May 4, 2007 14:16 Geophysical Journal International gji˙3430

Geophys. J. Int. (2007) doi: 10.1111/j.1365-246X.2007.03430.x

Determination of earthquake early warning parameters,

τ c and Pd , for southern California

Yih-Min Wu,1 Hiroo Kanamori,2 Richard M. Allen3 and Egill Hauksson2

1 Department of Geosciences, National Taiwan University, No. 1, Sec. 4th, Roosevelt Rd., Taipei 106, Taiwan. E-mail: drymwu@ntu.edu.tw
2 Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA
3 Seismological Laboratory, Earth & Planetary Science, UC Berkeley, CA, USA

Accepted 2007 February 28. Received 2007 February 28; in original form 2006 August 10

SUMMARY
We explore a practical approach to earthquake early warning in southern California by deter-
mining a ground-motion period parameter τc and a high-pass filtered displacement amplitude
parameter Pd from the initial 3 s of the P waveforms recorded at the Southern California Seis-
mic Network stations for earthquakes with M > 4.0. At a given site, we estimate the magnitude
of an event from τc and the peak ground-motion velocity (PGV ) from Pd. The incoming three-
component signals are recursively converted to ground acceleration, velocity and displacement.
The displacements are recursively filtered with a one-way Butterworth high-pass filter with a
cut-off frequency of 0.075 Hz, and a P-wave trigger is constantly monitored. When a trigger
occurs, τc and Pd are computed. We found the relationship between τc and magnitude (M) for
southern California, and between Pd and PGV for both southern California and Taiwan. These
two relationships can be used to detect the occurrence of a major earthquake and provide onsite
warning in the area around the station where onset of strong ground motion is expected within
seconds after the arrival of the P wave. When the station density is high, the methods can be

GJI Seismology
applied to multistation data to increase the robustness of onsite early warning and to add the
regional warning approach. In an ideal situation, such warnings would be available within 10 s
of the origin time of a large earthquake whose subsequent ground motion may last for tens of
seconds.
Key words: earthquake early warning, magnitude, P-waves, seismic hazard mitigation.

gional warning system that requires an average of 22 s to determine

1 I N T RO D U C T I O N
earthquake parameters with magnitude uncertainties of ±0.25. It
In the past decade, progress has been made towards implementation provides a warning for areas beyond about 70 km from the epicentre.
of earthquake early warning (EEW) in Japan, Taiwan, and Mexico Taiwan’s system has been in operation since 2002 with almost no
(e.g. Nakamura 1988; Espinosa-Aranda et al. 1995; Wu et al. 1998; false alarms and successfully reported many M > 6 events (Wu
Wu & Teng 2002; Odaka et al. 2003; Horiuchi et al. 2005, 2006a). & Teng 2002; Wu et al. 2006a). With the advancement of new
Two approaches have been adopted: (1) regional warning and (2) methodology and more dense seismic networks, regional systems are
Onsite warning. The first approach is the traditional seismological beginning to be able to provide early warnings to areas close to the
method in which data from a seismic network are used to locate epicentre (Tsukada & Ohtake 2002; Kamigaichi 2004; Horiuchi
an earthquake, determine the magnitude, and estimate the ground et al. 2005).
motion in the region involved. In (2), the beginning part of the The regional approach has also been used in Japan and Mexico.
ground motion (mainly P wave) observed at a site is used to predict The method used in Mexico is slightly different from the tradi-
the ensuing ground motion (mainly S and surface waves) at the tional seismological method. It is a special case of EEW system
same site. In this case, it is not necessary to locate the event and due to the relatively large distance of about 300 km between the
estimate the magnitude, although in some systems the hypocentre earthquake source region (west coast of Central America) and the
and magnitude are also determined in order to estimate the strength warning site (Mexico City). However, the warning is conceptually
of ground shaking in the region (Nakamura 1988; Odaka et al. 2003). ‘regional’ (Espinosa-Aranda et al. 1995).
The regional approach is more comprehensive, but usually takes In Japan, various EEW techniques have been developed and de-
a longer time and cannot provide early warnings at distances close ployed by the National Research Institute for Earth Science and Dis-
to the epicentre. The early warning system in Taiwan is a typical aster Prevention (NIED) and Japan Meteorological Agency (JMA)
example. The Taiwan Central Weather Bureau (CWB) uses a re- since 2000 (Odaka et al. 2003; Kamigaichi 2004; Horiuchi et al.


