Hazard Analysis

Seismic Hazard Analysis

Revised 2/28/04

Seismic Hazard Analysis• Deterministic Procedures• Probabilistic Procedures• USGS Hazard Mapping• ASCE 7 Hazard Mapping• Site Amplification• IBC/ASCE 7 Response Spectrum

Revised 2/28/04

Hazard Analysis 3

Seismic Hazard Analysisdescribes the potential for dangerous,earthquake related natural phenomenasuch as ground shaking, fault rupture,or soil liquefaction.

Seismic Risk Analysisassesses the probability of occurrence of losses(human, social, economic) associated withthe seismic hazards.

Hazard vs Risk

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Large earthquakes less frequent

How does CEUS and WUS Seismic Risk Compare?

Large earthquakes frequent vs.

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Example of inadequately reinforced, non-ductile structure – 1989 LP EQ:

Cypress Overpass

Following photo sequence from I. Idriss…

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This Type of Non-Ductile Infrastructure is Common in CEUS!

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WUS and CEUS Risk Comparison Summary:• CEUS has potential for recurring large EQs• Attenuation lower in CEUS• Abundance of weak, non-ductile structures in

CEUS; weakest not “weeded out”• Immature seismic practice in CEUS• “Human inertia” in CEUS; little awareness• Much more uncertainty in CEUS• Areas with poor soils in CEUS

• Bottom line ⇒ seismic risk in CEUS and WUS is comparable!

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• Good analogy⇒ Kobe is to Tokyo, as CEUS is to the WUS

• Kobe M6.9 (> $140 billion losses); costliest natural disaster in world history; infrastructure weak and old, poor soil conditions

• Remember⇒ before Katrina, most expensive US natural disaster (Northridge, EQ ∼$30 billion) was moderate EQ on minor fault on fringe of LA

• Since 1800: CA has had 11 EQ’s > M7.3, CEUS has had 4 EQ’s > M7.3.

Issues to Think About

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Approaches to Seismic Hazard Analysis

Deterministic“The earthquake hazard for the site is a peak groundacceleration of 0.35 g resulting from an earthquakeof magnitude 6.0 on the Balcones Fault at a distance of12 miles from the site. ”

Probabilistic“The earthquake hazard for the site is a peak groundacceleration of 0.28 g, with a 2 percent probability of beingexceeded in a 50 year period.”

Hazard Analysis 16

Probabilistic Seismic Hazard Analysis

C. Allin Cornell“Engineering Seismic Risk Analysis”Bulletin of the Seismological SocietyVol. 58, No. 5, October, 1968

Hazard Analysis 17

F1 BalconesFault

AreaSource

Site

“The earthquake hazard for the site is a peak ground acceleration of 0.35 g resulting from an earthquake of magnitude 6.0 on the Balcones Fault at a distance of 12 miles from the site. ”

Fixed Distance R

Fixed Magnitude M

Magnitude M

Distance

Peak

Acc

eler

atio

n

2) Controlling Earthquake

Steps in Deterministic Seismic Hazard Analysis1) Sources

4) Hazard at Site3) Ground Motion

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Fault Fault

AreaSource

SiteFault

Localizing Structure

SeismotectonicProvince

SOURCE TYPES

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Maximum EarthquakeMaximum Possible EarthquakeAn upper bound to size (however unlikely) determinedby earthquake processes (e.g. Maximum Seismic Moment)

Maximum Credible EarthquakeThe maximum reasonable earthquake size basedon earthquake processes (but does not imply likelyoccurrence.

Maximum Historic EarthquakeThe maximum historic or instrumented earthquake. Often is a lower bound on Maximum Possible or Maximum CredibleEarthquake

Maximum Considered Earthquake (Described later)

Hazard Analysis 20

Ground Motion Attenuation

Reasons:• Geometric Spreading• Absorption (Damping)

Magnitude M

Distance

Gro

und

Mot

ion

Para

met

er

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Attenuation with Distance

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Comparison of Attenuation for Four Earthquakes

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Ground Motion AttenuationSteps to Obtain Empirical Relationship

1) Obtain Catalog of Appropriate Ground Motion Records

2) Correct for Aftershocks, Foreshocks

3) Correct for Consistent Magnitude Measure

4) Fit Data to Empirical Relationship of Type:

