UPDATING FRAMEWORK FOR SITE-SPECIFIC
ATTENUATION RELATION OF SEISMICGROUND MOTION IN THAILAND
Poolcharuansin Kannika ∗MEE08162

Supervisor: Tsuyoshi TAKADA∗∗ABSTRACT
We propose the attenuation relations for peak ground acceleration (PGA) and 5% damped spectral
acceleration (Sa) applicable to the CMMT site which is located on rock. The CMMT site is located in
Chiang Mai, the northern part of Thailand. Thailand has only a few ground motion data and most ofpeak ground acceleration are smaller than 1 gal. To overcome this difficulty, a Bayesian update
technique was used to construct the attenuation relations for Thailand based on a past attenuation
relation proposed by Idriss (1993). In this study, we added a correction term (site effect term) anderror term to the Idriss attenuation relation using the Bayesian update technique. From the comparisonof the prediction by the Idriss attenuation relation and the observed data, we found that the Idriss
attenuation relation overestimates PGA but underestimates Sa. The prediction from the updated
attenuation relation for PGA and Sa proposed by this study is much closer to the observations thanthose by the Idriss attenuation relation.
Keywords: Attenuation relation, Bayesian updating, Site-specific.

1. INTRODUCTION
Thailand does not have an attenuation relation constructed by Thai data and uses attenuation relations
made by data of seismic prone countries such as Japan, USA and etc. Many researchers in Thailand
tried to find a suitable attenuation model for Thailand from Japanese and the United States attenuation
relations. Among 18 attenuation relations, Idriss (1993) examined difference between attenuation
equations and observed data by using the square root of mean square (RMS). It was found that theattenuation relation proposed by Idriss (1993) was the most suitable model for Thailand (Charoenyuth,2007).
Thailand has only a few ground motion data and most of peak ground acceleration aresmaller than 1 gal. Therefore, it is difficult to make attenuation relation with Thailand data by usingclassical statistics. The classical statistics can make attenuation relation by regression analysis of large
data set, while Bayesian statistics can make attenuation relation by updating existing attenuation
relation with a small number of ground motion data.

2. DATAThe ground motion data used in this study have been recorded at the CMMT station from the seismic
network of Thai Meteorological Department (TMD); they are 111 components of strong motion dataof 37 earthquakes with sampling rate 100 Hz from 2006 to 2008. The moment magnitudes of theevents are larger than 4. The rupture distance is within 2600 km.
∗

Meteorologist, Seismological Bureau, Thai Meteorological Department, Thailand.
Professor, Department of Architecture, Graduate School of Engineering, University of Tokyo, Japan.

∗∗1

We used TMD earthquake catalog (events in Thailand and adjacent areas), Harvard
Centroid Moment Tensor (CMT) catalog (2006-2009) and the catalog of United States Geological
Survey (USGS) which were downloaded from their websites. We selected earthquakes that occurred
between -8° to 32° N in latitude and 90°E to 110°E in longitude whose magnitudes are in the range
from 4.5 to 9.0. Most of events, 33 of 37, are included in the CMT catalog, while the information forthe other events were taken from TMD and PDE-USGS catalogs.
Figure 1 shows the location of the CMMT station. Figure
1 also shows the focal mechanisms from the Havard CMT
catalog, epicenters from the TMD catalog (red circles),and those from the PDE-USGS catalog (yellow circles).
Waveform data of the TMD network (SEED format) areconverted to SAC format by using the program rdseedv4.8
developed by Incorporated Research Institutions for
Seismology (IRIS). This software was downloaded fromthe IRIS website. Then we use a set of Matlab subroutines
named MatSAC that read and write SAC data in Matlab.
These Matlab subroutines are developed by Dr. Zhigang
Peng from Georgia Institute of Technology School ofEarth and Atmospheric Sciences. This Matlab subroutines
were downloaded from their website. We applied the band
pass filter with corner frequency of 0.1-20 Hz and thenused Bayesian Matlab code written by Wang and Takada(2006) to update attenuation relation of PGA and Sa
Figure 1. The focal mechanisms
proposed by Idriss (1993).
and epicenter of 37 events usedin this study
3. SITE-SPECIFIC ATTENUATION RELATION BASED ON BAYESIAN STATISTICS
Bayes’ Theorem is a theorem to obtain a posterior probability reflecting the fact that new data areobserved.
(1)f (θ | y ) = cL(θ | y ) p (θ )where θ is an unknown estimator (random variable), y is observed data, c is normalizing factor,p(θ ) is prior distribution associated with θ before new data are observed, L(θ | y ) is likelihood
function and f (θ | y ) is posterior distribution associated with after new data is observed.
3.1. Prior distribution of θ
The prior distribution can be used to express any subjective belief which exists before obtaining new
observed data. We know little about θ (non-informative case) for Thailand and we assume
independence between site effect (s) and variance of error ( σ ε2 ). Using Jeffrey’s rule, it is shown that1
non-informative prior for a parameter s is locally uniform andp (σ ε2 ) α 2 for σ ε2 . Therefore,σεthe non-informative prior isp( s, σ ε2 ) α