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2005). In particular, JMA has started sending early warning mes- Using data from Taiwan, Wu & Kanamori (2005b) showed that
sages to potential users responsible for emergency responses. The the peak initial displacement amplitude, Pd, correlates well with the
potential users include railway systems, construction companies, peak ground-motion velocity, PGV , at the same site. When Pd >
and others. They are familiar with the implications of early warn- 0.5 cm, the event is most likely damaging. Wu & Kanamori
ing messages, as well as the technical limitations of EEW. Allen & (2005a,b) demonstrated that the combination of the τc and Pd meth-
Kanamori (2003) also explored the feasibility of using data from ods can provide reliable threshold warnings within 10 s after the
the Southern California Seismic Network (SCSN) to issue regional occurrence of a large earthquake. Wu and Zhao (2006) investigated
early warnings. the attenuation of Pd with the hypocentral distance R in southern
In contrast, the onsite approach is faster, and could provide useful California as a function of magnitude M, and obtained the following
early warning to sites at short distances from the epicentre where relationships:
an early warning is most needed. Onsite early warning can be either
M Pd = 4.748 + 1.371 × log(Pd ) + 1.883 × log(R) and
a single station or a dense array operation. For a single station oper-
ation, signals from P waves are used for magnitude and hypocentre log(Pd ) = −3.463 + 0.729 × M − 1.374 × log(R). (1)
determination to predict strong ground shaking. Nakamura (1984) For regional warning approach, when an earthquake location
first proposed this concept and also introduced a simple strong- is determined by the P-wave arrival times at stations close to the
motion index for onsite EEW (Nakamura 2004). However, the reli- epicentre, this relationship can be used to estimate the earthquake
ability of earthquake information is generally less than that obtained magnitude. Their result shows that for earthquakes in southern Cali-
with the regional warning system. New techniques may be developed fornia the Pd magnitudes agree with the catalogue magnitudes with
to improve the onsite warning accuracy. There is always a trade-off a standard deviation of 0.18 for events less than magnitude 6.5.
between warning time and the reliability of the earthquake informa- They concluded that Pd is a robust measurement for estimating the
tion. Generally, an information updating procedure is necessary for magnitudes of earthquakes for regional early warning purposes in
any EEW system. southern California.
Onsite warning methods can be especially useful in regions where In this paper, following our study for Taiwan, we have explored
a dense seismic network is deployed. Kanamori (2005) extended the the use of τc and Pd methods for seismic early warning purposes in
method of Nakamura (1988) and Allen & Kanamori (2003) to deter- southern California using the data from the SCSN operated jointly by
mine a period parameter,
√ τc , from the
 τ initial 3 s ofPτ waves. τc is de- the United States Geological Survey (USGS) and the California In-
fined as τc = 2π/ r , where r = [ 0 0 u̇ 2 (t)dt]/[ 0 0 u 2 (t)dt] (u(t): stitute of Technology (Caltech). Fig. 1 shows the station distribution
ground-motion displacement; τ0 is the duration of record used, usu- of SCSN. We will determine various regression relations between
ally 3 s, and can be computed from the incoming data sequentially. τc magnitude and τc , and Pd and PGV from the SCSN archived dataset
represents the size of an earthquake. Wu & Kanamori (2005a) stud- (i.e. offline mode). The relationships determined in this paper can be
ied the records from Taiwan systematically to explore the usefulness used to guide the future implementation of early warning systems
of the τc method for early warning purposes. in real time.

