probabilistic seismic hazard analysis problem
DESCRIPTION
A solution of probabilistic seismic hazard analysis permormed to sevelar ideas.TRANSCRIPT
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Probabilistic Seismic Probabilistic Seismic Hazard Analysis Hazard Analysis
ProblemProblem
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Hazard AnalysisHazard AnalysisDefinitions: Definitions:
Hazard Hazard –– anticipated ground motion at siteanticipated ground motion at siteRisk Risk –– damage or losses to societydamage or losses to societyProbabilisiticProbabilisitic –– considers uncertainty in input parameters (e.g., considers uncertainty in input parameters (e.g., magnitude, ground motion)magnitude, ground motion)Uncertainty Uncertainty –– aleatory (random), epistemic (variability in mean aleatory (random), epistemic (variability in mean values for different modelsvalues for different modelsDeterministic Deterministic –– considers average level for scenarioconsiders average level for scenarioHazard level Hazard level –– probability level used for building designprobability level used for building designDisaggregationDisaggregation –– magnitude and distance that contribute mostmagnitude and distance that contribute mostMagnitudeMagnitude--frequency distribution frequency distribution –– sizes and rate of sizes and rate of earthquakesearthquakesTimeTime--dependence dependence –– probability increases with time since last probability increases with time since last earthquakeearthquake
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Cumulative Normal distribution at two standard deviations
Cumulative Normal distribution at one standard deviation
median +1 sd-2 sd
100%68%
-1 sd +2 sd
84%16%
98%2%
1.8 m
1.9 m1.7 m
Normal DistributionNormal Distribution
Area under curve is Area under curve is probabilityprobability
Normal distribution
Ex. Height: median = 1.8msd=0.1m
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median +1 sd-2 sd -1 sd +2 sd
HOWEVER GROUND MOTION FOLLOWS A LOGNORMAL DISTRIBUTION
medianmean
0.2 g
-1.6 -0.9 -0.2-2.3-3.0ln (0.05g) ln(0.1g) ln(0.2g) ln(0.4g) ln(0.8g)
Add 0.7 to ln(median)to get the +1sd
Standard deviation isfactor of two
mode
Pga
Pga
0.4g
Lognormal DistributionLognormal Distribution
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Seismic hazard analysis has two Seismic hazard analysis has two model components:model components:
(1)Earthquake-Rupture Forecast (ERF)
Probability of all possible fault-rupture events (M≥~5) for region & time span
(2) Intensity-Measure Relationship (IMR)
Gives Prob(IMT≥IML) for a given site and fault-rupture event
Attenuation Relationships(traditional)(no physics)
Full-Waveform Modeling
(developmental)(more physics)
ρÝ Ý u i = τ ij, j + fi
τ ij = λδijεpp + 2μεij
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a bccEarthquake Sources
Ground motion
d1
d2
d3
d4
r1
r2
r3
San Andreas fault
high seismicityzone
peak ground acceleration (pga)
Hazard curve
annu
al ra
te o
f ex
ceed
ing
pga
0.25g
M 7.6
distancepeak
gro
und
acce
lera
tion
M7.6
0.5g
To calculate the hazard curve (annual rate of exceeding ground mTo calculate the hazard curve (annual rate of exceeding ground motions) we:otions) we:
1. Determine magnitude, and distance, and rate of earthquake1. Determine magnitude, and distance, and rate of earthquake
2. Calculate ground motion distribution for that m and d.2. Calculate ground motion distribution for that m and d.
3. Calculate the product:3. Calculate the product:
annual rate of earthquake *probability that earthquake will exceannual rate of earthquake *probability that earthquake will exceed certain ground motion leveled certain ground motion level
4. Sum these rates for all earthquakes in the model at each grou4. Sum these rates for all earthquakes in the model at each ground motion to getnd motion to get
a hazard curve. This curve shows the rate of exceedance of a hazard curve. This curve shows the rate of exceedance of each ground motion.each ground motion.