2

1

σ ε2

(2)

3.2. Likelihood function
For an inexact model in the following eq. 3, a random correction term γ k has to be added to maintainthe equality for the k-th observation among n observations in the specified observatory.

yk = s + fˆk (m, r ,..) + γ k

k=1,2,…,n(3)

where yk is predicted ground motion, s is site factor, fˆk ( m, r ,..) is median of past attenuation
relation proposed by Idriss (1993) and γ k accounts for the model error and measurement error. If themeasurement error for a subset of the variables is judged to be small, the corresponding measured
values can be considered to represent the true values. Often it is not possible to distinguish the two
errors and it is assumed to be normal distribution with zero mean and variance of error ( σ ε2 ). The
following likelihood function is obtained.
2⎧⎫⎪ 1 ⎡⎢ n ( yi − gˆ i ( mi , ri ,...) − s ) ⎤⎥ ⎪2
2 −n / 2(4)
exp ⎨− ∑L ( s , σ ε ) α (σ ε )
⎬
σ ε2
⎥⎪
⎪⎩ 2 ⎢⎣ i =1⎦⎭
Defining the logarithmic deviation as the difference between the log of the observation and that of thevalue predicted from the past attenuation relation ε = y − fˆ (m, r ) and expanding the sum in the

(

)

1 n 2
∑ ε k , where mε isn k =1is the sample variance of the logarithmic deviations ε k . The likelihood canargument of the exponential function, and taking into consideration sε2 + mε2 =the sample mean and sε2
be written as

L ( s , σ ε ) α (σ ε )2 − n /2

2⎧⎪ 1 ⎡ ( s − m )2 + s 2 ⎤ ⎫⎪εεexp ⎨− ⎢⎥⎬2
σε n⎪⎩ 2 ⎣⎢⎦⎥ ⎭⎪(5)

3.3. Posterior Distribution
The marginal density of σ ε2 , f (σ ε2 ) is obtained by multiplying the likelihood function with the priordensity p ( s, σ ε2 ) and dividing by the conditional PDF f ( s σ ε2 )f (σ ε ) =2

f ( s, σ ε2 )f ( s / σ ε2 )∝L ( s, σ ε2 ) p ( s, σ ε2 )f ( s / σ ε2 )(6)

One option for model identification is to use point estimates of the parameters θ . The mean estimatesof parameters are adopted herein, so that the point estimators of s and σ ε2 ares = E [ s ] = mεσ ε2 = E ⎡⎣σ ε2 ⎤⎦ =

nsε2
n−3

(7)
(8)