Figure 1. Map of broadband stations recorded by the Caltech/USGS Southern California Seismic Network (SCSN). SCSN stations are shown as circles, Anza
Seismic Network stations as triangles, and Berkeley Digital Seismic Network (BDSN) as open squares. The epicentres of the earthquakes included in this study
are shown as stars.


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Determination of earthquake early warning parameters 3

acceleration during the 3 s after the P arrival on the vertical compo-

2 D AT A A N D A N A LY S I S nent, Pa, be greater than 2.5 Gal. Generally, the events with small
We selected a total of 27 events in southern California listed in Pa are not important for EEW purposes. Following the analysis of
the SCSN catalogue for the period from 1992 to 2005. Fifteen of Kanamori (2005), Wu & Kanamori (2005a,b), Wu et al. (2006b)
them are events with M ≥ 5–7 for which our automatic P-wave and Wu and Zhao (2006), we use a duration of 3 s for estimation of
detection algorithm picked the P arrival on at least three records τc and Pd. The longer the duration, the more reliable the magnitude
within the epicentral distance of 100, 200 and 300 km, respectively. estimate is, but the warning time gets shorter. The choice of 3 s is
The remaining twelve events are with 5 > M ≥ 4 for which the P based on the numerical experiment for moment-rate functions of
arrival was picked on at least 6 records within the epicentral distance Sato & Hirasawa (1973) model. As shown by Fig. 3 of Kanamori
of 30 km (Table 1 and Fig. 1). In the SCSN catalogue, the magnitudes (2005), if we use a duration of 3 s, τc increases with magnitude up to
are the local magnitude M L for M L ≤ 6, and the moment magnitude 7 beyond which it saturates. A shorter duration leads to τc saturation
M w for events with M L ≥ 6. Here, we denote the magnitude simply at a smaller magnitude. Although the moment rate functions of real
by M. earthquakes are different from the synthetic ones, this test suggests
Most SCSN stations have both high-gain broad-band velocity and that a duration of 3 s yields a good measure of the magnitude of the
low-gain force-balance acceleration (FBA) sensors (Hauksson et al. event up to M = 7. Depending on the specific application, a shorter
2001). Signals are digitized at 100 or 80 samples per second with or longer duration can be used, but the trade-off mentioned above
24-bit resolution. The low-gain channels record all large earthquakes should be kept in mind.
without clipping. The broad-band channels provide high signal-to-
noise (S/N) ratio data for the initial 3 s of the P waves used in this
3 R E S U LT S
study.
We used a total of 1161 waveforms (Table 1) in this study. Among Fig. 2 shows τc determined from the 431 records (Table 1) plotted as a
them, 431 vertical components are used to determine τc and Pd. The function of magnitude, M. Although logτc increases approximately
acceleration signals are integrated to velocity and displacement. The linearly with magnitude, the scatter is large for events with M <
velocity signals are differentiated to acceleration and integrated to 5.5. The large scatter is primarily due to the low S/N ratio when the
displacement. We apply a 0.075 Hz high-pass recursive Butterworth amplitude during the first 3 s is very small. However, the scatter is
filter to remove the low frequency drift after integration. An auto- smaller than that in the results for Taiwan (Wu & Kanamori 2005a),
matic P picker described by Allen (1978) is used to detect the P probably due to the higher S/N ratio achieved by the broad-band
arrival from the vertical acceleration records. Since the τc analysis SCSN instruments. We made τc determinations for the 27 events for
requires records with high (S/N) ratio, we set a threshold accelera- which at least three measurements are available for each event. The
tion amplitude for τc determination. We require that the peak ground three potentially damaging earthquakes with M > 6 all have τc > 1 s.

Table 1. List of 27 earthquakes used in this study.

