Inversion of earthquake slip distributions using synthetic aperture ...
Simulation of Synthetic Ground Motionsfor Specified Earthquake and Site Characteristics
Transcript of Simulation of Synthetic Ground Motionsfor Specified Earthquake and Site Characteristics
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Sanaz Rezaeian (Doctoral Candidate)
Armen Der Kiureghian (PI)
University of California, Berkeley
Simulation of Synthetic Ground Motions
for
Specified Earthquake and Site Characteristics
Sponsor: State of California through Transportation Systems Research Program of
Pacific Earthquake Engineering Research (PEER) Center
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Our Goal: Earthquake and site characteristics Suite of simulated design time-histories
(F, M, Rrup, Vs30 ,)
Objective:
F: Faulting mechanismM: Moment magnitude
Rrup: Closest distance to ruptured area
Vs30: Shear wave velocity of top 30mControlling Fault
Site
What we have done so far:
Developed a stochastic site-based model for far-field strong ground motions. Developed empirical predictive equations for the model parameters. Compared elastic response spectra (median and variability) to NGA relations.Ongoing activity and what we plan to accomplish by May 2010:
Simulate orthogonal horizontal ground motion components. Extend the model to near-field ground motions. Scrutinize the simulated motions for inelastic structural responses.
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Ground Motion Model:
0 5 10 15 200
Acceleration
High-pass Filtering
0 5 10 15 200
Time, sec
Unit-variance process
Controls spectral nonstationarity
0 5 10 15 200
Time, sec
Time modulating function
Controls temporal nonstationarity
0 5 10 15 200
Time, sec
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Ground Motion Model Parameters:
t0 tn
Let:
0 tn
0 tn
: Arias intensity
: Time at the middle of strong shaking
: Effective duration
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Ground Motion Model Parameters:
t0 tn
Let:
0 tn
0 tn
: Time at the middle of strong shaking
: Effective duration
If the model parameters are given, time-histories can be simulated.
: Arias intensity
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Simulate a suite of ground motions for a given design scenario:
Simulate a given accelerogram:Applications in Practice:
GivenEarthquake/Site characteristics
(design scenario)
Generateseveral possible sets of
model parameters
Simulations0 5 10 15 20 25 30 35 40 45 50
-0.1
0
0.1
-0.1
0
0.1
0.1
-0.1
0
modelformulation
F, M, Rrup, Vs30
predictiveequations
Ia, tmid, D5-95
mid, ,
Matchstatistical
characteristicsRepresenting:
IntensityFrequencyBandwidth
Identifymodel parameters
mid, ,
Ia, tmid, D5-95Recorded0 40
-0.25
0
0.15
Time, secAcceleration,g
modelformulation
Simulations
-0.25
0
0.15
0-0.25
0
0.15
-0.25
0
0.15
40
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Simulate a suite of ground motions for a given design scenario:
Simulate a given accelerogram:Applications in Practice:
GivenEarthquake/Site characteristics
(design scenario)
Generateseveral possible sets of
model parameters
Simulations0 5 10 15 20 25 30 35 40 45 50
