Quick identification of damage earthquakes from initial
portion of P waves
Yih-Min Wu1, Hiroo Kanamori2, and Ta-liang Teng3
1. Department of Geosciences, National Taiwan University, Taipei, Taiwan
2. Seismological Laboratory, California Institute of Technology, Pasadena, California 91125, USA.
3. Southern California Earthquake Center, University of Southern California, Los Angeles, California
90089-0740, USA
Abstract
We introduce an empirical method of real-time early warning, for damage crustal
earthquakes identification. Period and peak values of filtered (high-pass at 0.75Hz)
displacement from 3 seconds after the vertical P arrival of the strong-motion records were
used in identifying potential damaging earthquakes. Past Mw > 5.0 crustal earthquakes
records in Taiwan from stations within epicentral distance less than 30 km are used in this
study. Results show damage earthquakes can be identified reasonably reliably within 10 s –
a time allowing early warning for areas of epicentral distance greater than 25 km.
Introduction
For timely seismic emergency response, how to immediately and accurately identify a
forthcoming damage earthquake is a very important issue, especially in the operation of the
seismic early warning system (Kanamori et al, 1997; Teng et al., 1997; Wu and Teng, 2002;
Allen and Kanamori, 2003). The potential of an earthquake to cause damage relate to many
parameters. Such as the earthquake magnitude, location, intensities, proximity to populated
areas, frequency contains of ground motions in relation with important structures, and others.
With a small area and a 23 million population rather uniformly distributed in Taiwan except
in the high Central Mountain ranges, Taiwan ranks among the top in population density in
the world. So, essentially any on-land large and shallow earthquake is a damaging
earthquake.
In general, most researchers investigated the relationships between seismic losses and
peak ground accelerations (Tsai et al., 2001; Wu et al, 2002; 2003; 2004). However, for
seismic emergency response, we need to identify areas subject to potential damage as early
as possible. Thus, we may not have time to wait strong peak ground motion. Make it clear
that we need to take a broader range of measures, including some unconventional ones, in
order to minimize the great human suffering and economic loss.
To achieve early identification of a damage earthquake, the initial portion of P-waves is
employed in this study. An earthquake excites both P and S waves in the near source region.
Generally, S waves carry major destructive energy, and the smaller amplitude P waves arrive
about 70% sooner. On the other hand, the initial portion of the P waves, despite its small and
non-destructive amplitude, may carry magnitude information of the earthquake. And a good
determination of magnitude provides information of the degree of strong shaking to be
brought on by the following S waves. In this paper we will present the results derivable
from the initial P-wave motions relationships that are useful in identifying damage
1
earthquakes based on the near source strong motion recordings in Taiwan.
Data and analysis
Big and shallow earthquakes often cause most serious damage. Thus, we selected
twenty-six events in Taiwan for this study (Table 1). The selection criteria are MW > 5.0 and
focal depth < 35 km listed in both the CWB and the Harvard catalogs. All events were well
recorded by Taiwan Strong Motion Instrumentation Program (TSMIP) network. These events
occurred from 1993 to 2003 and were widely felt in Taiwan. With about 650 modern digital
accelerographs installed at free-field sites (Fig. 1), the TSMIP station signals are digitized at
200 samples per second or higher at 16-bit resolution. Most accelerographs have clipping
recording ranges of ±2g.
A total of 208 TSMIP records are used for this study. Those are the closest eight
records by each event within epicentral distance less than 30 km. For quick identification
purpose, near source records are most important.
Vertical component strong motion records were used in this study. Input acceleration
signals were integrated twice to displacement records. We applied a 0.075 Hz high-pass
recursive type Butterworth filter to remove low frequency signals after the integration. An
automatic P picker by Allen (1978) was used to detect P arrival from vertical acceleration
records. Period (named  c ) and peak values (Pk3s) determined from 3 sec filtered
displacement signals after P arrival were used for this study.
We use the following procedure to determine  c which is similar to that used by
Nakamura (1988). We take the ground-motion displacement, u (t ) , and velocity, u (t ) , from
the vertical component record and compute the following ratio, r.
0
 u
r 
 u
2
0
0
2
0
(t )dt
(1)
(t )dt
where the integration is taken over the time interval (0, 0 ) after the onset of P wave. Usually,
 0 is set at 3 sec. Using Parseval's theorem,
2

r
4 2  f 2 uˆ ( f ) df
0


0
2
 4 2 f 2
(2)
uˆ( f ) df
where uˆ( f ) is the frequency spectrum of u (t ) , and f 2 is the average of f 2 weighted by
2
uˆ( f ) . Thus,
c 
1
f

2
2
r
(3)
here  c can be used as a parameter representing the "period" of the initial portion of the P
wave. The longer the "period", the larger the event is expected to be. This method is different
from Nakamura's (1988) in that we compute  c using the displacement u (t ) over a fixed time
window after the P-wave onset.
