simulation of synthetic ground motions for specified earthquake

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

Our Goal: Earthquake and site characteristics Suite of simulated design time-histories (F, M, Rrup, Vs30 ,…)

Objective:

F: Faulting mechanism M: Moment magnitude

…

Rrup: Closest distance to ruptured area

Vs30: Shear wave velocity of top 30m Controlling 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.

Ground Motion Model:

0 5 10 15 20

0

Acceleration

High-pass Filtering

0 5 10 15 20

0

Time, sec

Unit-variance process

Controls spectral nonstationarity

0 5 10 15 20

0

Time, sec

Time modulating function

Controls temporal nonstationarity

0 5 10 15 20

0

Time, sec

Ground Motion Model Parameters:

t0 tn

Let:

0 tn

0 tn

: Arias intensity

: Time at the middle of strong shaking

: Effective duration

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

  Simulate a suite of ground motions for a given design scenario:

  Simulate a given accelerogram:

Applications in Practice:

Given Earthquake/Site characteristics

(design scenario)

Generate several possible sets of

model parameters

Simulations … 0 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

…

model formulation

F, M, Rrup, Vs30

predictive equations

Ia, tmid, D5-95 ωmid, ω’ , ζ

Match statistical

characteristics Representing:

•  Intensity •  Frequency •  Bandwidth

Identify model parameters

ωmid, ω’ , ζ Ia, tmid, D5-95 Recorded

0 40 -0.25

0

0.15

Time, sec Acc

eler

atio

n, g

model formulation

Simulations …

…

-0.25

0

0.15

0 -0.25

0

0.15

-0.25

0

0.15

40

  Simulate a suite of ground motions for a given design scenario:

  Simulate a given accelerogram:

Applications in Practice:

Given Earthquake/Site characteristics

(design scenario)

Generate several possible sets of

model parameters

Simulations … 0 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

…

model formulation

F, M, Rrup, Vs30

predictive equations

Ia, tmid, D5-95 Regression

Predictor variables

Response variables

Done for many records to get observational data for predictor and response variables

ωmid, ω’ , ζ

Match statistical

characteristics Representing:

•  Intensity •  Frequency •  Bandwidth

Identify model parameters

ωmid, ω’ , ζ Ia, tmid, D5-95 Recorded

0 40 -0.25

0

0.15

Time, sec Acc

eler

atio

n, g

model formulation

Simulations …

…

-0.25

0

0.15

0 -0.25

0

0.15

-0.25

0

0.15

40

Ground Motion Database (far-field):

Earthquake #ofrecords1 ImperialValley 2

2 Victoria,Mexico 2

3 Morganhill 10

4 Landers 4

5 BigBear 10

6 Kobe,Japan 4

7 Kocaeli,Turkey 4

8 Duzce,Turkey 2

9 Sitka,Alaska 2

10 Manjil,Iran 2

11 HectorMine 16

12 Denali,Alaska 4

13 SanFernando 14

14 Tabas,Iran 2

15 Coalinga 2

16 NPalmSprings 12

17 LomaPrieta 28

18 Northridge 38

19 ChiChi,Taiwan 48

Strike-slip

Reverse Mom

ent M

agni

tude

Rrup , km 10 20 30 40 50 60 70 80 90 100

8.0

7.5

7.0

6.5

6.0

Strike-slip Reverse

Vs30 > 600 m/sec

Two horizontal components

Shallow crustal earthquakes in tectonically active regions

Total: 206 Accelerograms

Predictive Equations (Regression):

Independent Normally-distributed

errors

Observed Data Fitted PDF

Norm

alize

d Fr

eque

ncy

(Tot

al:2

06)

5 10 15 20 25 30 35 40 45 0

0.02

0.04

0.06

-2 -1.5 -1 -0.5 0 0.5 0

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

1

2

3

4

0 5 10 15 20 25 0

0.04

0.08

0.12

0.16

0 5 10 15 20 25 30 35 40 0

0.02

0.04

0.06

0.08

ln(Ia, sec.g) D5-95, sec tmid, sec

ω'/(2π), Hz/sec ζ ωmid/(2π), Hz

-7.5 -5.5 -3.5 -1.5 0 0

0.1

0.2

0.3

0.4 Normal Beta Beta

Gamma Two-Sided Exponential

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 θ transformed to the

standard normal space

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:

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)

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:

Acce

lera

tion,

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

RealizaVonsofmodelparameters:

0.01217.236.276.88‐0.010.14

0.14512.306.785.900.120.26

0.05514.227.224.48‐0.160.38

0.01414.076.3110.75‐0.240.26

0.03614.878.324.36‐0.150.03

Ia sec.g

D5-95 sec

tmid sec

ω’/(2π) Hz/sec

ζ ωmid /(2π) Hz

(1978 Tabas at Dayhook)