εln)(ln),(ln)(ln)(lnˆln 43211 +++++= iPfRMfRfMfbY

Hazard Analysis 24

Ground Motion AttenuationBasic Empirical Relationships

εln)(ln),(ln)(ln)(lnˆln 43211 +++++= iPfRMfRfMfbY

1b

)(1 Mf

)(2 Rf

),(3 RMf

)(4 iPfε

Scaling factor

Function of Magnitude

Function of Distance

Function of Magnitude and Distance

Other Variables

Error Term

Y Ground Motion Parameter (e.g. PGA)

Hazard Analysis 25

Ground Motion AttenuationRelationships for Different Conditions

• Central and Eastern US• Subduction Zone Earthquakes• Shallow Crustal Earthquakes• Near-Source Attenuation• Extensional Tectonic Regions• Many Others

May be Developed for Any Desired Quantity(PGA, PGV, Spectral Response)

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Ground Motion AttenuationRelationships

Seismological Research LettersVolume 68, Number 1January/February, 1997

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Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)

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PGA Attenuation – 1989 Loma Prieta EQ

soft soil sites

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Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)

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)2())exp(ln()5.8()ln( 7654321 +++++−++= ruprup rCMCCrCMCMCCy

T C1 C2 C3 C4 C5 C6 C7

PGA -0.624 1.000 0.000 -2.100 1.296 0.250 0.0000.07 0.110 1.000 0.006 -2.128 1.296 0.250 -0.0820.1 0.275 1.000 0.006 -2.148 1.296 0.250 -0.0410.2 0.153 1.000 -0.004 -2.080 1.296 0.250 0.0000.3 -0.057 1.000 -0.017 -2.028 1.296 0.250 0.0000.4 -0.298 1.000 -0.028 -1.990 1.296 0.250 0.0000.5 -0.588 1.000 -0.040 -1.945 1.296 0.250 0.0000.75 -1.208 1.000 -0.050 -1.865 1.296 0.250 0.0001 -1.705 1.000 -0.055 -1.800 1.296 0.250 0.0001.5 -2.407 1.000 -0.065 -1.725 1.296 0.250 0.0002 -2.945 1.000 -0.070 -1.670 1.296 0.250 0.0003 -3.700 1.000 -0.080 -1.610 1.296 0.250 0.0004 -4.230 1.000 -0.100 -1.570 1.296 0.250 0.000

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)

Table for Magnitude <= 6.5

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Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)

0.001

0.01

0.1

1

1 10 100 1000

Distance, KM

Peak

Gro

und

Acc

eler

atio

n, G

45678

Magnitude

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0.001

0.01

0.1

1

10

1 10 100 1000

Distance, KM

0.2

Sec.

Spe

ctra

l Acc

eler

atio

n, G

45678

0.001

0.01

0.1

1

10

1 10 100 1000

Distance, KM

1.0

Sec.

Spe

ctra

l Acc

eler

atio

n, G

45678

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)

Magnitude Magnitude

0.2 Second Acceleration 1.0 Second Acceleration

Hazard Analysis 33

Source 1

Source 2

Site

Source 3

Source M D PGA(km) (g)

1 7.3 23.7 0.422 7.7 25.0 0.573 5.0 60.0 0.02

D1

D2D3

Example Deterministic Analysis (Kramer)

From Attenuation RelationshipClosest DistanceMaximum on Source

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F1 BalconesFault

AreaSource

Site

M1

Distance

Peak

Acc

eler

atio

n

Steps in Probabilistic Seismic Hazard Analysis1) Sources

4) Probability of Exceedance3) Ground Motion

Magnitude M

Log

# Q

uake

s > M

2) Recurrence

M2M3

Uncertainty

Prob

abili

ty o

f Exc

eeda

nce

Ground Motion Parameter

Hazard Analysis 35

0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10

Magnitude

Mea

n A

nnua

l Rat

e of

Exc

eeda

nce

Empirical Gutenberg-RichterRecurrence Relationship

bmam −=λlog

mλ = mean rate ofrecurrence(events/year)

a and b to be deter-mined from data

λ m

mλ/1 = return period

Hazard Analysis 36

Uncertainties Included inProbabilistic Analysis

Attenuation Laws Recurrence Relationship

Distance to Site

][][],*[1 1 1

* kjkj

N

i

N

j

N

kiy rRPmMPrmyYPv

S M R

==>=∑∑∑= = =

λ

Hazard Analysis 37

Poisson Distribution (for one event)