-0.1
0
0.1
-0.1
0
0.1
0.1
-0.1
0
modelformulation
F, M, Rrup, Vs30
predictiveequations
Ia, tmid, D5-95Regression
Predictor variables
Response variables
Done for many records to get observational datafor predictor and response variables
mid, ,
Matchstatistical
characteristicsRepresenting:
IntensityFrequencyBandwidth
Identifymodel parameters
mid, ,
Ia, tmid, D5-95Recorded0 40
-0.25
0
0.15
Time, secAcceleration,g
modelformulation
Simulations
-0.25
0
0.15
0-0.25
0
0.15
-0.25
0
0.15
40
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Ground Motion Database (far-field):
Earthquake #ofrecords
1 ImperialValley 22 Victoria,Mexico 2
3 Morganhill 10
4 Landers 4
5 BigBear 10
6 Kobe,Japan 4
7 Kocaeli,Turkey 4
8 Duzce,Turkey 29 Sitka,Alaska 2
10 Manjil,Iran 2
11 HectorMine 16
12 Denali,Alaska 4
13 SanFernando 14
14 Tabas,Iran 215 Coalinga 2
16 NPalmSprings 12
17 LomaPrieta 28
18 Northridge 38
19 ChiChi,Taiwan 48
Strike-slip
Reverse Momen
tMagnitude
Rrup , km
10 20 30 40 50 60 70 80 90 100
8.0
7.5
7.0
6.5
6.0
Strike-slipReverse
Vs30 > 600 m/sec
Two horizontal components
Shallow crustal earthquakes in
tectonically active regions
Total: 206Accelerograms
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Predictive Equations (Regression):
Independent
Normally-distributed
errors
Observed DataFitted PDF
NormalizedFrequency(Total:206)
5 10 15 20 25 30 35 40 450
0.02
0.04
0.06
-2 -1.5 -1 -0.5 0 0.50
1
2
3
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
0 5 10 15 20 250
0.04
0.08
0.12
0.16
0 5 10 15 20 25 30 35 400
0.02
0.04
0.06
0.08
ln(Ia, sec.g) D5-95, sec
tmid, sec
'/(2), Hz/sec mid/(2), Hz
-7.5 -5.5 -3.5 -1.5 00
0.1
0.2
0.3
0.4Normal Beta Beta
Gamma Two-SidedExponential
Beta
Distributions assigned to the model parameters:
Regression model (for jth earthquake and kth record of that earthquake):
Predicted mean
conditioned on
earthquake and site characteristics
Model parameter
transformed to the
standard normal space
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Standard deviation of
1.844 0.071 2.944 1.356 0.265 0.27 0.59 0.65
6.195 0.703 6.792 0.219 0.523 0.46 0.57 0.73
5.011 0.345 4.638 0.348 0.185 0.51 0.41 0.66
2.253 0.081 1.810 0.211 0.012 0.69 0.72 1.00
2.489 0.044 2.408 0.065 0.081 0.13 0.95 0.96
0.258 0.477 0.905 0.289 0.316 0.68 0.76 1.02
Regression Results (Predictive Equations):
if
if
Maximum Likelihood Estimation:
Formulation:
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Regression Results (Correlations):
1 0.36 0.01 0.15 0.13 0.01
1 0.67 0.13 0.16 0.20
1 0.28 0.20 0.22
1 0.20 0.28
1 0.01
1
Transformed model parameters:
Symmetric
(given the earthquake and site characteristics)
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F = 1 (Reverse)M = 7.35
Rrup =14 km
VS30 = 660 m/sec
Example 1 : Acceleration
4 simulated motions and 1 real recording for the given design scenario:
Acceleration,g
Time, sec
0 5 10 15 20 25 30 35
-0.2
0
0.2
0 5 10 15 20 25 30 35-0.2
0
0.2
0 5 10 15 20 25 30 35-0.1
0
0.1
0 5 10 15 20 25 30 35-0.1
0
0.1
0 5 10 15 20 25 30 35
-0.1
0
0.1
Simulated
Recorded
Simulated
Simulated
Simulated
Realizaonsofmodelparameters:
0.01217.236.276.880.010.14
