-
Broadband Nonparametric Ground-Motion Evaluation of Horizontal
Shear-Wave Fourier Spectra
2004. 11. 15presented for
OECD-NEA Workshop on seismic input motions, incorporating recent
geological studies
by
KWAN-HEE YUN*, DONG-HEE PARK (Korea Electric Power Research
Institute)JEONG-MOON SEO (Korea Atomic Energy Research
Institute)
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ContentsIntroduction
Analysis method
Data and preprocessing
Numerical validationInversion of stochastic ground-motion model
parametersGeneration of artificial datasetEvaluation of path bias
terms using synthetic data
Nonparametric inversion results
Discussion and conclusion
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IntroductionParametric method
Assume path functions– e.g. Q0fη + Geometrical spreading
(bilinear, trilinear linear segments)
Adopted in most of the previous studies due to small number of
available earthquake data
– there are wide variety of Q models reported in KoreaNeed to
verify the parametrically inverted path functions and determine the
best model to simulate strong GM models
Nonparametric methodIndependent of physical models → capable of
being used as a reference GM attenuationLarge earthquake dataset
accumulated from nation-wide seismic networksProvide additional
information of the observed data → complement the parametric
method
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Nonparametric methodY(fc)ij = Log (Horizontal Fourier Amp.)
= [E`(fc)i + F(fc)] + Site(fc)j + Lk(R)Dk(fc)
* i, j = index for source (excitation) and sitesLk(R) = linear
interpolation function for a path term Dk(fc)
Obtain a least-square solution by matrix inversion with
constraints= 0
Smoothness of Dk termsD(Rref, fc) = 0
( )c jj
Site f∑
Source Path
F(fc) = a dummy factor common to all the eqk. events
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253 shallow crustal events from 1992(‘99) to 2003 (ML >
2.0)6,203 records, 134 stationsCatalogs of earthquake source
parameters to calculate the hypocentral distances
KMA, KIGAM, ISC
Earthquake data resourcesDomestic major seismic networks
– KMA, KIGAM, KEPRI, KINS, universities, NPPsForeign seismic
networks
– KSRS Array (U.S. Air Force)– IRIS (INCN, SEO), PASSCAL (XI,
XL)– F-net (IZH), JMA (JTU), PS (TJN, PHN)
Earthquake Database
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10 1001.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mag
nitu
de
Hypocentral Distance(km)
30
25
20
15
10
5
0
0 2 4 6 8 10 12 14 16
% of occurrence
Dep
th(k
m)
KMA
KIGAM
KEPRI
KINS
KSRS
UNIV.
Foreign
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Data ProcessingPreprocessing
screening seismic recordsS wave-train windowing (5% tapering)→
Vg= 2.6-3.6km/sec used for automatic windowing at distances >
100kminstrumental correction for short-period
seismometercalculation of Fourier spectra for horizontal
acceleration components and vector summation (1024pts,
df=0.05Hz)select available frequency band (S/N > 3 - 4)→ mainly
between 2.0 ∼ 30.0 HzNo smoothingusing velocity (for low
frequency), acceleration (for high frequency) data
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Numerical validation
Nonparametric method applied to artificial dataset generated by
using inverted stochastic GM model parameters (Boore, ‘03)
Possible bias of the inverted path terms was investigated by
numerical simulation
There are more earthquake records from small earthquakes at
short distance ranges
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Inversion of stochastic GM model parameters
