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CHARACTERIZATIONOFGROUNDRESPONSETOSHAKING(15)

I MainTopics(seeUSGSProfessionalPaper1360)

A GroundResponse"EquaNons"B LinearresponseofgroundC Useofshearwavevelocityasapredictorofshaking

D Frequency-dependenteffects

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II GroundresponseGroundresponse=f(sourcestrength,path,"receiver")

A EquaNonsareempiricalbutintendedtocapturephysics

B EquaNonofJoynerandBoore(PP1360:p.204)for5.0≤Mw≤7.7logy=c0+c1(Mw-6)+c2(Mw-6)2+c3logr+c4r+S

y=ground-moNonparametercx=frequency-dependentconstants

Mw=Momentmagnitude

r=(d2+h2)1/2: d=dist.fromsurfacetraceoffault;h=pseudodepth

S=0(rocksites);S=c6log(Vshear/V0)(soilsites)

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II GroundresponseGroundresponse=f(sourcestrength,path,"receiver")

C Evernden'sground-moNonequaNon(seelecture10)

(PP1360:p.201)

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I = 3(0.5+ log A1γ11.8+1.5M10

n⎛

⎝⎜⎞

⎠⎟

1γ−kγ

iR +C( )i = 1

n∑

⎛

⎝⎜

⎞

⎠⎟

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪)

Evernden'sground-moNonequaNonGroundresponse=f(sourcestrength,path,"receiver")

•  A=0.779•  M=localmagnitude•  n=#offaultsegments•  γ=0.25•  R=epicentraldistance(km)

•  C=pseudodepth(km)•  k=akenuaNonfactor

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I = 3(0.5+ log A1γ11.8+1.5M10

n⎛

⎝⎜⎞

⎠⎟

1γ−kγ

iR +C( )i = 1

n∑

⎛

⎝⎜

⎞

⎠⎟

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪)

AkenuaNonmapshowingvaluesofk

Fig.66ofUSGSProf.Paper1360

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II GroundresponseGroundresponse=f(sourcestrength,path,"receiver")

D AriasIntensity(acceleraNon)equaNon(PP1360:p.331-333)

logIa=Ko+KmMw-2logr+KσP

Ia=Ariasintensity(unitsofm/sec)KoandKm=constantsMw=Momentmagnitude

r=distancefromslipsurface(unitsofkm)KσP=probabilityterms

(toaccountforpath[geology]effects)

Hasbeenusefulforstudyingtriggeringoflandslides

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IA =π2g

a0

Td∫ (t)2dt

DuraNonofsignalabovethreshold

MeasuredacceleraNon

GravitaNonalacceleraNon

IIILinearbehaviorA AssumpNon:theresponsetoasmall

sNmuluscanbescaleduplinearlytopredicttheresponsetoalargesNmulus

B GroundresponsetoarNficialsources(e.g.,Vibroseis,explosives)usedtopredictresponsetoseismicwaves(Eventhoughstrainsfromblastsaretwoordersofmagnitudeorsolessthanforearthquakes)

C GroundresponsetoliklequakesÞgroundresponsetolargequakes

D LinearresponsenotadequatetotreatliquefacNonphenomena;thenear-epicenterresponsetolargequakesisnonlinear.

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Exampleoflinearbehavior

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VUseofshearwavevelocity(Vs)forpredicNnggroundresponse

A

StrainsareinverselyproporNonaltoshearmodulusμ

B

LowVsimplieslowμ

C ShearwaveamplitudeAFromJoynerandFumal(1985,p.203-220)

DecreaseinVsorμyieldsanincreaseinS-waveamplitude

F S-wavevelociNescanbeusedtopredicttherelaNveamplitudeshakingatdifferentsites.

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Vs = µ ρ

ε xy =σ xy

2µ

ρ=density

A ~ 1ρVs

IVFrequency-dependenteffects

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A Fourieranalysis:representsafuncNonofNme(e.g.acceleraNon,velocity,displacement)asafuncNonoffrequency(f)orperiod(T),wheref=1/T.

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IVFrequency-dependenteffects•  FIGURE31.-RecordingsofN.