0.14512.306.785.900.120.26
0.05514.227.224.480.160.38
0.01414.076.3110.750.240.26
0.03614.878.324.360.150.03
Iasec.g
D5-95sec
tmidsec
/(2)
Hz/secmid/(2)
Hz
(1978 Tabas at Dayhook)
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F = 1 (Reverse)M = 7.35
Rrup =14 km
VS30 = 660 m/sec
4 simulated motions and 1 real recording for the given design scenario:
Velocity,m/sec
Time, sec
0 5 10 15 20 25 30 35
-0.2
0
0.2
0 5 10 15 20 25 30 35-0.2
0
0.2
0 5 10 15 20 25 30 35-0.05
0
0.05
0 5 10 15 20 25 30 35-0.1
0
0.1
0 5 10 15 20 25 30 35-0.1
0
0.1
Example 1 : Velocity
Simulated
Recorded
Simulated
Simulated
Simulated
Realizaonsofmodelparameters:
0.01217.236.276.880.010.14
0.14512.306.785.900.120.26
0.05514.227.224.480.160.38
0.01414.076.3110.750.240.26
0.03614.878.324.360.150.03
Iasec.g
D5-95sec
tmidsec
/(2)
Hz/secmid/(2)
Hz
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F = 1 (Reverse)M = 7.35
Rrup =14 km
VS30 = 660 m/sec
4 simulated motions and 1 real recording for the given design scenario:
Displacement,m
Time, sec
0 5 10 15 20 25 30 35
-0.1
0
0.1
0 5 10 15 20 25 30 35
-0.1
0
0.1
0 5 10 15 20 25 30 35-0.05
0
0.05
0 5 10 15 20 25 30 35-0.05
0
0.05
0 5 10 15 20 25 30 35
-0.05
0
0.05
Example 1 : Displacement
Simulated
Recorded
Simulated
Simulated
Simulated
Realizaonsofmodelparameters:
0.01217.236.276.880.010.14
0.14512.306.785.900.120.26
0.05514.227.224.480.160.38
0.01414.076.3110.750.240.26
0.03614.878.324.360.150.03
Iasec.g
D5-95sec
tmidsec
/(2)
Hz/secmid/(2)
Hz
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Realizaonsofmodelparameters:
0.14512.306.785.900120.26
0.14512.799.867.480.520.13
0.14522.1116.248.050.090.12
0.1458.145.317.340.020.30
0.14511.0110.304.430.120.29
Example 2 :
F = 1 (Reverse)M = 7.35
Rrup =14 km
VS30 = 660 m/sec
If desired, a fixed value may be assigned to one or more of the model parameters:
Acceleration,g
Time, sec
0 5 10 15 20 25 30 35 40-0.5
0
0.5
0 5 10 15 20 25 30 35 40-0.5
0
0.5
0 5 10 15 20 25 30 35 40-0.5
0
0.5
-0.5
0
0.5
0 5 10 15 20 25 30 35 40-0.5
0
0.50 5 10 15 20 25 30 35 40
Recorded
Simulated
Simulated
Simulated
Simulated
Iasec.g
D5-95sec
tmidsec
/(2)
Hz/secmid/(2)
Hz
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Example 3 : Response Spectrum (5% damped)
2 horizontal components of a recorded motion (1994 Northridge at LA Wonderland Ave)
Vs.
50 simulated motions
Corresponding to earthquake and site characteristics:
Period, sec
De
format
ion
Response
Spec
trum,
m
10-1 10010-4
10-3
10-2
10-1
100
510010-1
10010-3
10-2
10-1
100
101
5100
Period, sec
Pseu
do-Accel
era
tion
Response
Spec
trum,
g
Recorded
Simulated
F = 1 (Reverse)
M = 6.69
Rrup = 20.3 km
VS30 = 1223 m/sec
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Comparison with NGA Models:
10-3
10-2
10-1
100
M=6.0, R=20km
Campbell-Bozorgnia (z2.5 = 1km)
Abrahamson-Silva (z1.0 = 34m)
Chiou-Youngs (z1.0 = 24m)
Boore-Atkinson
5%
Damp
edPseu
do-Acce
lera
tion
Resp
onse
Spec
trum,
g
10-3
10-2
10-1
100
M=7.0, R=20km M=7.0, R=20km
M=7.0, R=10km
Period, sec
0.1 1.0
M=7.0, R=40km
5.0
F = 0 (Strike-Slip)
Vs30 = 760 m/sec
Avg NGA 500 Simulations
Median
Median 1 logarithmic stdv.
Median +1 logarithmic stdv.