Velo

city,

m/s

ec

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


0.01217.236.276.88‐0.010.14

0.14512.306.785.900.120.26

0.05514.227.224.48‐0.160.38

0.01414.076.3110.75‐0.240.26

0.03614.878.324.36‐0.150.03

Ia sec.g

D5-95 sec

tmid sec

ω’/(2π) Hz/sec

ζ ωmid /(2π) Hz



Disp

lace

men

t, 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


0.01217.236.276.88‐0.010.14

0.14512.306.785.900.120.26

0.05514.227.224.48‐0.160.38

0.01414.076.3110.75‐0.240.26

0.03614.878.324.36‐0.150.03

Ia sec.g

D5-95 sec

tmid sec

ω’/(2π) Hz/sec

ζ ωmid /(2π) Hz


0.14512.306.785.900120.26

0.14512.799.867.48‐0.520.13

0.14522.1116.248.05‐0.090.12

0.1458.145.317.34‐0.020.30

0.14511.0110.304.430.120.29

Example 2 :


If desired, a fixed value may be assigned to one or more of the model parameters:

Acce

lera

tion,

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

0.5 0 5 10 15 20 25 30 35 40

Recorded

Simulated

Simulated

Simulated

Simulated

Ia sec.g

D5-95 sec

tmid sec

ω’/(2π) Hz/sec

ζ ωmid /(2π) Hz

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

Def

orm

atio

n R

espo

nse

Spec

trum

, m

10 -1 10 0 10 -4

10 -3

10 -2

10 -1

10 0

5×10 0 10 -1 10 0 10 -3

10 -2

10 -1

10 0

10 1

5×10 0 Period, sec

Pseu

do-A

ccel

erat

ion

Res

pons

e Sp

ectru

m, g

Recorded Simulated

F = 1 (Reverse) M = 6.69 Rrup = 20.3 km VS30 = 1223 m/sec

Comparison with NGA Models:

10 -3

10 -2

10 -1

10 0

M=6.0, R=20km

Campbell-Bozorgnia (z2.5 = 1km) Abrahamson-Silva (z1.0 = 34m) Chiou-Youngs (z1.0 = 24m) Boore-Atkinson

5% D

ampe

d Ps

eudo

-Acc

eler

atio

n R

espo

nse

Spec

trum

, g

10 -3

10 -2

10 -1

10 0

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 = 20km Rupture 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

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(τ) and w2(τ) are statistically independent.

Model is fitted to the rotated database to estimate correlations: ρα1, α2 and ρλ1, λ2

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 the fault-normal component. 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 the fault-parallel component. 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.

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.

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.

Thank You

  Cumulative energy

  Cumulative number of zero-level up crossings – a measure of dominant frequency

  Cumulative number of positive minima and negative maxima – a measure of bandwidth

Features of target accelerogram

0 5 10 15 20 25 30 35 40 0

0.005

0.01

0.015

0.02

0.025

0.03

Cum

ulat

ive

ener

gy

0 5 10 15 20 25 30 35 40 0

20

40

60

80

100

120

140 160

Cum

ulat

ive

num

ber o

f zer

o - level

up - cro

ssin

gs

Time, sec

0 5 10 15 20 25 30 35 40 0

20

40

60

80

100

120

140

Cum

ulat

ive n

umbe

r of n

egat

ive m

axim

a a

nd p

ositiv

e m

inim

a

Response spectrum

Discretized white noise (input)

Unit-variance process with spectral nonstationarity

Linear time-varying filter

Fully non-stationarity process

Time modulation

High-pass filter

Simulated ground motion (output)

Post-processing is needed for long-period range. A critically damped oscillator is used as a high-pass filter.

corner frequency

10 10 0 10 1 10 -3

10

10

10

10

T (sec)

A(g)

-1

-1

-2

0

1

After high-pass filtering

10 10 0 10 1

T (sec) -1

10 -3

10

10

10

10

A(g)

-1

-2

0

1

Acce

lera

tion,

g

Recorded motion

0 5 10 15 20 25 30 35 40 -0.2

-0.1

0

0.1

0.2

0 5 10 15 20 25 30 35 40 -0.2

0

0.2

0 5 10 15 20 25 30 35 40 -0.2

-0.1

0

0.1

0.2

Time (sec)

Simulation

Simulation

Northridge earthquake

Acce

lera

tion,

g

Recorded motion

Time (sec)

Simulation

Simulation

Kobe earthquake

simulation of synthetic ground motions for specified earthquake

Documents