14°E.componentofhorizontalgroundmoNonatPacoimadamsitefor1971SanFernandoearthquake(fromPageandothers,1975).Velocity(B)anddisplacement(C)recordsareobtainedbyintegraNngaccelerogram(A)onceandtwice,respecNvely.

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FIGURE31.-RecordingsofN.14°E.componentofhorizontalgroundmoNonatPacoimadamsitefor1971SanFernandoearthquake(fromPageandothers,1975).Velocity(B)anddisplacement(C)recordsareobtainedbyintegraNngaccelerogram(A)onceandtwice,respecNvely.

AcceleraN

on

Velocity

Displacem

ent

IVFrequency-dependenteffectsB Examples(fromProfPaper

1360,Rogersetal.,p.221-248)

1 Velocityvs.Nmeresponsesat8sitesintheLosAngelesregionfromnucleartestsinNevada

2 ShakingvelociNesincreaseasalluvialthicknessincreases

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FIGURE105.-RadialcomponentNme-historiesofgroundmoNonfromadistantundergroundnuclearexplosioninNevadarecordedsimultaneouslyateightsitesintheLosAngelesregionandgroupedaccordingtothetypeofgeologicmaterialsimmediatelybeneatheachrecordingstaNon.TheamplitudelevelsatlocaNonsunderlainbyalluviumclearlyaregreaterthanthoseatlocaNonsunderlainbyrock.ThedegreeofamplificaNonalsoappearstoberelatedtothethicknessofunderlyingalluvium:HOI,HolidayInn,300m;MIL,MillikanLibrary,372m;ATH,Athenaeum,372m;MB,GlendaleMunicipalBuilding,120m;FS4,FireStaNon4,15m.GOC,CIT,and3838arerocksites.

300m

372m

372m

120m

15m

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VFrequency-dependenteffectsB Examples(fromProfPaper1360,

p.227-228)1  T<0.5sec(f>2Hz)

ShakingonQuaternarysedimentarydepositsis3-4Nmesthatofsitesfoundedoncrystallinerock

2 T>0.5sec(f<2Hz)ShakingincreasesasthicknessofQuaternarydepositsincreasesand/orasdepthtobasementrockincreasesa GroundmoNondepends

onµ"average”b µQuat.deposits<µBasementrocks

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FIGURE106.-SpectralraNosoftheradialcomponentsofgroundmoNon(seefig.105)recordedonsiteshavinggeologiccondiNonsdifferentfromthecrystalline-rocksite(CIT).ThesediagramsshowthatspectralsiteamplificaNonrangesfromabout1togreaterthan12;thehighestraNosoccuratsitesunderlainbyalluvium.SiteFS4displaysaresonantfrequencybetween2and3Hz,whereasothersiteshavemoreuniformamplificaNon,averagingasmuchas6insomefrequencybands.

300m 372m 372m

120m 15m

VelocityspectrarelaNvetobedrock(CIT)site

f=2Hz

0

6

12

0

6

12

0

6

12

Spectralra

No

f

VFrequency-dependenteffectsB Examples(fromProfPaper

1360,p.227-228)3 Depthoverwhichthe

sedimentthicknessisimportantscaleswiththewaveperiodandthereforethewavelength(longerwavelengthwavessNmulatematerialatgreaterdepths).

4 Sitewiththinalluvium(FS4)amplifiesshakingoveranarrowerfrequencyrangethansiteswiththickalluvium

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FIGURE106.-SpectralraNosoftheradialcomponentsofgroundmoNon(seefig.105)recordedonsiteshavinggeologiccondiNonsdifferentfromthecrystalline-rocksite(CIT).ThesediagramsshowthatspectralsiteamplificaNonrangesfromabout1togreaterthan12;thehighestraNosoccuratsitesunderlainbyalluvium.SiteFS4displaysaresonantfrequencybetween2and3Hz,whereasothersiteshavemoreuniformamplificaNon,averagingasmuchas6insomefrequencybands.

300m 372m 372m

120m 15m

VelocityspectrarelaNvetobedrock(CIT)site