4. PROPOSED ATTENUATION RELATION FOR SITE CMMT
4.1 Proposed Attenuation Relation of PGA for CMMT Site
Bayesian theorem can make attenuation relation for PGA by updating attenuation relation for PGA
proposed by Idriss (1993) with 37 observed data from site CMMT. The equation is as follows:3ln Y = [C1 + exp(C2 + C3 M )] − [ exp(C4 + C5 M )] ln(rrup + 20) + 0.2 F + S + ε(9)where Y is horizontal PGA (g), M is local magnitude for M≤6 and surface wave magnitude M > 6(in essence, M represents moment magnitude), rrup is shortest distance to the rupture plane (km),F is fault mechanism such that F=0 for strike slip, 0.5 for oblique and 1 for reverse, ε is an error term
(random variable), The mean of deviation E[σε] = 1.12, S is the mean of site factor term E[θ] = -2.78.
C1 = -0.150, C2 = 2.261, C3 = -0.083, C4 = 1.602 and C5 = -0.142 for M ≤ 6.0
C1 = -0.050, C2 = 3.477, C3 = -0.284, C4 = 2.475 and C5= -0.286 for M > 6.0
The left panel of Fig. 2 shows the comparison between the original Idriss attenuation curve of PGA
and the observed PGA and the right panel of Fig.2 shows the comparison between the updated Idriss
attenuation curve (this study) of PGA and the observed PGA and the two dashed curves represent theuncertainty of this attenuation relation. It can be seen that the prediction of the updated attenuation
relation for PGA (this study) is closer to the observed PGA than the Idriss attenuation relation.

Figure 2. The comparison of the attenuation relation for PGA of the original Idriss and this study tothe observed PGA for the earthquake (Source : TMD) occurred on 19 August 2007 (time 11:17:02(UTC), the epicenter at Thailand-Myanmar boarder, Magnitude 4.0, rupture distance 117 km andHorizontal PGA 0.2 gal).
4.2. Proposed Attenuation Relation of Sa for CMMT Site
The Bayesian theorem can make attenuation relation for Sa by updating the attenuation relation for Sa
proposed by Idriss (1993) with 37 observed data from site CMMT. The equation is as follows:ln (Y ) = [α 0 + exp(α1 + α 2 M ) ] + [ β 0 − exp( β1 + β 2 M ) ] ln(rrup + 20) + 0.2 F + S + ε(10)where Y is spectral acceleration. The variables M, rrup, F, S and ε in this equation have the same
meaning with eq. 9. The variables S and ε for each period are shown in Table 1.
Based on 37 observed data from site CMMT, the site effect term ( S ) and error term ( ε ) for eachperiod were obtained with Bayesian theorem (Table1). Values of α 0 , α1 , α 2 and β 0 for pseudo
absolute horizontal spectral acceleration for 22 periods at 5% spectral damping are given in Table 1.
β1 = 1.602 and β 2 = -0.142 for M≤6

β1 = 2.475 and β 2 = -0.286 for M>6
Figure 3 shows the comparison among the original Idriss attenuation curve of Sa (the blue dashedcurve), the observed Sa (the red curve) and this study (the black dashed and doted curves). The twodashed curves show the uncertainty ( ± E [σ ε ] ) of the attenuation relation of this study. It can be seen4

that the prediction of the updated attenuation relation for Sa (this study) is closer to the observed Sa
than the original Idriss attenuation relation.
Table 1. Updated results on attenuation relation of Sa for CMMT site
Period
(s)

α0

β0

S

E [σ ε ]

0.03
0.05
0.075
0.1
0.11
0.13
0.15
0.2
0.25
0.3
0.35
0.4
0.5
0.6
0.7
0.8
0.9
1
1.5
2
3
4
5

-0.050-0.278-0.308-0.318-0.328-0.338-0.348-0.358-0.429-0.486-0.535-0.577-0.648-0.705-0.754-0.796-0.834-0.867-0.970-1.046-1.143-1.177-1.214

0
0.066
0.070
0.072
0.073
0.075
0.076
0.078
0.080
0.082
0.087
0.092
0.099
0.105
0.111
0.115
0.119
0.123
0.136
0.146
0.160
0.169
0.177

3.03
3.63
3.48
3.34
3.30
3.25
3.25
3.16
3.22
3.23
3.27
3.37
3.46
3.62
3.75
3.89
4.04
4.16
4.62
4.80
4.62
4.09
3.95

1.94
1.53
1.84
1.98
2.07
2.19
2.24
2.26
2.51
2.65
2.61
2.59
2.66
2.61
2.60
2.49
2.54
2.63
2.48
2.56
2.50
2.59
2.96

M>6

M≤6

α1

α2

α1

α2

3.477
3.426
3.359
3.327
3.289
3.233
3.185
3.100
3.034
2.982
2.943
2.906
2.850
2.803
2.765
2.728
2.694
2.662
2.536
2.447
2.295
2.169
2.042