Event time Lat. Long. Depth M Records

(N) (W) (km) Va NEb

1992/06/28 11:57:34.13 34.200 116.437 1.0 7.30 6 4
1994/01/17 12:30:55.39 34.213 118.537 18.4 6.70 13 4
1994/01/17 12:31:58.12 34.275 118.493 6.0 5.89 3 4
1997/04/26 10:37:30.67 34.369 118.670 16.4 5.07 15 30
1998/03/06 05:47:40.34 36.067 117.638 1.8 5.23 6 12
1998/03/07 00:36:46.84 36.076 117.618 1.7 5.04 4 8
1999/10/16 09:46:44.13 34.594 116.271 0.0 7.10 89 16
1999/10/16 09:59:35.20 34.678 116.292 10.8 5.77 9 18
1999/10/21 01:54:34.17 34.874 116.391 1.0 5.06 5 10
2000/02/21 13:49:43.13 34.050 117.252 15.4 4.37 12 24
2001/01/14 02:26:14.06 34.284 118.404 8.8 4.26 15 30
2001/01/14 02:50:53.69 34.289 118.403 8.4 4.05 15 30
2001/02/10 21:05:05.78 34.289 116.946 9.1 5.13 62 124
2001/09/09 23:59:18.04 34.059 118.388 7.9 4.24 33 60
2001/10/31 07:56:16.63 33.508 116.514 15.2 5.09 72 140
2002/01/02 12:11:28.68 33.379 116.434 12.6 4.21 11 20
2002/01/29 05:53:28.93 34.361 118.657 14.2 4.18 14 28
2002/02/22 19:32:41.75 32.319 115.322 7.0 5.70 12 22
2002/09/03 07:08:51.87 33.917 117.776 12.9 4.75 23 44
2002/09/21 21:26:16.64 33.225 116.113 14.6 4.31 7 14
2003/02/22 12:19:10.58 34.310 116.848 1.2 5.37 75 146
2004/05/09 08:57:17.30 34.395 120.022 4.4 4.40 7 12
2004/09/29 22:54:54.24 35.390 118.624 3.5 5.04 32 64
2005/01/06 14:35:27.67 34.125 117.439 4.2 4.42 17 32
2005/01/12 08:10:46.38 33.953 116.395 7.6 4.26 8 16
2005/04/16 19:18:13.55 35.027 119.178 10.3 5.15 8 16
2005/06/16 20:53:26.02 34.058 117.011 11.6 4.90 14 24
a Vertical component used for determination of τc and Pd.
b Both north–south and east–west components are used for determination of PGV .


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4 Y.-M. Wu et al.

Figure 3. Relationship between peak initial displacement amplitude (Pd)

measurements and peak ground velocity (PGV ) for 199 records with epi-
Figure 2. The τc measurements (open circles) from 431 records with Pa > central distances less than 30 km from the epicentre in Southern California
2.5 Gal versus M. Solid diamonds show the average for the 27 events. (red solid circles) and the results from Taiwan (blue diamonds). Solid line
shows the least squares fit and the two dashed lines show the range of one
standard deviation.

The regression with errors in both coordinates of M and τc results 4 E X T E N S I O N O F O N S I T E WA R N I N G

