Synopses of Master Papers

Bulletin of IISEE, 47, 61-66, 2013

ESTIMATION OF SITE EFFECT, ATTENUATION
AND SOURCE PARAMETERS IN WENCHUAN
EARTHQUAKE BY SPECTRAL INVERSION METHOD
Yefei REN ∗MEE11611

Supervisor:

Hiroaki YAMANAKA ∗∗ABSTRACT
With the demands of engineers and scientists, the spectral inversion method was used inpresent study to estimate simultaneously the site response, source parameters and S-wave attenuation(Q value) for the aftershocks of the Great 2008 Wenchuan Earthquake. In this regard, 602 recordings
from 96 earthquakes associated at 28 stations were selected as a database.
After getting the inversion results, we compared the site response with the one calculatedby the HVSR method and 1-D theory computation, and regressed the relationship between the site
amplification and Vs20 (the average uppermost-20m shear wave velocity) for different frequency
bands. In addition, the inversed site response was used to identify the soil nonlinearity during strong
motion. In present study, a new distance measure called the asperity distance D Aspt was proposed forreasonably characterizing the source-to-site distance in large earthquake.
Furthermore, the term of S-wave attenuation, Q factor was obtained as a frequencydependent function, Q( f ) = 100.6f 1.1. The source parameters for each earthquake including theseismic moment (M 0 ), corner frequency (f 0 ), stress drop (Δσ) and source radius (r) were estimated byfitting a ω-2 model with the source spectrum from the inversion. A regression analysis yielded thevaluable relationship between M 0 and f 0 , logM 0 and M s and between M w and M s , respectively.
Keywords: Wenchuan Earthquake, Site effect, Source parameter, Q value, Spectral inversion.

1. INTRODUCTION, 2. METHODOLOGY, 3. DATABASE AND DATA PROCESSING
Due to page limitation, see my thesis paper.

4. RESULTS AND DISCUSSION
4.1. S wave attenuation
As one of the importance factor charactering ground motion
attenuation, the quality factor Q(f) value was obtained withdependent frequency. Considering the form of power function, itwas fitted by Q( f ) = 100.6f 1.1, with the correlation coefficient of0.961. We compared our result with the one in Tangshan Area:Q( f ) = 67f 1.1 (Zhang et al., 2001). They used the same methodwith us to analysis the data from the aftershocks of 1976
Tangshan Earthquake. From Figure 1, we can find the Q value in∗Institute of Engineering Mechanics (IEM), CEA, Harbin, China.
Professor, Tokyo Institute of Technology (TIT), Yokohama, Japan.

∗∗Figure 1. The quality factor Q( f )from our spectral inversion

Sichuan Area is larger than in Tangshan Area but both of them have the same frequency dependence(same power value). That means the attenuation of S wave of Sichuan Area is lower than Tangshan
Area that seems disagreeing with the accepted principle that the ground motion attenuation of theWestern China is faster than the Eastern China. But it should be noted that the hypocenter distance ofthe data used by Zhang et al. (2001) is much closer (less than 50km) than this study that means theseismic wave propagate in the shallower crust. This is the most likely reason to explain why they got
the lower Q value.
Furthermore, we compared out result with other studies which also focused on the Sichuan
Area where the Wenchuan Earthquake occurred and affected. They are Q( f ) = 217.8f 0.816 by Zhang etal. (2007) and Q( f ) = 334.4f 0.581 by Qiao et al. (2006). As Figure 1 shows, the Q values of them areboth larger than ours. As we above explained, the possible reason is that both of them used the datawith farther hypocenter distance (10-400km) than our study that means the seismic wave propagate in
the deeper crust.
4.2. Site effect4.2.1 Site response analysis
The site response of 28 selected strong motion stations was achieved
expectedly by the separation of source, path, and site effect.
Meanwhile we calculated the site response by using 1-D theoreticalcomputation and compared both of them with the results by HVSRmethod (Wen et al., 2011). Figure 2 shows the results of the station
51GYZ. It should be noted that because we considered the freesurface amplification that means the site response represents 2E 0 /E,
we multiplied 2 of site amplification by HVSR method. There has agood agreement between the results from spectral inversion methodand HVSR method in some stations, such as 51CXQ, 51GYQ,51GYS, 51QLY and 62WIX. For most of stations, the site
amplification of HVSR method is lower than the spectral inversion
method, but the same predominant frequency.