-0.284-0.269-0.252-0.243-0.236-0.225-0.216-0.201-0.190-0.182-0.177-0.173-0.169-0.166-0.165-0.164-0.163-0.162-0.160-0.160-0.159-0.159-0.157

2.261
2.365
2.334
2.319
2.294
2.255
2.219
2.146
2.073
2.010
1.977
1.921
1.818
1.704
1.644
1.593
1.482
1.432
1.072
0.762
0.194
-0.466-1.361-0.083-0.092-0.081-0.075-0.070-0.062-0.055-0.042-0.030-0.020-0.016-0.009
0.003
0.017
0.022
0.025
0.039
0.043
0.084
0.121
0.191
0.280
0.410

Observed No.17, magnitude = 4.0000, distance =112.000

0

10

-1

10

-2

Sa (gal)

10

-3

10

-4

10

Observed Sa
Original Sa
Updated Sa-510± E[ σ ε]

-6

10

-2

10

-1

0

10

10

1

10

Period T (sec)Figure 3. The comparison among the attenuation relation for Sa of the original Idriss, this study andthe observed Sa of earthquake (Source : TMD) that occurred on 19 August 2007 (time 11:17:02 (UTC),the epicenter at Thailand-Myanmar boarder, Magnitude 4.0 and rupture distance 117).

55. CONCLUSIONS
The attenuation relations for PGA and Sa for the CMMT station in Thailand have been proposed inthis study. These attenuation relations for PGA and Sa were determined based on the Bayesian
updating technique by using 111 components of strong motion data of 37 earthquake events. By using
the Bayesian updating technique we constructed site-specific attenuation relation base on the past
proposed attenuation relation (Idriss, 1993). The specific site in this study is the CMMT station which
is located on the rock site.
In this study, we added correction term (site effect) and error to the Idriss attenuation
relation by using the Bayesian updated technique. The parameters in the Bayesian approach are treatedas random variables only for the CMMT site, while the original attenuation relation does not have site
effect term; the error of this attenuation relation is point estimators and used for all sites. The error of
attenuation model proposed in this study accounts for all uncertainties including model error andmeasurement error which is useful in the probabilistic hazard analysis, risk analysis and many otherengineering fields.
The prediction of the updated attenuation relation for PGA (This study) is smaller than theIdriss attenuation relation. The residual value (natural logarithmic unit) is calculated by the difference
between the observed and the predicted ground motions. The residuals of PGA of the Idriss
attenuation relation are negatively biased. Therefore we can conclude that the PGA of the Idriss
attenuation relation are overestimates. The comparison between the attenuation relation for Sa of Idriss
shows that the Sa of the Idriss attenuation relation are underestimates. The predictions of the updated
attenuation relation for PGA and Sa (This study) are closer to the observed PGA and Sa than the Idriss
attenuation relation.
The Bayesian update technique used in this study is suitable for making attenuation
relation for Thailand and can be used with new observations. It is expected that this method will beapplied to observation sites throughout the country.
AKNOWLEDGEMENT
I would like to give my sincere thanks to Dr. Tatsuhiko Hara, Dr. Tosiaki Yokoi and Mr. Masahiro
Ohbuchi for their valuable suggestion and help on my study.

REFERENCES
Charoenyuth. M., 2007, Master thesis, Dept. Civil Engineering, Chulalongkorn Univ., Thailand.
Idriss, I.M., 1993, Dept. Civil and Environmental Engineering, Univ. California.
Wang, M., and Takada, T., 2006, AIJ, 607, 183-191.
Wang, M., 2007, Doctor thesis, Dept. Architecture Graduate School of Engineering, Univ. Tokyo.
Website: U.S. Geological Survey , Earthquake Search Rectangular Area
http://neic.usgs.gov/neis/epic/epic_rect.html.
Website: Global CMT Catalog Search http://www.globalcmt.org/CMTsearch.html.
Website: IRIS, http://www.iris.washington.edu/software/downloads/.
Website: Matsac, http://geophysics.eas.gatech.edu/people/zpeng/Teaching/Sac_Tutorial_2006/.

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