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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
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