Parametric inversion of stochastic GM model parameters was
previously performed (’02, OECD/NEA Workshop)
Stochastic GM model parameters:Source: Brune’s omega-2 model
(’70, 71)Path: Q(f), trilinear G(R), crustal amp (=1.67 at high
frequencies)Site: site-dependent kappa (Anderson, ’04)
Simultaneous nonlinear inversion of the model parameters
performed by using the modified Levenberg-Marquardt’s method
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Inversion results
0.1 1 10100
1000
Q(f)=348f0.54
Q(f)=Q1(1+(f/0.3)eta1)/(f/0.3)2
Q1 = 168.4eta1= 2.54
Q(f)
Frequency(Hz)(a)
10 100-1.0
-0.5
0.0
0.5
(1/65)1.11(65/R)0.02
(1/65)1.11(65/117)0.02(117/R)0.5
1/R1.11
Trilinear Geo. Att. modelNormalized to 21.54km
Log1
0(G
eo(R
hyp)
)
Rhyp(km)(b)
2 3 4 51
10
100
1000
Stre
ss D
rops
(bar
s)
Mw
SD
0 50 100
0.01
0.1
Kap
pa(s
ec)
Site ID
kappa
Path Source Site
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Evaluation of path bias terms (1)Generated two types of
artificial dataset by using inverted stochastic GM model parameters
and perform nonparametric inversion
2 3 4 51
10
100
1000
Stre
ss D
rops
(bar
s)
Mw
SD
+
D/B
#1 Dkinv(M, SD, κ0)
Dkinv(M0, SD0, κ0)
D/B
#2
Inversion
+κ0 = (0.016,…,0.016)Crustal amp.(f) =0
10 100-1.5
-1.0
-0.5
0.0
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)
Fq1 Fq3 Fq5 Fq10 Fq20 Fq30
Forward
Mw=(3.5,…,3.5)SD(bars)=(50,…,50)
Exact path terms
Difference = bias!!!
Q(f)+G(R) Type 1 path terms
Type 2 path terms
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Evaluation of path bias terms (2)Calculated biases between
estimated and exact path terms
Bk = Dkinv(M, SD, κ0) - Dkinv(M0, SD0, κ0) (Bk(ref) =
0)Dkinv(M0, SD0, κ0) is considered to be exact path terms
6 frequency bands & 17 discrete distances to calculate
Di(fc)
5 10 15 20 25 30
10
100
Fq30Fq20Fq10Fq5Fq3Fq1
Hyp
ocen
tral D
ista
nce(
km)
Frequency(Hz)
FqcFqc-0.25Fqc+0.25
0.5
1.0
wei
ght
Frequency weighting function
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Calculation of path bias terms
10 100
-0.04
-0.02
0.00
0.02
0.04
fq1 fq3 fq5 fq10 fq20 fq30
Bia
s of
the
inve
rted
path
term
s (B
k)
Rhyp(km)(a)
10 100-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10 Frequency(Hz): 0.99 - 1.49
D kinv(M0,SD0,k0)
D kinv(M ,SD ,k0)
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)(b)
Bk = Dkinv(M, SD, κ0) - Dkinv(M0, SD0, κ0) (Bk(ref) = 0)
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10 100-1.5
-1.0
-0.5
0.0
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)
: ExactEstimated
Fq1 Fq3 Fq5 Fq10 Fq20 Fq30
Comparison of bias-corrected path terms with exact path
terms
10 100
-1.0
-0.5
0.0
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)
fq1 fq3 fq5 fq10 fq20 fq30
Dkinv(M, SD, κ0) terms
Correction with Bk
Normalization
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10 100
-4
-3
-2
-1
0
1
Freqeuency(Hz): 2.97 - 3.46
Mw 2.2-2.5 2.8-3.1 3.4-3.7 4.0-4.3 4.6-4.9
Mw: 2.5-2.8: 3.1-3.4: 3.7-4.0: 4.3-4.6
Freqeuency(Hz): 2.97 - 3.46
log(
FS(c
m/s
ec))
Rhyp(km)10 100
-4
-3
-2
-1
0
1
Rhyp(km)
An example of raw data of Fourier acceleration spectrum between
2.97-3.46Hz according to the moment magnitude ranges
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Nonparametric inversion resultsTrilinear type of change is
observed Avg. of Log standard deviation = 0.024 for fq3
10 100-2.0
-1.5
-1.0
-0.5
0.0
0.5
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)
fq1 fq3 fq5 fq10 fq20 fq30
10 100-1.5
-1.0
-0.5
0.0
0.5
1.0
Bootstrap result for fq3
Rhyp(km)