PROBABILISTIC SEISMIC HAZARD METHODOLOGYPROBABILISTIC SEISMIC HAZARD METHODOLOGY
M7.6 every 250yrsM7.6 every 250yrs-- 0.004 event/yr0.004 event/yr
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Probabilistic Seismic HazardProbabilistic Seismic Hazard
Annual rate of exceedance for a given ground motion, zAnnual rate of exceedance for a given ground motion, z
Sources (already discussed)Sources (already discussed)Normal distributionNormal distributionLognormal distributionLognormal distributionMultiplying source rates and probability of exceeding Multiplying source rates and probability of exceeding ground motion levelground motion levelAdding exceedances for a ground motion level to get total Adding exceedances for a ground motion level to get total hazard curvehazard curveApplying Poisson relation to get 10% probability of Applying Poisson relation to get 10% probability of exceedance in 50 yearsexceedance in 50 years
( ) ( ) ( ) ( )1 0
| ,u
o
m rN
i i ii m r
E z f m f r P Z z m r dmdrα=∞
= =
= >∑ ∫ ∫
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Earthquake Earthquake sourcesource
Ground Ground motionmotion
15 km
0.2 g
M 6.5, 15 km
PGA
freq
uenc
y
median
Fault 1M 6.5, 15 kmRecurrence: 50 yearsAnnual rate: 0.02
Example 1Example 1
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.05 g0.05 g pga given M 6.5 earthquake occurs?pga given M 6.5 earthquake occurs?
Almost all earthquakes (98%) of M 6.5 at a distance Almost all earthquakes (98%) of M 6.5 at a distance of 15 km will cause ground motion that will exceed of 15 km will cause ground motion that will exceed 0.05g.0.05g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.2
M 6.5, 15 km
0.1 0.3 0.4 PGA
frequency
median0.05 g
2%
98%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance and simplify for a single source, exceedance and simplify for a single source, distance and magnitude:distance and magnitude:
Ground motion:Ground motion: 0.05g0.05g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.020.02
( ) ( )| ,E z P Z z m rα= >
( )0.05 0.02*0.98 0.02E = =
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.2 g0.2 g pga given M 6.5 earthquake occurs?pga given M 6.5 earthquake occurs?
50% of earthquakes of M 6.5 at a distance of 15 km 50% of earthquakes of M 6.5 at a distance of 15 km will cause ground motion that will exceed 0.2g.will cause ground motion that will exceed 0.2g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.2
M 6.5, 15 km
0.1 0.3 0.4 PGA
frequency
median0.05 g
50%
50%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance and simplify for a single source, exceedance and simplify for a single source, distance and magnitude:distance and magnitude:
Ground motion:Ground motion: 0.05g 0.2g0.05g 0.2g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.02 0.010.02 0.01
( ) ( )| ,E z P Z z m rα= >
( )0.2 0.02*0.50 0.01E = =
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.4 g0.4 g pga given M 6.5 earthquake occurs?pga given M 6.5 earthquake occurs?
16% of earthquakes of M 6.5 at a distance of 15 km 16% of earthquakes of M 6.5 at a distance of 15 km will cause ground motion that will exceed 0.4g.will cause ground motion that will exceed 0.4g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.2
M 6.5, 15 km
0.1 0.3 0.4 PGA
frequency
median0.05 g
84%
16%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance and simplify for a single source, exceedance and simplify for a single source, distance and magnitude:distance and magnitude:
Ground motion:Ground motion: 0.05g 0.2g 0.4g0.05g 0.2g 0.4g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.02 0.01 0.0030.02 0.01 0.003
( ) ( )| ,E z P Z z m rα= >
( )0.4 0.02*0.16 0.003E = =
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Ann
ual r
ate
grou
nd m
otio
n is
ex
ceed
ed
PGA0.001
0.01
0.1
0.1 g 0.2 g 0.3 g 0.4 g
10% probability of exceedance in 50 years
Hazard CurveHazard Curve
Ground motion:Ground motion: 0.05g0.05g 0.2g0.2g 0.4g0.4gRate of Ground motion exceedance:Rate of Ground motion exceedance: 0.020.02 0.010.01 0.0030.003
0.5 g
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15 km
0.4 g
M 7.9, 20 km
PGA
freq
uenc
y
median
Fault 1M 6.5, 15 kmRecurrence: 50 yearsAnnual rate: 0.02
Example 2Example 2
20 km
Fault 2M 7.9, 20 kmRecurrence: 250 yearsAnnual Rate: 0.004
Earthquake Earthquake sourcessources
Ground Ground motionmotion
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.05 g0.05 g pga given M 6.5 and M 7.9 pga given M 6.5 and M 7.9 earthquakes occur?earthquakes occur?
