SITE EFFECT AND Q-FACTOR ESTIMATION OF
ARASBARAN (AHAR-VARZAGHAN) EARTHQUAKE,
IRAN BY SPECTRAL INVERSION METHOD
Sepehr RAJABI BANIANI*
MEE12605

Supervisor: Toshiaki YOKOI**

ABSTRACTThis study is done in order to obtain site effect and attenuation regarding the Arasbaran (AharVarzaghan) Earthquake on August 11th, 2012 in Iran. The region has one of the highest levels ofseismic hazard. However, there are no advanced studies in this area in order to obtain site effect andQ-factor. Thus, the main aim of this study is to figure out the site effect and amplification by using thespectral inversion method with respect to geological parameters on the region. We selected 35 eventsand 13 stations to estimate the site effect and Q-factor. ω-2 model was used to estimate source
parameters such as the corner frequency (f0) and the seismic moment (M0). Eventually, we obtained Q= 45.85 f 1.495. Furthermore, the result shows high amplifications in Meshgin Shahr, Horand, Damirchi,
Chaykandi, Khajeh and Kharvanagh. Although the reference site is not necessary, the usage of thereference events, especially the determination of the source parameters, can be quiet tough. It may bebetter to use a rock site or to conduct the geophysical exploration in sites where not so deep sedimentis expected.
Keywords: Arasbaran (Ahar-Varzaghan) earthquake, site effect, Q-value, ω-2 model

1. INTRODUCTION
Iran is on the plate located between the Arabian plate and Eurasia plate. Due to this situation, thecountry has high seismic hazard. Almost all parts of the country are covered by major faults and highhazard areas. On August 11th , 2012 the Arasbaran (Ahar-Varzaghan) twin earthquakes occurred near
Varzaghan and Ahar in Eastern Azerbaijan Province of the Northwest of Iran at 16:53 and 17:04(local time) with magnitude 6.2 (IGUT) and 6.0 (IGUT) respectively with the depth around 12 km(The Institute of Geophysics, University of Tehran). For the quantitative estimation of strong groundmotions, the site, path and the source effects are essential and these parameters are indispensable forpredicting seismic ground motions. Thus, the main aim of the present paper is to determine the site
effect and Q value using accelerograms of the Arasbaran twin earthquakes and their aftershocks basedon the ω-2 model of seismic source.

2. ANALYSIS
The method which was used in this study is categorized as spectral inversion method that was first
proposed by Andrews (1986), of which the biggest advantage is that the method can separate thesource, path and site terms (Iwata and Irikura, 1988). The observed spectra of an earthquake in thefrequency domain can be written as the product of the source, path, and site effects as,
Oij( f ) = Si( f )Gj( f )Rij-1e- fRij /Q( f )β,*Geological Survey of Iran.
**Director, International Institute of Seismology and Earthquake Engineering, BRI, Japan.
1(1)where Oij(f) denotes the observed spectra of the i-th earthquake at the j-th station, Si(f) the source of
the i-th earthquake, Gj(f) the site effect at the j-th station, Rij the hypocentral distance from the i-th
event to the j-th station, β the shear wave velocity, and Q(f) the frequency dependent quality factor(Iwata and Irikura, 1988). From Eq. (1), the observed amplitude spectral ratio for the i-th event
between divisor site Oir(f) and other stations Oij(f) is,,(2)

where subscript r indicates the divisor site. Taking logarithm of Eq. (2) gives,ln[Gj(f)] – ln[Gr(f)] - f(Rij-Rir)/Q(f)β = ln[

(f)

],

(3)

where
is the ratio of the observed spectra of the i-th event at the j-th site with respect to thedivisor site andis hypocentral distance ratio between i-th event at j-th station with regard to thedivisor site. If there are earthquakes of which seismic moment and corner frequency are known, thefollowing constraint equation is available.
ln[Gj( f )] - fRij/Q(f)β = ln[Oij( f )Rij] - ln[Si( f )](4)