PE = 1 - e-λt

where λ = rate of exceedance (events/year) ⇐ key!!t = exposure interval (50 years typical)

1/λ = return period

Hazard Analysis 38

Common Probabilistic Design Levels

• (1) 10% PE in 50 years, a.k.a.“500-year motion*” (actually is 475-yr. event; rate is 1/475 or 0.0021 events/yr.).

• (2) 5% PE in 50 years, a.k.a. “1000-year motion” (actually is 975-yr. event; rate is 1/975 or events/year or 0.001 events/yr).

• (3) 2% PE in 50 years a.k.a. “2500-year earthquake” (actually is 2475-yr. event; rate is1/2,475 or 0.0004 events/yr).

_______*Does not mean EQ occurs once every 500 yrs., etc.!Rather, the EQ with chance of 1/500 of occurring in 1 year.

Hazard Analysis 39

0.0 0.4

10-6

10-4

10-2

10-7

10-5

10-3

10-1

10-8

0.2 0.6 0.8

10-0

10-1

Peak Horizontal Acceleration (g)M

ean

Ann

ual R

ate

of E

xcee

danc

e SEISMIC HAZARD CURVE

PGA=0.33g

10% Probability in 50 yearsReturn Period = 475 yearsRate of Exceedance = 1/475=0.0021

Use of PGA Seismic Hazard Curve

Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.810% in 50 YearElastic ResponseSpectrum

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0.0 0.6

10-6

10-4

10-2

10-7

10-5

10-3

10-1

10-8

0.2 0.4 0.8

10-0

10-1

0.2 Sec Spectral Acceleration (g)M

ean

Ann

ual R

ate

of E

xcee

danc

e SEISMIC HAZARD CURVE

.2 Sec accn = 0.55g

10% Probability in 50 yearsReturn Period = 475 yearsRate of Exceedance = 1/475=0.0021

Use of 0.2 Sec. Seismic Hazard Curve

Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.8

10% in 50 yearElastic ResponseSpectrum

Hazard Analysis 41

Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.8

10% in 50 year Elastic Response Spectrum (UHS)

UHS is envelope of maximums

Each point on curve could be from a different earthquake sources

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Uniform Hazard Spectrum (UHS)

Large DistantEarthquake

Small NearbyEarthquake

Uniform Hazard Spectrum

Period

Response

Hazard Analysis 43

Uniform Hazard Spectrum (UHS)

All ordinates have equal probability of exceedance

Developed from Probabilistic Analysis

Represents contributions from small local,large distant earthquakes

May be overly conservative for modal responsespectrum analysis

May not be appropriate for artificial ground motiongeneration

Hazard Analysis 44

Probabilistic vs DeterministicSeismic Hazard Analysis

“The deterministic approach provides a clear andtrackable method of computing seismic hazard whoseassumptions are easily discerned. It providesunderstandable scenarios that can be related to theproblem at hand.”

“However, it has no way for accounting for uncertainty.Conclusions based on deterministic analysis can easilybe upset by the occurrence of new earthquakes”.

Hazard Analysis 45

Probabilistic vs DeterministicSeismic Hazard Analysis

“The probabilistic approach is capable of integratinga wide range of information and uncertainties intoa flexible framework .”

“Unfortunately, its highly integrated framework canobscure those elements which drive the results, and itshighly quantitative nature can lead to false impressionsof accuracy.

Hazard Analysis 46

U.S.G.S. PROBABILISTIC HAZARD MAPS(Project 97)

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years

HAZARD MAP RESPONSE SPECTRA

Hazard Analysis 47

U.S.G.S. PROBABILISTIC HAZARD MAPS(and NEHRP MAPS)

Earthquake SpectraTheme Issue : Seismic Design Provisions and GuidelinesVolume 16, Number 1February, 2000

Hazard Analysis 48

Maximum Considered Earthquake (MCE)

The MCE Ground Motions are defined asthe maximum level of earthquake shakingthat is considered as reasonable to designnormal structures to resist.