Almost all earthquakes (99.9%) of M 7.9 at a Almost all earthquakes (99.9%) of M 7.9 at a distance of 20 km will cause ground motion that distance of 20 km will cause ground motion that will exceed 0.05g.will exceed 0.05g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.4
M 7.9, 20 km
0.2 0.6 0.8 PGA
frequency
median0.05 g
0.1%99.9%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance and simplify for a single source, exceedance and simplify for a single source, distance and magnitude:distance and magnitude:
Ground motion:Ground motion: 0.05g0.05g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.0240.024
( ) ( )2
1| ,i
iE z P Z z m rα
=
= >∑( )0.05 0.02*0.98 0.004*0.999 0.024E = + =
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.2 g0.2 g pga given M 6.5 and M 7.9 earthquake pga given M 6.5 and M 7.9 earthquake occur?occur?
84% of M 7.9 at a distance of 20 km will cause 84% of M 7.9 at a distance of 20 km will cause ground motion that will exceed 0.2g.ground motion that will exceed 0.2g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.4
M 7.9, 20 km
0.2 0.6 0.8 PGA
frequency
median0.05 g
16%84%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance:exceedance:
Ground motion:Ground motion: 0.05g 0.2g0.05g 0.2g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.024 0.0130.024 0.013
( ) ( )2
1| ,i
iE z P Z z m rα
=
= >∑( )0.2 0.02*0.50 0.004*0.84 0.013E = + =
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What is the annual rate that ground motion will What is the annual rate that ground motion will exceed exceed 0.4 g0.4 g pga given M 6.5 and M 7.9 earthquake pga given M 6.5 and M 7.9 earthquake occur?occur?
50% of M 7.9 at a distance of 20 km will cause 50% of M 7.9 at a distance of 20 km will cause ground motion that will exceed 0.4g.ground motion that will exceed 0.4g.
Annual Rate of ExceedanceAnnual Rate of Exceedance
0.4
M 7.9, 20 km
0.2 0.6 0.8 PGA
frequency
median0.05 g
50%50%
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Annual Rate of ExceedanceAnnual Rate of Exceedance
Recall the equation for the annual rate of Recall the equation for the annual rate of exceedance:exceedance:
Ground motion:Ground motion: 0.05g 0.2g 0.4g0.05g 0.2g 0.4g
Rate of 0.05 g exceedance:Rate of 0.05 g exceedance: 0.024 0.013 0.0050.024 0.013 0.005
( ) ( )2
1| ,i
iE z P Z z m rα
=
= >∑( )0.2 0.02*0.16 0.004*0.50 0.005E = + =
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Ground motion:Ground motion: 0.05g0.05g 0.2g0.2g 0.4g0.4gFault 1:Fault 1: 0.020.02 0.010.01 0.0030.003Fault 2:Fault 2: 0.0040.004 0.0030.003 0.0020.002Rate of Ground motion exceedance:Rate of Ground motion exceedance: 0.0240.024 0.0130.013 0.0050.005
Ann
ual R
ate
grou
nd m
otio
n is
ex
ceed
ed
PGA0.001
0.01
0.1 g 0.2 g 0.3 g 0.4 g
10% probability of exceedance in 50 years
Hazard CurveHazard Curve
0.5 g
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HAZARD PRODUCTSHAZARD PRODUCTS http://http://eqhazmaps.usgs.goveqhazmaps.usgs.gov
2002 Hazard Maps - PGA-rock2% probability of exceedance in 50-years
Purple-0.3g and greaterYellow -0.1g and greater
Deaggregations