Figure 2. Site response of thestation 51GYZ calculated bythree methods

4.2.2 Predominant frequency and site amplification
We compared the predominant frequency and average site
amplification calculated by spectral inversion method and HVSR
method (Wen et al., 2011). As Figure 3 shows, the predominantfrequency from two methods has a good agreement within 30%
deviation. Another agreement is that there are two predominantfrequencies for station 51LXS and 51WUD calculated by bothmethods with close values. But the average site amplification fromHVSR method is lower than the spectral inversion method for
frequency band 1.0-5.0Hz, 5.0-10.0Hz and 1.0-10.0Hz, as Figure 4shows. For the frequency 0.5-1.0Hz band, it seems an agreement
between them. The reason is the site response for this frequency
band is slight even no amplification for some stations, almost
Figure 3. Comparison of the equals to 2. Therefore, it can be concluded that the HVSR method
predominantfrequency can correctly evaluate the site predominant frequency but
calculated by spectral inversion underestimate the site amplification. Such conclusion also has
been made by some other previous studies.
method and HVSR method
4.2.3 Relation between site amplification and Vs20
There is available 20m borehole data for some stations. So we calculated the average shear wave
velocity of upper 20m Vs20 and the average site amplification for 0.5-10.Hz, 1.0-5.0Hz, 5.0-10.0Hz
and 1.0-10.0Hz frequency bands. We plotted the average site amplification versus Vs20 in logarithmic

scale and found there has some relationship between them for each frequency band except 0.5-10.Hz,
as Figure 5 shows. As we mentioned in above section, for 0.5-10.Hz frequency band, the site response
is slight even no amplification for some stations. Because most of our used stations locate attall-mountain area, the shallow surface soil layers only induce the high-frequency amplification.

Figure 4. Comparison of the average site amplification calculated by spectral
inversion method and HVSR method for each frequency band
We took a linear fitting in logarithmic scale and got the functions of site amplification as
Vs20 for each frequency band, as seen in Figure 5. The results show it has a low correlation for
0.5-10.Hz band, but high correlation for other frequency bands.

Figure 5. Average site amplification for 0.5-10.Hz, 1.0-10.0Hz, 1.0-5.0Hz
and 5.0-10.0Hz frequency bands as a function of Vs20
4.2.4 Soil nonlinearity identification for aftershocks
For analyzing soil nonlinearity, we would compare the site amplification during strong motion andweak motion. For the weak motion, we alreadyobtained the site amplification of each site by using
spectral inversion method. Also we already obtained
the path effect by means of frequency-dependent Q
value, and the source spectrum as well. So the Eq.
(3) of my thesis can be transformed into Eq. (14).
As we set the criteria to build thedatabase in section 3, the definition of weak motionis that the average PGA of two horizontal
Figure 6. The obvious evidence presenting components is below 100gal, on the contrary thesoil nonlinearity for station 51SFB
strong motion is above 100gal. Therefore, wecalculated the site effect by using Eq. (14) of my thesis for those recordings with PGA > 100gal.
Figure 6 shows for the station 51SFB it was identified there has a clear evidence of soil
nonlinearity in the earthquake EQ080512144315 and EQ080512150134 that site amplification shifts
towards the lower frequency during the strong motion than the weak motion, namely lower
predominant frequency and deamplification in the high frequency part.