Hazard Analysis 49

U.S.G.S. SEISMIC HAZARD REGIONS

Note: Different attenuation relationships used for different regions

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U.S.G.S. SEISMIC HAZARD SOURCE ZONES

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U.S.G.S. SEISMIC HAZARD WUS FAULTS

Hazard Analysis 52

USGS Seismic Hazard Curves for Various Cities

Hazard Analysis 53

Uniform Hazard Spectra for San Francisco, CA

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years

Hazard Analysis 54

Uniform Hazard Spectra for Charleston, S.C.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years

Hazard Analysis 55

http://eqhazmaps.usgs.gov/2002April03/US/USpga2500v4.gif

USGS SEISMIC HAZARD MAP (PGA)

2% in 50 years

Hazard Analysis 56

USGS SEISMIC HAZARD MAP OF US (0.2 sec)

2% in 50 years

Hazard Analysis 57

USGS SEISMIC HAZARD MAP OF US (1.0 sec)

2% in 50 years

Hazard Analysis 58

U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [PGA]

2% in 50 years

http://eqint.cr.usgs.gov/eq/html/zipcode.shtml

Hazard Analysis 59

U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [0.2 sec]

2% in 50 years

Hazard Analysis 60

U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [1.0 sec]

2% in 50 years

Hazard Analysis 61

U.S.G.S. SEISMIC HAZARD MAP ofSouthern California [PGA]

2% in 50 years

Hazard Analysis 62

U.S.G.S. SEISMIC HAZARD MAPof Southern California [0.2 sec]

2% in 50 years

Hazard Analysis 63

U.S.G.S. SEISMIC HAZARD MAPof Southern California [1.0 sec]

2% in 50 years

Hazard Analysis 64

http://eqint.cr.usgs.gov/eq/html/zipcode.htmlUSGS Web Site: Zip Code Lookup

Hazard Analysis 65

USGS Seismic Hazard Maps• Probabilistic analysis used for maps• Most recent published versions: April 2003• Hazard in some areas increased in new maps

relative to older-generation maps (i.e., 1996) • Maps developed for motions on B-C boundary

rock)• Maps developed for 2%, 5%, and 10% PE• Maps adopted by ASCE 7 and used as basis for

building code maps; USGS and ASCE 7 identical in all US areas other than CA and AK

• Maps do not account for regional geological effects such as deep sediment profiles

Hazard Analysis 66

Relative PGA’s in the USA key point to remember….

Hazard Analysis 67

Soil is the great equalizer:Many CEUS areas with poor soils

Hazard Analysis 68

ASCE 7-05 Seismic Hazard Maps5% Damped, 2% in 50 Years, Site Class B (Firm Rock)

0.2 Second and 1.0 Second Spectral Ordinates Provided

On certain faults in California, Alaska, and Hawaii,ASCE 7 values are deterministic cap times 1.5. Outsideof deterministic areas, NEHRP maps are the sameas the USGS maps.

USGS Zip Code and Longitude/Latitude Values areProbabilistic MCE. To Avoid Confusion, ALWAYSUse ASCE-7 Maps for Design Purposes

Hazard Analysis 69

NEHRP Seismic Hazard Maps0.2 Second Spectral Response (SS)

Hazard Analysis 70

NEHRP Seismic Hazard Maps1.0 Second Spectral Response (S1)

Hazard Analysis 71

Deterministic CapApplies only where probabilistic values exceedhighest design values from old (Algermissen & Perkins)maps.

Deterministic Procedure for Mapping:applies for known “active” faultsuses characteristic largest earthquake on faultuses 150% of value from median attenuation

Use deterministic value if lower than 2% in 50 year value

Hazard Analysis 72

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

Period, sec.

Spec

tral

Acc

eler

atio

n, g

.