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200 250 300 350 4000.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1
2
3
4
A
B
C
D
a
b
c
d
Q(f)=168(1+(f/0.3)2.55)/(f/0.3)2
fc(Hz) 12.101.24 14.081.73 16.052.23 18.033.22 1 20.004.20 A
21.985.19 a 23.956.18 25.937.17 27.908.15 29.889.14 32.8410.13
35.8011.12 38.77
slope=1/Q
-(D(r)
-0.5
*log(
1/r))
*Vs/
(pi*f
q*lo
g(e)
) Vs=
3.5k
m/s
Hypocentral distance (km)
0.1 1 10
103
Qua
lity F
acto
r
Frequncy(Hz)
3-30Hz
Comparison of Q(f) function with nonparametrically inverted Q’s
values for R>200km where R-0.5 attenuation is justified
Parametrically inverted Q(f) function validated for Fq’s between
3-30Hz
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10 100-1.0
-0.5
0.0
0.5
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)(a)
Nonpar. fq1 fq3 fq5 fq10 fq20 fq30
Parametric path functions
Comparison with two types of parametric results“Par. path
function” = Q(f) + G(R) “Par. path residuals” = Obs. F.S. – Source
(Mw,SD,Rref) – Site (kappa)
10 100-1.0
-0.5
0.0
0.5
1
2
3
45
6
7
8
9
10
11
12
Parametric path residual
fq1 fq3 fq5 fq10 fq20
1 fq30
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)(b)
Nonpar.
fq1 fq3 fq5 fq10 fq20 fq30
Good agreement!!For Fq > 3Hz and R > 100km
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Par. path residual better fits the nonparametric results
Par. path function is overestimated for short distance ranges
less than 100km for fq1
Abrupt increase of nonparametric path terms and par. path
residuals observed at greater than 200km
presence of more than two phases
Explains the misfit for the frequencies below 3Hz
10 100-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4For fq1
Nonparametric Path functions Par. path residual
Geo. spreading fn. R-1.3,R-1.5,R-2.0
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
Rhyp(km)( )
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Steeper than R-1 observed for short distances less than 50km
Less rapid attenuation for higher Fq’s than for lower Fq’s.
reverse of what par. path functionpredicts
3
4
5
6
20 30 40 50 60 70 8090100-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10Geo. spreading fn.
R-1.3,R-1.5,R-2.0
fq1 fq3
with error bar fq5 fq10 fq20
1 fq30
Rhyp(km)
log(
FS)+
log(
Rhy
p/21
.54)
(cm
/sec
)
20 30 40 50 60 70 80 90 100
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8Anelastic function Q(f)=217f0.7 used
Geo
met
rical
Slo
pe (=
R-S
lope
)
Rhyp(km)
fq1 fq3 fq5 fq10 fq20 fq30 Mean
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Conclusion(1)
The inverted path terms with the bias correction show three
distinct linear regions roughly divided by hypocentral distances of
65km and 117km.
The use of parametrically inverted Q functions was validated
over the frequency band between 3-30Hz and distance range beyond
200km.
Mixing of more than two wave phases was found in the low
frequency band within the time window for spectral calculation
beyond 200km in hypocentral distances.
Parametrically estimated Q at 1Hz is overestimated because of
fitting to the spectral data at the far distance range.
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Conclusion(2)Steep attenuation comparable to R-1.3 geometrical
spreading is found at distances less than 50km.
Unresolved phenomena is found that implies possible change of Q
according to distances and different geometrical spreading
according to the frequencies at short distances less than
100km.
Parametric and nonparametric method should be used in
complementary way to reduce the uncertainty in simulating strong
GM