Then matrix for inversion is taken from Eqs. (3) and (4):(5)
A corresponds to the left member of Eq. (3) and c is the left member of Eq. (4) , x is theunknown parameters that are site effects Gj(f) and Q-1(f), and b and d are right members of Eq. (3) andEq. (4), respectively. This study differs from Moya and Irikura (2003); they use the observed
displacement spectra for Oij(f), whereas in this study the observed acceleration spectra is used. Thus
the Eq. (6) written as following,Si(f) = aoi/{1+(foi/f)2},(6)

where aoi=(2πfoi)2Ωoi denotes the high frequency asymptote of the acceleration spectra, i.e., theacceleration flat level, Ωoi=0.55Moi/4πρβ3, ρ=2,700 kg/m3, β=3.0 Km/s. Here, the radiation coefficient
averaged over azimuth and take-off angle on the logarithmic axis, 0.55 is used (Boore and Boatwright,
1984).
Figure 1. Epicenters and stations
used for analysis.
In this study mainly the digital
accelerograms provided by thestrong motion observation networkof the Building and Housing
Research Center (BHRC), Iran wereused. The digital seismograms ofbroadband stations of the IranianNational
Broadband
Seismic
Network belongs to International
Institute of Engineering Earthquake
and Seismology (INSN-IIEES)
were used also for the estimation of
the corner frequency of thereference events.
2

Moreover, 138 records of 33 aftershocks were obtained at 13 stations (Figure 1).
2.1. Fourier Spectral Analysis of the First Mainshock
The first mainshock was selected as the reference event and its corner frequency was estimated using
the digital seismogram of Maku station of INSN. First, the data of Maku station are analyzed by Fast
Fourier Transform (FFT) using the time window of 63 to 127 seconds from S-wave on set. Cornerfrequency was determined around 0.178 Hz for the first mainshocks using the flat level of thedisplacement spectra Ω0 and that of the acceleration spectra a0 and from Eq. (7) the corner frequency
was estimated. However, the reading value can have uncertainty and affect the result of analysis.
f0 =

(7)

2.2. Pre-Processing of the Strong Motion Records
In this study, the three-component waveforms recorded at 57, 75, 18 stations of the Iranian strongmotion network of BHRC during the first, second mainshocks and 33 aftershocks, respectively were
downloaded. According to the BHRC the magnitude for the first mainshock was 6.2 and the second
mainshock was 6.0. On the other hand, IRSC determined 6.5 and 6.3 for the first and the second
mainshock, whereas USGS gave 6.4 for the first one. 35 events were chosen and 257 waveforms wereanalyzed including mainshocks and aftershocks started from August 11th, 2012 12:23:18 UTC to
November 7th, 2012 06:26:31UTC and ranged magnitude from 3.7 to 6.2 with local depth less than 20
km. In order to obtain the Fourier spectra of S-waves which is the strongest part of the shaking, Husid
plot was used (Husid, 1967). The window which was used for this calculation was 0.05 and 0.95 times
to the total energy. In this part, the Husid plot is obtained from S-wave and it is indispensable to checkthe S-wave arrival time. Where the Husid plot H(t) is defined as follow,(8)

H(t) =

where a(t) is acceleration time history. In this study, the S-wave arrival was determined using
H(t)=0.05, whereas the duration of the time window for Fast Fourier Transform is fixed at 10
seconds.
2.3. Fourier Spectral Analysis of the Strong Motion Records
Waveforms were analyzed to calculate amplitude and displacement spectra to make sure that the data
quality is acceptable for the 35 events at the 75 stations, in total 170 spectra, by FFT. The increasing
amplitude at the frequency band lower than 0.4 Hz was emphasized in the displacement amplitude
spectra this is due to the low frequency noise included in accelerograms which may disturb theanalysis.
2.4. Spectral Ratio Analysis for another Reference Event.
The frequency range of analysis was chosen from 0.2 Hz to 10 Hz, and then the records of which peakground acceleration (PGA) is between 10 and 200 cm/s2 were selected in order to exclude the records
that may include the effect of non-linearity and also those of insufficient Signal to Noise ratio.
Varzaghan (VAZ009), Horand (HUR004) and Mehtarloo (MHL013) were selected as the divisor sites.
The first mainshock was selected for a reference event, whereas the second mainshock was not used
due to the possibility of a complex rupture process. The event 1211070626 was selected as the second
reference event to cover the second group of the records. From Eq. (1), the ratio of the observed
spectra corrected using the hypocentral distance is formulated as follows.
3F(f)= Ois Ris /Oil Ril =

