

11earthquakesoccurringoveraperiodof24yearstomonitor

thefundamentalfrequencyofabuildingafterapplyingdecon-

volutioninterferometry.Thefundamentalfrequenciestheyes-