2
Results
Figure 2 shows, for twenty-six events, average log(  c ) versus Mw, with  c unit in sec.
Results show log(  c ) values linearly increase with the Mw. But for Mw less than 5.5 the
log(  c ) readings give large scatter. In general, damage events show large log(  c ) values, as
they are indicated in Table 1 and Figure 1.
Figure 3 shows, for the same twenty-six events, averaged log(PK3s) versus Mw, with
Pk3s unit in cm. The log(PK3s) values are also linearly increase with the Mw - a pattern
similar with that of log(  c ) . log(PK3s) rapidly increases between Mw 5.0 to 6.5 and reaches
a plateau for Mw large than 6.5. This phenomenon may represent the P-wave amplitude
saturation problem. It is very interesting that only damage earthquakes occur with large
log(PK3s) values. The log(PK3s) = -0.2 can be a demarcation line of damage events.
Discussions and Conclusions
In this study, we present results showing damage earthquakes closely correlate with
both large measurements of  c and PK3s (Fig. 2 and 3). Thus, we combine these two
parameters as an indicator. Figure 4 shows a plot for the twenty-six events with averaged
log(  c *PK3s) versus Mw. Obviously, by using log(  c *PK3s) as an indicator that can more
clearly isolate damaging events from non-damaging events. Thus, the log(  c *PK3s) = 0.0
can be considered as a good threshold for identifying damage earthquakes.
Displacement data reflect more low frequency signals than velocity or acceleration
data which emphasize more high-frequency signals. We also checked the peak values of
velocity and acceleration waveforms during the period up to 3 sec after P arrival. But these
two measurements are not well correlate to damage earthquakes nor Mw. Especially for peak
values of acceleration (PGA), small events can raise high PGA values due to waveform
focusing and special site conditions that are particularly sensitive to give variable PGA
values. Thus, this variation will introduce too much uncertainty to this analysis. So, PK3s,
the filtered displacement values within the first 3 sec, is a better indicator for damage
earthquake identification Combination of  c and PK3measurements further improves the
reliability of this analysis.
Large earthquake occurred in the populated region is an important criterion to
determine whether an event is likely to be damaging. The high population density of Taiwan
and the fact that the TSMIP stations are more densely installed in the populated regions in
Taiwan reduce the uncertainty of this criterion in this study as it is applied to a region like
Taiwan. The past factual damaging data do support our conclusions.
Further improvement can increase the applicability of the earthquake warning method
outlined above. Now almost every populated region now-a-days has internet connection,
especially in Taiwan. Modern strong motion instruments are equipped with this networking
function. All of the processes discussed in this study are carried out in automatic and realtime operation mode. For the case of Taiwan, the TSMIP network, it is possible that
parameters determination processes of the P arrival,  c and PK3s can be installed on site.
Once P arrival produces a trigger, only P arrival,  c and PK3s values (instead of the entire
3
waveforms) are sent to the control center. By using the averaged values from first eight
stations as indicators, a quick identification of a damage earthquake can be achieved within
10 s in Taiwan. By the way, P arrivals and  c measurements can be used for the
determination of the hypocenter and magnitude, respectively.
Figure 5 shows the travel time curves of the P and S waves for a reference local event
of focal depth at 10 km. Using P waves of the strong motion records from stations within 30
km of the epicenter. Figure 5 shows P waves need only about 6 seconds to reach 30 km. And
this method needs only 3 seconds of waveform data. So, the total data-gathering process
needs about 9 seconds. All other  c and PK3s calculations require negligible computer time.
At less than 10 sec time, S waves have just propagates to about 25 km from the epicenter.
Thus, this method can provide quick early warning to areas greater than this 25 km distance
where all emergency responses can commence before the onslaught of the large strong
shaking motions.
Acknowledgments
This research was supported by the National Taiwan University, Central Weather
Bureau and the National Science Council of the Republic of China.
References
Allen, R. V. (1978). Automatic earthquake recognition and timing from single traces, Bull. Seism. Soc.
Am. 68, 1521-1532.
Allen, R. M. and H. Kanamori (2003). The potential for earthquake early warning in Southern
California, Science 300, 685-848.
Central Weather Bureau (2003). One hundred questions about earthquake, Central Weather Bureau,
Taipei, Taiwan, 66pp. (in Chinese)
Kanamori, H., E. Hauksson, and T. Heaton (1997). Real-time seismology and earthquake hazard
mitigation, Nature, 390, 461-464.
Nakamura, Y. (1988). On the urgent earthquake detection and alarm system (UrEDAS). Proceeding of
9th world conference on earthquake engineering, Tokyo-Kyoto, Japan.
Teng, T.L., Y. M. Wu, T.C. Shin, Y.B. Tsai and W.H.K. Lee (1997). One minute after: strong-motion
map, effective epicenter, and effective magnitude, Bull. Seism. Soc. Am. 87, 1209-1219.