(

/

)

(9)

where
is the ratio of the low frequency flat level of the smaller event to the bigger event, fos is thecorner frequency of the smaller event and fol is of the bigger event. In other words, the smaller event is
the numerator and the bigger the denominator. The low frequency asymptote of F(f) is given by
and the high frequency one, namely, the ratio of the acceleration flat level.
Figure 2 (b) shows the observed spectral ratios with thin curves and their average over the available
stations with a thick curve. To this thick curve the theoretical F(f) is fitted using a heuristic search; a
combination of Down Hill Simplex Method with Very Fast Simulated Annealing (DHSM-VFSA;
Press et al., 2002; Ingber 1989; Yokoi 2005). Figure 2 (c) shows this averaged curve and the bestfitting curve of F(f). The high frequency asymptote h of the averaged curve can be seen clearly in
Figure 2(c), whereas the low frequency one g cannot be seen due to growing of the curve from around
0.4Hz toward the lower frequency side.
(a)

(b)

(c)

fo
h
g
fa

Figure 2. Example of analysis. (a) Acceleration spectra of the smaller event (Numerator:
Event 1208111230) and the bigger event (Denominator: Event 1208151749) obtained atvarious stations. (b) Spectral ratio at various stations (thin curves) and their average overstations (thick curve). (c) Best fitting curve to the average spectral ratio curve, red arrowshows the determined corner frequency of the big event (fa).
3. RESULT AND DISCUSSION
The spectral inversion was conducted using the above mentioned three divisor sites and two reference
events. Due to the sparsity of available records, it was necessary to eliminate same aftershocks thatwere recorded at only few stations and same stations that obtained records during only few
earthquakes. The final results were obtained using 13 stations and 35 earthquakes, among them threedivisor sites and two reference events. Figure 3 shows the result of analysis for Q-1(f). In general, thespectral inversion method implicitly assumes that the radiation coefficient is the average value overazimuth and take-off angle. It is widely known that this assumption works well for the frequency
range higher than around 5Hz; that the radiation coefficient follows the theory at the frequency range
lower than around 1.0Hz; and that it has a transient behavior between them (e.g., Liu and Helmberger,
1985; Takemura et al., 2009). If various events are recorded at various stations evenly distributed, an
averaging effect can be expected in the inversion process. However, in this study the records weresparsely obtained and each used pairs has only few spectral ratio curves. Therefore, it is expected thatthe method itself can fail in the low frequency range. The inverted Q-1(f) in Figure 3(b) (blue curve)
shows the different trend below and above 2.3Hz. Considering the above mentioned condition, I
selected the frequency range for the regression analysis above it (black curve). Fitting by the
regression analysis was conducted on log(f) - log(Q-1) plot as shown in Figure 3(a). The result is,4

Q(f) = 45.85 f 1.495,(10)

where 45.85 is the value for Q0.
Figure 4 shows the site effects for 13 stations inverted simultaneously. Damirchi(DMC002) has only one peak at around 7 Hz that reaches to 12 times of amplification. Khajeh(KJH007) has only one peak at around 3Hz that reaches to 10 times of amplification. Others show
more complicated feature.
(a)

(b)

0

0.1
Q_INV

y = -1.495x - 1.6614
R² = 0.6128-1

Q_INV used for analyzing
Q=45.85f^1.495

Q-1

Log10(Q-1)

