Broadband Nonparametric Ground-Motion Evaluation of ......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(Rhyp/21.54)

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)

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

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

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

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

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

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

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

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

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

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

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

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)

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)


Dkinv(M, SD, κ0) terms

Correction with Bk

Normalization

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

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)


10 100-1.5

-1.0

-0.5

0.0

0.5

1.0

Bootstrap result for fq3

Rhyp(km)

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

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.


Good agreement!!For Fq > 3Hz and R > 100km

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)( )

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

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.

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

Documents

Broadband Nonparametric Ground-Motion Evaluation of ......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(Rhyp/21.54)