Tsai, Y. B., T. M. Yu, H. L. Chao, and C. P. Lee, 2001: Spatial distribution and age dependence of
human-fatality rates from the Chi-Chi, Taiwan, Earthquake of 21 September 1999. Bull. Seism.
Soc. Am., 91, 1298-1309.
Wu, Y. M., N. C. Hsiao, T. L. Teng, and T. C. Shin (2002). Near real-time seismic damage
assessment of the rapid reporting system. TAO, 13, 313-324.
Wu, Y. M. and T. L. Teng (2002). A virtual sub-network approach to earthquake early warning. Bull.
Seism. Soc. Am 92, 2008-2018.
Wu, Y. M., T. L. Teng, T. C. Shin, and N. C. Hsiao (2003). Relationship between peak ground
acceleration, peak ground velocity, and intensity in Taiwan. Bull. Seism. Soc. Am 93, 386-396.
Wu, Y. M., N. C. Hsiao, and T. L. Teng (2004). Relationships between strong ground motion peak
values and seismic losses during the 1999 Chi-Chi, Taiwan earthquake. Natural Hazards in press.
4
Table 1 Twenty-six events were used in this study.
Origin time (UT)
Lat.
(N)
Long.
(E)
1993/12/15 21:49:43.10 23.213 120.524
1994/06/05 01:09:30.09 24.462 121.838
1995/01/10 07:55:19.56 23.680 121.432
1995/02/23 05:19:02.78 24.204 121.687
1995/05/27 18:11:11.12 23.008 121.465
1995/12/18 16:17:54.53 24.018 121.692
1996/11/26 08:22:23.71 24.164 121.695
1998/01/18 19:56:51.71 22.725 121.089
1998/07/17 04:51:14.96 23.503 120.663
1998/11/17 22:27:32.52 22.832 120.790
1999/09/20 17:47:15.85 23.855 120.816
1999/10/22 02:18:56.90 23.517 120.423
1999/10/22 03:10:17.46 23.533 120.431
1999/10/30 08:27:49.50 24.017 121.319
2000/02/15 21:33:18.15 23.316 120.740
2000/07/14 00:07:32.46 24.048 121.728
2000/08/23 00:49:16.58 23.636 121.635
2000/09/10 08:54:46.53 24.085 121.584
2001/06/14 02:35:25.78 24.419 121.928
2001/06/19 05:16:15.46 23.177 121.077
2001/06/19 05:43:39.17 23.197 121.098
2002/02/12 03:27:25.00 23.741 121.723
2002/04/03 18:06:10.79 24.322 121.868
2002/05/15 03:46:05.91 24.651 121.872
2003/06/16 18:33:38.85 23.543 121.654
2003/12/10 04:38:13.52 23.067 121.398
# Data from Central Weather Bureau (2003)
* Caused damage under investigation
25
Depth
(km)
Mw
12.50
5.30
3.81
21.69
19.73
22.06
26.18
3.28
2.80
16.49
8.00
16.59
16.74
14.36
14.71
7.19
27.48
17.74
17.29
6.58
11.70
29.98
12.87
8.52
28.26
17.73
5.4
6.3
5.1
6.2
5.7
5.2
5.2
5.2
5.7
5.3
7.6
5.8
5.5
5.4
5.2
5.4
5.3
5.8
5.9
5.3
5.1
5.7
5.3
6.1
5.5
6.8
Number of
house
damage#
0
25
0
0
0
0
0
0
183
0
106685
69
0
0
0
0
0
0
0
0
0
0
0
0
0
*
650 TSMIP
Latitude (N)
24
Figure 1 Distribution of stations of
Taiwan
Strong
Motion
Instrumentation Program (TSMIP)
and epicenters of twenty-six events
(stars) used in this study. The larger
open stars are the five damaging
earthquakes.
23
22
(km)
0
120
121
50
100
122
Longitude (E)
5
1
0.8
log(tau_c*PK3s)
log(tau_c)
0.4
0
Damage events
No Damage
0
-1
Damage
Damage
No Damage
No Damage
-0.4
-2
5
6
7
5
8
6
7
8
Mw
Mw
Figure 4 Relationship between averaged
log(  c * PK 3s) values for twentysix events and Mw.
Figure 2 Relationship between averaged
log(PK3s) for twenty-six events
and Mw.
30
0.4
0
S arrival time
20
For focal depth 10 km
10
9 sec
Time (sec)
log(PK3s)
Damage events
No Damage
-0.4
-0.8
P arrival time
-1.2
Quick Warning
6 sec
Damage
No Damage
-1.6
0
5
6
7
0
8
Mw
20
40
60
80
100
Epidistance (km)
Figure 3 Relationship between averaged
log(  c ) for twenty-six events and
Mw.
Figure 5 Rapid reporting time and
earthquake early warning distance.
6