Estimation of Strong Response Spectra from Weak Motion Data for Earthquakes
in Taiwan
Yi-Ben Tsai and Hsiao-Ling Chao
Institute of Geophysics, National Central University
Chung-Li, Taiwan
ABSTRACT
We have developed and tested an empirical approach for rapid estimation of
strong ground motion response spectra that are useful for making timely damage
assessment following a strong earthquake. This approach takes advantage of the
unique features of two operational strong ground motion networks in Taiwan: the
Taiwan Rapid Earthquake Information Release System (TREIRS), currently
consisting of about 80 real-time digital accelerographic stations and the dense Taiwan
Strong Motion Instrumentation Program (TSMIP) network, currently consisting of
about 650 free-field digital accelerographic stations. The TREIRS can quickly provide
complete ground acceleration time histories at its stations after a strong earthquake,
whereas the TSMIP network can provide dense spatial coverage of populated areas at
about 5-km grid spacings. By this approach we can make rapid estimation of dense
spatial patterns of ground motion response spectra within minutes after a strong
earthquake. In this approach, we first calculate the response spectra from recorded
acceleration time histories at the TREIRS stations immediately after a strong
earthquake. We then use pre-established inter-station spectral ratio functions between
a TSMIP station and a nearby TREIRS station to obtain the corresponding response
spectra for individual TSMIP stations. This empirical approach is based on the fact
that for a given station the response spectral shape, after removal of source and
propagation path effects, is highly repeatable from earthquake to earthquake. We use
an average response spectral shape of regional stations to represent the source and
propagation path effects. This regionally averaged spectral shape is next used to
normalize the response spectral shape at individual stations. The resultant spectral
shape represents primarily the local site response effects. We can obtain a smooth
local site response spectral shape for each station by averaging over many earthquakes.
We have obtained an average local site response spectral shape for each of the 650
free-field stations by using recordings of harmless ground motion from more frequent,
moderate earthquakes. Once a strong earthquake takes place, we can use the actual
recording at a TREIRS station to calculate the response spectrum. We then use this
spectrum as a regional reference to estimate the response spectra at nearby free-field
stations. This empirical approach was tested satisfactorily on the recordings of the
1999 Chi-Chi, Taiwan earthquake sequence.
1
Introduction
Estimation of strong ground motions from large earthquakes is essential for
seismic hazard assessement and loss estimation. Here we develop an empirical
approach to estimate strong ground motion response spectra from a large earthquake
by using much more frequent weak motion data. The approach uses the response
spectral shape normalized by the MSA (Mean Spectral Acceleration), instead of by
PGA (Peak Ground Acceleration). Figure 1 shows the average response spectral
shapes and their dispersions of four California earthquakes. On top we show the
results from normalizing by PGA, whereas at the bottom we show the results from
normalizing by MSA. It is noted that the dispersion is not uniform over the frequency
band of interest when normalized by PGA. In the following analysis, we use the
MSA-normalized spectral shape as our working ground motion parameter.
Strong Ground Motion Data from the Chi-Chi Earthquake Sequence
When the M7.6 Chi-Chi, Taiwan earthquake of September 21, 1999 struck,
Taiwan was instrumented by a very dense strong ground-motion network to record the
main shock and many aftershocks. Figure 2 shows the locations of the free-field
strong motion stations as well as the epicenters of the nine earthquakes in the Chi-Chi
sequence. Figure 3 shows the distribution of the four types of recording site
classification: Site B for rock sites, Site C and D for terrace and gravel sites, and Site
E for soft soil sites.
Local Site Response of Ground Motion
Figure 4 shows the Fourier amplitude spectra normalized at high-frequency band
for the horizontal and vertical components. It is evident that the local site effects are
most pronounced over the frequency band from 0.1 to 5 Hz on the horizontal
component. This is also shown in Figure 5 where the average response spectral shapes
for the four site classes from the Chi-Chi earthquakes are distinctively different.
In addition to local site effects, the response spectral shapes also depend on the
source effects, as shown in Figure 6 which shows the average response spectral
shapes for the nine earthquakes in the Chi-Chi sequence.