4.2.5 Soil nonlinearity identification for main shock
Among 28 stations of our database, only 51GYQ didn’t capture the recording in the main shock
because of the instrument malfunction. We added other 27 recordings into our database to take thespectral inversion again on the basis of the assumption that these recordings were obtained fromanother 26 stations except the reference station 62WIX. Then we can get another site response for eachstation after the spectral inversion. To compare them with previous result during weak motion we canidentify the existence of soil nonlinearity in the main shock.
There has a basic assumption of earthquake point source for spectral inversion method.
However, for the great Wenchuan Earthquake, the fault rupture process took long time and far distance.
The point source assumption is not suitable for such large earthquake that means it should be took careof the distance R ij . In this study, we proposed to use a new source-to-site distance measure calledasperity distance D Aspt by the following equation:ln DAspt =1
ln D(x, ξ ) dsA ∑∫(1)

where, D(x, ξ) means the distance from the station x to apoint ξ on the asperity region Σ, A is the total area ofasperity. In fact D Aspt represents a mean distance from theFigure 7. Two asperities werestation to asperity. For the slip model of Wenchuan
identified for Wenchuan Earthquake.
Earthquake, here we used the inversion result of finite
Fault slip model is derived from USGS.
fault model from USGS. According to the definition ofasperity area by Somerville et al. (1999), we identified two asperities for Wenchuan Earthquake asshown in figure 7 and calculated the D Aspt by Eq. (1). Also we calculated another three kinds ofsource-to-site distance measures which were widely used for ground motion attenuation analysis.
There are the rupture distance (D Rup , the shortest distance from the station to the rupture surface),
Joyner–Boore distance (D JB , the shortest horizontal distance to the vertical projection of the rupture)and hypocentral distance D Hyp .
Figure 8 shows an example of the comparison betweensite amplification during weak motion and strong motion in the mainshock. Finally it can be found there has apparent evidence of soil
nonlinearity for station 51GYZ, 51SFB, 51WCW as significantly
shifting predominant frequency F p to low frequency part. It is
deserved to notice that the recordings of these three stations havehigh PGA and PGV. Also the soil nonlinearity can be identified forstation 51GYS, 51LXM, 51LXS, 51LXT, 51MXD, 51MXN, 62WUD
which have the feature of F p shift.
For finding the correlation between the nonlinearity
Figure 8. The example of thelevel and ground motion level, we picked up the F p for each stationcomparison between site
during weak motion and strong motion respectively and took the ratio
amplification during weakofthem.
motion and strong motion inFigure9
the main shock of Wenchuan
shows
thisEarthquake
ratio versus
the mean PGA and PGV of two horizontal
components separately. It shows when thePGA > 300 cm/s2 or PGV > 20 cm/s, the F pwill become much smaller for strong motion(a)(b)
than for weak motion, namely the soil Figure 9. The predominant frequency Fp as weaknonlinearity will significantly happen. And if motion over strong motion versus PGA and PGVwe see the shaded area of Figure 9, it can be found that the nonlinearity level will become larger when
PGA value becomes larger.
4.3. Source parameters estimation
In present study, we proposed to use grid search technique to find the appreciate source parameters foreach earthquake. We divided a range M s (M l )-0.5 ≤ M w ≤ M s (M l )+0.5, 2-0.3 ≤ γ i ≤ 2+0.3 as aconvenient preconception for high frequency spectral fall-off
range by supposing ω2 model, and 0.1 ≤ f 0i ≤ 5.0Hz considering
the magnitude range of 3.7 ≤ M s (M l ) ≤ 6.5 to estimate an
optimal set of M w, γ i and f 0i for the best fitting source spectrum
by using Eq. (2):M 0i
M 0i ( f ) =(2)γi f 1+   f 0i 
when the defined root mean square error between our inversed
Figure 10. The inversed (circles) seismic moment density and its empirical value by Eq. (3) isand the best-fitting (red line) smallest as follows,N
seismic moment density for an[log(M 0Invi ( f j ))-log(M 0i Emp ( f j ))]2∑
exemplified event
j(3)R.M .Si (M w ,γ , f 0 ) =N
where, M 0Invi ( f j ) , M 0Empi ( f j ) are the inversed and empirical seismic moment density at jth frequency
for ith earthquake, respectively. N means the number of available frequency points.
Figure 10 shows a demonstration of the best-fitting
seismic moment density for one event. The relationship between
and M 0 and f 0 was linearly fitted in logarithmic scale as follows:log(M 0 ) = (22.77 ± 0.04) - (2.37 ± 0.08) log(f 0 ) (4)Considering the assumption of M 0 ∝f 0 -3 by Aki(1967), which corresponds to constant stress drop, the regressionof the data yieldedlog(M 0 ) = (22.83 ± 0.42) - (3) log(f 0 )Figure 12. Seismic moment versus
source radius for each event(5)