0.01
-2

0.001
-3

0.0001

-4
0

0.2

0.4
0.6
0.8
Log10 (Frequency)

1

0.1

1.2

1

10
Frequency (Hz)100

Figure 3. (a) Relation of inverted Q-1(f) against log(f) to find linear regression line; (b)Comparison of fitting: blue curve shows the inverted Q-1(f); black curve the data range
used for regression analysis in the panel (a); red line the regression curve.
Meshgin Shahr (MES010), Kharvanagh (KHV006), Sheykh-Khomloo (SHK012) andAhar (AHR001) have similar shape of amplification but different amplification, i.e., a lower peak ataround 7 Hz and broad peaks from 1.5 Hz to 4 Hz. Only SHK012 has the highest peak at 1.5Hz.
Hoorand (HUR004) has the site effect reaches to 10 times in the frequency range from 5 Hz to 7 Hz
with minor ones at lower frequency. Peak at around 7 Hz appears at Chaykandi (CHK018) also butwith peaks of similar height at 3.5 Hz and 1.5 Hz. Ahar (AHR001), Varzaqan (VAZ009) and Nahand(NHN008) show the site effect of which peaks are less than 5.0. Mehtarloo (MHL013), Haris(HAS003) and Kaleibar (KAL005) have a peak slightly bigger than 5.0. These 6 stations can be
categorized as relatively low amplification sites. Nahand (NHN008) is the lowest. In contrast,
Meshgin Shahr (MES010), Kharvanagh (KHV006), Damirchi (DMC002), Hoorand (HUR004) andChaykandi (CHK018) are the group of relatively high amplification sites. By comparison between
these stations the effects of sedimentary medium, including Lahar which is also rock formation suchas conglomerates and breccia, on site effect become clear. Hence, more information from these typesof ground materials is needed. Moreover, ground and underground identification with regard to
topography, crash zones and fragmented regions is essential. Therefore, for these especial regions, inorder to understand the geological structure responsible for these site effects more field activity
including geotechnical data, seismic engineering and geological engineering data will be needed(Herrin et al., 2002).
16
14

Amplification

12
10

Figure 4. Site effects obtained from13 stations using 35 events.

8
6
4
2
0
0

2

5

4

6

Frequency (Hz)

8

10

12

AHR001
DMC002
HAS003
HUR004KAL005
KHV006
KJH007NHN008
VAZ009MES010
SHK012
MHL013
CHK018

4. CONCLUSION
75 stations and 35 events were selected for analyzing, however, for stable solution,
finally by using 13 stations and 35 events were used. In order to get even better result 3 divisor sites
were introduced, i.e., Varzaghan (VAZ009), Horand (HUR004) and Mehtarloo (MHL013). Finally,
two reference events were selected, 1208111223 as the first mainshock with magnitude 6.2 and1211070626 as the aftershock with magnitude 5.3. By using these data, Q-factor was obtained which
was 45.85 f 1.495. The site effect shows significant amplification in Meshgin Shahr (MES010),
Kharvanagh (KHV006), Damirchi (DMC002), Hoorand (HUR004), Khajeh (KJH009) and Chaykandi(CHK018). The advantage of the spectral inversion method using the reference events is that in caseof lack of data especially that of the reference site or when the reference site does not record enoughdata, reliable result including site effect and Q-factor can be obtained. Although the reference sites are
not necessary, the usage of the reference events, especially the determination of the source parameters,
can be quiet tough. It may be better to use a rock site or to conduct the geophysical exploration in sites
where not so deep sediment is expected.

ACKNOWLEDGEMENTS
I would like to send my gratitude to Dr. Noorbakhsh MIRZAEI, head of Iranian Seismological Center(IRSC) and all staff members from the Institute of Geophysics University of Tehran (IGUT).
Waveforms data obtained by Building and Housing Research Center (BHRC) Iranian National
Broadband Seismic Network belongs to International Institute of Engineering Earthquake andSeismology (INSN-IIEES). Geological data used in this study belongs to Geological Survey of Iran(GSI).

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