2% in 50 Year 5% Damped MCE Elastic SpectraSite Class B (Firm Rock)

S1=0.30g

Ss=0.75g

Curve is S1/T

PGANot Mapped

Hazard Analysis 73

A

B

A

B

Time

Acc

eler

atio

n

Rock

Shale

Sand

Site Amplification Effects

Hazard Analysis 74

Site Amplification Effects

• Amplification of Ground motion

• Longer Duration of Motion

• Change in Frequency Content of Motion

• Not the Same as Soil-Structure Interaction

Hazard Analysis 75

Site Amplification; Seed et al

Hazard Analysis 76

Site Amplification; Loma Prieta Earthquake

SoftRock

Hazard Analysis 77

Site Effects on Ground Motions

• Conservation of energy drives amplification

Hazard Analysis 78

Soft Soils Commonly Amplify Motions Relative To Bedrock

(1989 Loma Prieta EQ)

Hazard Analysis 79

Site Amplification; Loma Prieta& Mexico City Earthquakes

Hazard Analysis 80

Cypress Structure Collapse

Hazard Analysis 81

Hazard Analysis 82

Cypress Structure Collapse

Hazard Analysis 83

A Hard Rock vs > 5000 ft/sec

B Rock: 2500 < vs < 5000 ft/sec

C Very Dense Soil or Soft Rock: 1200 < vs < 5000 ft/sec

D Stiff Soil : 600 < vs < 1200 ft/sec

E Vs < 600 ft/sec

F Soft Clays or Liquefiable sands -- Site Specific Requirements

ASCE 7 SITE CLASSES (based on top 30 m)

Hazard Analysis 84

NEHRP/IBC– General Procedure• Determine Fa & Fv values from Ss, S1 and site class:

Hazard Analysis 85

NEHRP Site Amplification for Site Classes A through E

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Short Period Ss (sec)

Am

plifi

catio

n Fa

ABCDE

Site Class

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Long Period S1 (sec)

Am

plifi

catio

n Fv

ABCDE

Site Class

Hazard Analysis 86

0.00

0.21

0.42

0.63

0.84

1.05

0 1 2 3 4 5

Period, sec.

Spec

tral

Acc

eler

atio

n, g

.SMS=FASS=1.2(0.75)=0.9g

SM1=FVS1=1.8(0.30)=0.54g

2% in 50 Year 5% Damped MCE Elastic SpectraModified for Site Class D

Basic

Site Amplified

Hazard Analysis 87

Buildings designed according to current proceduresassumed to have margin of collapse of 1.5

Judgement of “lower bound” margin ofcollapse given by current design procedures

Design with current maps (2% in 50 year) butscale motions by 2/3

Results in 2/3 x 1.5 = 1.0 deterministic earthquake(where applicable)

Scaling of NEHRP Spectra by 2/3for “Margin of Performance”

Hazard Analysis 88

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

Period, sec.

Spec

tral

Ace

lera

tion,

g.

2% in 50 Year 5% Damped ElasticDesign Spectra (Scaled by 2/3)

SDS=(2/3)(0.90)=0.60g

SD1=(2/3)(0.54)=0.36g

Basic

Site Amplified

Scaled

Hazard Analysis 89

Basis for Reduction of Elastic Spectrum by R

Inelastic Behavior of Structures

Methods for obtaining acceptable inelastic response are presented in later topics

Hazard Analysis 90

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years 2/3 of 2% in 50 years

Effect of Scaling, Western U.S.

Hazard Analysis 91

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years 2/3 of 2% in 50 years

Effect of Scaling, Eastern U.S.

Hazard Analysis 92

Old Maps vs New MapsCharleston, S.C.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Period, T, sec

Seis

mic

Coe

ffici

ent,

Cs(

g)

94 Site B00 Site B

Hazard Analysis 93

Directionality and “Killer Pulse” EarthquakesFor sites relatively close to the fault, thedirection of fault rupture can have an amplifyingeffect on ground motion amplitude

Hazard Analysis 94

Forward directivity

Backward directivity

Rupture direction

Rupture direction

The areas under the far-field displacementpulses are equal, but the amplitudesand durations differ. This has majoreffects on the ground velocity and acceleration.

Ground Displacement

To Receiver

To Receiver

Hazard Analysis 95

Towards

Away

Effect of Directionality on Response Spectra

Hazard Analysis 96

Effect of Directionality on Ground Motion