Figure 11 shows the relation Figure 11. Seismic momentof Eq. (5) by the solid line. versus corner frequency obtained
The shaded area of this figure from inversion analysis
means the area of one standard deviation of the mean value. Eq.
(5) also can be written as M 0 f 0 3 = 6.76 × 1022 dyne·cm
corresponding to a constant stress drop 12.4 bars.
According to the ω2 model of, the source radius (r i )and stress drop (Δσ i ) for ith event can be calculated by Eq.(28)and Eq.(29) of my thesis.
Figure 12 shows the seismic moment versus source
radius for 96 aftershocks of the Wenchuan Earthquake. It can befound that expect for one event, the stress drop varies between 1bars to 100bars. Figure 13 shows the regression analysis between
log M 0 and M s , M w and M s . It yielded the relationship:log M 0 =(1.475 ± 0.06) M s + (16.09 ± 0.31)

(6)

Mw =
(0.917 ± 0.04) M s + (0.33 ± 0.19)(7)Then we compared Eq. (6) with the accepted
relationship between log M 0 and M w : log M 0 =1.5 M w + 16.05. The result shows that tworelationships are in close agreement with eachother, in other words, M w almost can be replaced
by M s in Wenchuan area approximately that is
also deduced from Eq. (7).

(a)

(b)

Figure 13. The regression between log M0 and Ms(a), Mw and Ms (b)5. CONCLUSIONS
Using spectral inversion method, the source spectrum, site response and attenuation (representation ofQ factor) of S wave were separated for the aftershocks of the 2008 Great Wenchuan Earthquake. By
analyzing the inversion results, we concluded that:(1) The site response of 28 strong motion stations was evaluated by inversion method,
HVSR method and 1-D theoretical computation. (2) The deficiency of HVSR method was also foundin present study through comparing with the inversion results that it can reasonably estimate the site
predominant frequency but underestimate the site amplification. (3) The site amplification in
Wenchuan Area was evaluated as a function of Vs20 (the average uppermost-20m shear wave velocity)
for 1.0-5.0Hz, 5.0-10.0Hz and 1.0-10.0Hz frequency bands, respectively. (4) It was identified the soilnonlinearity in the aftershocks of Wenchuan Earthquake was existed only at the station coded 51SFB(5) A new distance measure called the asperity distance D Aspt was proposed for reasonably
characterizing the source-to-site distance in large earthquake, like Wenchuan Earthquake of present
study . (6) The comparison of site response between main shock and aftershocks shows ten stations
induced soil nonlinearity during main shock. It was found that a threshold PGA > 300 cm/s2 or PGV >20 cm/s was obviously existed for soil nonlinearity in Wenchuan Earthquake and the nonlinearity level
was significantly dependent on the ground motion level corresponding to the PGA and PGV. (7) Thequality factor Q in terms of S-wave attenuation was estimated by a frequency dependent function Q( f )= 100.6f 1.1 at the frequency band 0.5-20.0 Hz within the propagation distance range of 30-150 km. (8)The grid search technique was proposed in this study for determining the best appreciate source modelfor each earthquake. Then the source parameters including M 0 , f 0 , Δσ and r were estimated finally.
The regression analysis yielded a relationship between seismic moment and corner frequency M 0 f 0 3 =6.76 × 1022 dyne·cm corresponding to a constant stress drop 12.4 bars, in the M 0 range of 1021 ≤ M 0 ≤1027 dyne·cm. Moreover, the regression analysis also yielded two linear relationships between logM 0and M s and between M w and M s which can be used for further research.
ACKNOWLEDGEMENT
I would like to express my sincere gratitude to my adviser Dr. T. Kashima for his helpful suggestions
for choosing this topic and some comments of final review of this paper.
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