in relationships T O R E G I O N A L WA R N I N G

log τc = 0.237M − 1.462 ± 0.091 and For onsite warning, only near-source signals are used and, in princi-
ple, the determinations of τc and Pd from a single station are all that
M = 4.218 log τc + 6.166 ± 0.385. (2) are needed. When we have a very dense network, however, we can
combine the data from multiple stations to increase the robustness
The standard deviation of the estimate of M is 0.39 for all the events. of warning and also add the regional warning approach. We ex-
This regression is based on the average τc for each event with at least plored this possibility using 13 events selected from the list given in
three measurements. Table 1. These events are from 1998 to 2005 for which at least four
Fig. 3 shows the relationship between Pd and PGV for the 199 stations within 30 km of the epicentre are available. Our algorithm
records with epicentral distances less than 30 km (red solid circles). automatically picks the P arrival and determines τc and Pd for all the
PGV values increase with Pd approximately logarithmically, as ob- records within 30 km of the epicentre. Then, we average the τc and
served in our previous results from Taiwan (Wu & Kanamori 2005b) Pd values determined at these stations. We use the average values to
shown by blue diamonds in Fig. 3. So far, the data from southern predict the average PGV for the area using eq. (3). Fig. 4 shows the
California are for relatively small ground motions. In contrast, the relationship between the predicted and measured average PGV . The
results from Taiwan include the data from sites with large ground average ratio of predicted to observed PGV is 0.940 with a small un-
motions. However, the trend is similar for Taiwan and southern certainty of 0.143 on the logarithmic scale. The uncertainty is much
California. Combining the data from Taiwan and southern Califor- smaller than that in Fig. 3. The uncertainty of intensity prediction
nia helps to extrapolate the present southern California results to- is now reduced from 1.1 to 0.5 units. Thus, dense array deployment
ward larger ground motions. For the combined data set, we obtained can be a practical means to reduce the uncertainty of onsite EEW.
a regression relation To add the regional warning approach, we use 4–6 earliest P
arrivals (not every event has six stations within the distance range
log(P GV ) = 0.903 log(Pd) + 1.609 ± 0.309 of 30 km) to locate the event. A simple half-space velocity model
(P GV in cm/sec and Pd in cm). (3) is used with a P-wave velocity of 5.8 km s–1 . This velocity is em-
pirically obtained from traveltime curves within 30 km from the
The southern California instrumental intensity scale for large epicentre. Once the hypocentre is determined, we can estimate the
events is defined with respect to PGV (Wald et al. 1999a,b). From magnitude from Pd at each station using (1), and take the average
these empirical relationships we can predict PGV or intensity from over all the stations to estimate the event magnitude. Fig. 5 shows
the initial 3 s of P waves for early warning purposes. In southern the comparison between the magnitude estimated from Pd (denoted
California, instrumental intensity (I MM ) is related to PGV by I MM = by M pd ) and the magnitude computed from τc (denoted by Mτc ). For
3.51 log (PGV ) + 2.35 for V ≤ I MM ≤ IX (Wald et al. 1999a). Thus, some of the events shown by red solid square symbols in Fig. 5,
the standard deviation of 0.309 in log(PGV ) leads to an uncertainty we do not have multiple stations to locate the hypocentre. For
of 1.1 in intensity. those events, we used the catalogue locations to compute M pd . The


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Determination of earthquake early warning parameters 5

source approximation, because the source dimensions of damaging

earthquakes are larger than 6 km.

5 P R A C T I C A L I S S U E S A S S O C I AT E D
W I T H O N L I N E I M P L E M E N T AT I O N
In the online mode, when τ c , Pa and Pd are measured, no information
about the event magnitude and the epicentral distance is available.
As we discussed earlier, when Pd or Pa is small, the measurement of
τ c cannot be made reliably. Such an event with small Pd or Pa is not
important for early warning purposes and we can ignore such events.
If Pd or Pa is larger than a threshold value, the measured Pd and τ c
can be used to estimate the shaking intensity and M, respectively,
although the value of M is not directly used for onsite early warning
purposes. In principle, a single measurement of τ c and Pd is enough
for onsite warning, but in practice it is desirable to have more than
one pair of measurements to increase the reliability and robustness of
the warning. In the offline result presented above, the average of five
readings provides a fairly reliable estimate. However, in the online
mode, the time after the first trigger is the key parameter. If the event
is located inside a dense network, then the five-station average can be
obtained fairly rapidly. However, if the station distribution is sparse,
Figure 4. Relationship between predicted and observed PGV of 13 test
it will take too long to get the five-station average to be useful for
events. Solid line shows 1:1 line and the two dashed lines show the range of early warning. Exactly how long we should wait depends on many
one standard deviation. practical factors, and cannot be decided until actual implementation
is achieved.
To establish the empirical relationships between M and τ c ,
and Pd and PGV in real-time mode, we need to test the algo-
rithms for a sufficiently long time. Such a testing of algorithms
is presently planned within California Integrated Seismic Network
(CISN).
By necessity for early warning purposes, the two parameters, τ c
and Pd, are determined only from the very beginning of a seismic
record and considerable scatter in the τ c versus M and Pd versus
PGV relationships is inevitable. The errors in estimation of M and
PGV may lead to false alarms and missed alarms. How to deal with
false alarms and missed alarms is an important issue in EEW, but
it must be discussed in relation to the specific use of early warning
information, which is beyond the scope of this paper.