Estimation of Strong Motion Response Spectra from Weak Motion Data
We next obtain the average response spectral shape at each station from the eight
smaller earthquakes in the sequence. We then use one or two stations at each of the
seven regions as a reference station. Spectra of the reference station are multiplied by
the spectral ratio between the target and reference stations which are obtained from
the weak motion records. Figures 7 and 8 show the comparison between the actual
2
and estimated response spectra for the Chi-Chi main shock at some of the stations in
the TCU and CHY regions. From these figures we can see that actual ground motion
at majority of stations was satisfactorily estimated in terms of both spectral amplitude
and shape. We also noticed that the ground motions at stations west of the Chelungpu
fault were consistently overestimated. This is because we use a reference station on
the hanging wall of the Chelungpu fault where the ground motion was significantly
greater than the footwall stations west of the fault. Finally, Figure 9 shows the average
and dispersion of the ratio between the observed and estimated response spectra in the
seven regions of Taiwan. It can be seen that five of the seven regions are very
accurately estimated. On the other hand, the ground motions were underestimated in
TAP and TCU regions. In addition, the dispersion in TCU region is significantly
greater than the rest.
In conclusion, ground motion response spectra from the M7.6 Chi-Chi
earthquake can be estimated satisfactorily from the response spectra of smaller
earthquakes. With a combination of the dense free-field network and the rapid
earthquake reporting system operated by the CWB, it is possible to obtain spatial
patterns of ground motion response spectra only in a few minutes following a strong
earthquake.
3
Figure 1. Mean Response spectral shapes and their dispersions for four California
Earthquakes. Top: Normalized by PGA; Bottom: Normalized by MSA
4
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TAP
TCU
ILA
HWA
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CHY
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KAU TTN
11 ChiChi
ChiChi Earthquake
Earthquake
2~7
2~7 ChiChi
ChiChi Aftershock
Aftershock
88 Chiayi
Chiayi Earthquake
Earthquake
99 Rayli
Rayli Earthquake
Earthquake
震央
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車籠埔斷層
車籠埔斷層
觸發之測站
觸發之測站

 未觸發之測站
未觸發之測站
Figure 2. Free-field strong motion stations and the nine earthquakes in the Chi-Chi
sequence.
5
Figure 3. Site classification of the free-field strong motion stations in Taiwan.
6
Horizontal Mean Normalized Fourier Spectrum
100
10
1
EQ 1
All Sites (396)
class-B (52)
class-C (58)
class-D (187)
class-E (99)
0.1
0.01
0.1
1
10
100
10
100
Frequency(Hz)
Vertical Mean Normalized Fourier Spectrum
100
10
1
EQ 1
All Sites (396)
class-B (52)
class-C (58)
class-D (187)
class-E (99)
0.1
0.01
0.1
1
Frequency(Hz)
Figure 4. Average Fourier amplitude spectral shapes for the four types of site from the
Chi-Chi main shock. Top: Horizontal component; Bottom: Vertical component.
7
Spectral Acceleration (g)
10
V
1
0.1
0.1
1
10
100
Frequency (Hz)
Spectral Acceleration (g)
10
EW
1
0.1
0.1
1
10
100
Frequency (Hz)
Spectral Acceleration (g)
10
NS
1
EQ 1
All sites (396)
class-B (52)
class-C (58)
class-D (187)
class-E (99)
0.1
0.1
1
10
100
Frequency (Hz)
Figure 5. Average response spectral shapes for the four types of site from the Chi-Chi
main shock. Top: Vertical component; Middle: EW component; Bottom: NS
component.
8
Spectral Acceleration (g)
10
V
1
0.1
0.1
1
10
100
Frequency (Hz)
Spectral Acceleration (g)
10
EW
1
0.1
0.1
1
10
100
Frequency (Hz)
Spectral Acceleration (g)
10
EQ1,Mw=7.6
EQ2,Mw=6.3
EQ3,Mw=6.4
EQ4,Mw=6.4
EQ5,Mw=6.4
EQ6,Mw=6.4
EQ7,Mw=6.5
EQ8,Mw=5.8
EQ9,Mw=5.7
NS
1
0.1
0.1
1
10
100
Frequency (Hz)
Figure 6. Average response spectral shapes for the nine earthquakes in the Chi-Chi
sequence. Top: Vertical component; Middle: EW component; Bottom: NS component.