NGA Parameters: Rupture width = 20kmRupture depth = 1km
Selected NGA Models:
Note:Models based on different subsets of NGA database.
Observe:
Except for M=6.0 (lower bound of database),
deviations are much smaller than the variability
present in the NGA prediction equations.
Synthetics are in close agreement with NGA.
Period, sec
10-3
10-2
10-1
10
0
M=8.0, R=20km
0.1 1.0 5.0
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Current & Future Developments:
Simulating correlated orthogonal horizontal ground motion components.Component 1:
Component 2:
Motions in the database are rotated to the principal axes so that w1() and w2() are statistically independent.
Model is fitted to the rotated database to estimate correlations: 1,2 and 1,2
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Current & Future Developments:
Simulating near-field ground motions.Separately model and superimpose:
1) The directivity pulse
Long period pulse in the velocity time-series of thefault-normalcomponent.
Develop prediction equations for characteristics of the pulse in terms of earthquake/site parameters.
Collaboration with Jack Baker:
Using wavelet analysis, directivity pulse extracted from a database of near-field motions,
this database will be used to develop prediction equations.
2) The fling step
Permanent displacement may exist in thefault-parallelcomponent.
Incorporate the available seismological models (e.g., Somerville 1998, Abrahamson 2001).
3) The residue motion
The total motion minus the directivity pulse and the fling step.
Model by a modified version of the far-field stochastic ground motion process.
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Current & Future Developments:
Scrutinize the simulated motions for inelastic structural responses.Compare inelastic response spectra (for given ductility ratios) of synthetic motions with real recordings and
existing prediction equations (e.g., Bozorgnia et. al., 2010).
Case Study:
Compare inelastic response of a multi-degree-of-freedom structure to simulated and recorded motions.
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Related Publications:
Rezaeian, S. and A. Der Kiureghian,
"A stochastic ground motion model with separable temporal and spectral nonstationarities,"
Earthquake Engineering and Structural Dynamics, July 2008, Vol. 37, pp. 1565-1584.
Rezaeian, S. and A. Der Kiureghian,
"Simulation of synthetic ground motions for specified earthquake and site characteristics,"
Earthquake Engineering and Structural Dynamics, 2009. Submitted.
MATLAB software to be made available
Current abilities:
Fitting the stochastic model to a target accelerogram.Simulating far-field strong motions on firm-ground for specified F, M, Rrup, Vs30.
Will be added by May 2010:
Two component simulation.
Near-field simulation.
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Thank You
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Cumulative energy
Cumulative number of zero-levelup crossings a measure of
dominant frequency
Cumulative number of positive minima andnegative maxima a measure of bandwidth
Features of target accelerogram
0 5 10 15 20 25 30 35 4000.0050.01
0.0150.02
0.0250.03
Cumulativeenergy
0 5 10 15 20 25 30 35 40020406080100120140160
Cumulativenumberofzero-levelup
-crossin
gs
Time, sec
0 5 10 15 20 25 30 35 40020406080100
120140
Cumulativenumberofnegativemaxima
andpositiveminima
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Response spectrum
Discretizedwhite noise(input)
Unit-variance process withspectral nonstationarity
Lineartime-varyingfilter
Fully non-stationarityprocess
Time modulation
High-passfilter
Simulatedground motion(output)
Post-processing is needed for long
-period range. A critically damped
oscillator is used as a high-pass filter.
corner frequency
10 100 10110-310101010
T (sec)
A(g)
-1
-1
-2
0
1
After high-pass filtering
10 100 101T (sec)
-110-310101010
A(g)
-1
-2
0
1
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Acceleration,g
Recorded motion
0 5 10 15 20 25 30 35 40-0.2-0.1
00.10.2
0 5 10 15 20 25 30 35 40-0.20
0.2
0 5 10 15 20 25 30 35 40-0.2-0.1
00.10.2
Time (sec)
Simulation
Simulation
Northridge earthquake
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Acceleration,g
Recorded motion
Time (sec)
Simulation
Simulation
Kobe earthquake