6 D I S C U S S I O N S A N D C O N C LU S I O N S
The period parameter τc from SCSN is smaller than that for a sim-
ilar magnitude earthquake in Taiwan. For most events with M >
5 in Taiwan, τc > 1 s while for the events with M > 6 in south-
ern California,τc > 1 s. This may be due to the difference in S/N
ratio, especially for smaller earthquakes. Records from Taiwan are
16-bit strong-motion data, and those from SCSN are mainly from
24-bit broad-band data, especially for small earthquakes. The use of
Figure 5. Magnitudes estimated from τc versus those estimated from Pd. strong-motion data involves double integration which occasionally
Blue solid circles show the measurements for the 27 events. Red solid squares results in long-period drift and larger τc . However, the difference
show the measurements for the 13 test events. Solid line shows 1:1 line and in τc is expected to decrease as the event size increases. For practi-
the two dashed lines show the range of one standard deviation 0.39. cal early warning purposes, we are concerned with the events with
M > 6.
Considerable uncertainties in magnitude determination or inten-
agreement between M pd and Mτc is good, and using Pd, in addition sity prediction using the initial P waves are inevitable. If the seismic
to τc , for magnitude estimation increases the robustness of early network is dense we can significantly reduce the uncertainties by
warning. With the hypocentre and the magnitude having been esti- taking the average of the measurements from several stations. In
mated, we can extend our method to regional warning, if desired. our test, the uncertainties of magnitude determination and intensity
The hypocentre location error is about 6 km for the 13 events listed can be reduced to 0.3 and 0.5, respectively, if more than four stations
in Table 1. The location error of 6 km is acceptable within the point are available within 30 km of the epicentre.


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6 Y.-M. Wu et al.

30 km from the epicentre. The warning information could include

earthquake location, magnitude and estimated intensity. Because
the SCSN system was not specifically designed for early warning
purposes, considerable delays occur during data processing. If the
delays in the system including those during signal transmission are
shortened in the future, early warning information may be available
at sites with a distance shorter than 30 km. For deeper events such
as the 1994 Northridge earthquake that had a hypocentral depth of
16 km, the minimum distance where early warning is available can
be even shorter.

Figure 6. τc residuals (deviation of τc from the average of each event) versus

AC K N OW L E D G M E N T S
hypocentral distance for the 431 records with Pa > 2.5 Gal. The first author wishes to thank Dr. Li Zhao and David M. Tratt
for providing many thought-provoking comments. We thank the
SCSN and the Southern California Earthquake Data Center for pro-
In our model, τc is a source parameter and should not depend on viding public access to the seismological data, and the staff at the
the distance. To test this, we plot in Fig. 6 the deviation of τc from the Seismological Laboratory at Caltech and U. S. Geological Survey
average τc for each event as a function of the hypocentral distance. In at Pasadena. This research was supported by the National Science
total, 431 records with Pa > 2.5 gal from the nine events in Table 1 Council of the Republic of China (NSC95-2119-M-002-043-MY3
are used. At the distance less than 150 km, τc does not depend on & NSC94-2116-M-002-021), and Caltech’s Tectonics Observatory.
distance, but τc tends to be positive at distances larger than 150 km. Contribution number 9119, Division of Geological and Plan-
It is possible thatτc increases with distance as the waves are more etary Sciences, California Institute of Technology (Caltech),
attenuated. In practical applications, we measure τc at short dis- Pasadena.
tances, mostly less than 100 km, and the distance dependence can
be ignored.
From the results of our off-line experiment, we estimate that the
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Journal compilation 
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