9
0921 Chichi
TCU Horizontal-component
TCU039
TCU017
TCU006
1
0.1
0.01
0.1
1
10
Frequency (Hz)
1
Sa (g)
Sa (g)
Sa (g)
1
0.1
0.01
0.1
100
1
10
Frequency (Hz)
0.1
0.01
0.1
100
1
10
Frequency (Hz)
TCU059
TCU072
1
Sa (g)
Sa (g)
1
0.1
0.01
0.1
1
10
Frequency (Hz)
0.1
0.01
0.1
100
TCU070
100
1
Sa (g)
Sa (g)
1
10
Frequency (Hz)
TCU074
1
0.1
0.01
0.1
1
10
Frequency (Hz)
0.1
0.01
0.1
100
TCU048
1
10
Frequency (Hz)
100
TCU089
1
Sa (g)
1
0.1
1
10
Frequency (Hz)
TCU122
TCU110
0.1
1
10
Frequency (Hz)
100
TCU082
0.1
0.01
0.1
1
10
Frequency (Hz)
1
1
Sa (g)
1
0.01
0.1
0.1
0.01
0.1
100
Sa (g)
0.01
0.1
Sa (g)
Sa (g)
100
1
10
Frequency (Hz)
100
TREIRS stations
0.1
0.01
0.1
1
10
Frequency (Hz)
100
Calculated
Observed
Figure 7. Comparison of the observed with estimated response spectral in the TCU
area for the Chi-Chi main shock.
10
100
0921 Chichi
CHY Horizontal-component
CHY004
CHY002
CHY080
1
0.1
0.01
0.1
1
10
Frequency (Hz)
100
Sa (g)
1
Sa (g)
Sa (g)
1
0.1
0.01
0.1
1
10
Frequency (Hz)
0.1
0.1
100
1
10
Frequency (Hz)
CHY012
CHY046
1
Sa (g)
Sa (g)
1
0.1
0.01
0.1
1
10
Frequency (Hz)
0.1
0.01
0.1
100
CHY058
100
1
Sa (g)
Sa (g)
1
10
Frequency (Hz)
CHY014
1
0.1
0.01
0.1
1
10
Frequency (Hz)
0.1
0.01
0.1
100
CHY067
100
Sa (g)
1
0.1
1
10
Frequency (Hz)
0.01
0.1
CHY070
Sa (g)
Sa (g)
1
1
0.1
1
10
Frequency (Hz)
100
1
10
Frequency (Hz)
CHY019
CHY022
1
0.01
0.1
0.1
100
Sa (g)
0.01
0.1
1
10
Frequency (Hz)
CHY079
1
Sa (g)
100
0.1
0.01
0.1
1
10
Frequency (Hz)
100
TREIRS stations
0.1
0.01
0.1
1
10
Frequency (Hz)
100
Calculated
Observed
Figure 8. Comparison of the observed with estimated response spectra in the CHY
area for the Chi-Chi main shock.
11
100
2
2
ILA-Horizontal
1
ln (OBS/CAL)
ln (OBS/CAL)
TAP-Horizontal
0
-1
-2
0.1
1
Frequency (Hz)
10
1
0
-1
-2
0.1
100
10
100
10
100
10
100
HWA-Horizontal
TCU-Horizontal
1
ln (OBS/CAL)
ln (OBS/CAL)
Frequency (Hz)
2
2
0
-1
-2
0.1
1
Frequency (Hz)
10
1
0
-1
-2
0.1
100
2
1
Frequency (Hz)
2
CHY-Horizontal
TTN-Horizontal
1
ln (OBS/CAL)
ln (OBS/CAL)
1
0
-1
-2
0.1
1
Frequency (Hz)
10
100
1
0
-1
-2
0.1
1
Frequency (Hz)
2
ln (OBS/CAL)
KAU-Horizontal
1
0
-1
-2
0.1
1
Frequency (Hz)
10
100
Figure 9. Ratio between the observed and estimated response spectra for the seven
areas in Taiwan.
12