of 9
Short Note
A New Trigger Criterion for Improved Real-Time Performance of Onsite
Earthquake Early Warning in Southern California
by M. Böse, E. Hauksson, K. Solanki, H. Kanamori, Y.-M. Wu, and T. H. Heaton
Abstract
We have implemented and tested an algorithm for onsite earthquake
early warning (
EEW
) in California using the infrastructure of the Southern California
Seismic Network (
SCSN
). The algorithm relies on two parameters derived from the
initial 3 sec of
P
waveform data at a single seismic sensor: period parameter
τ
c
and
high-pass filtered displacement amplitude
P
d
. Previous studies have determined em-
pirical relationships between
τ
c
and the moment magnitude
M
w
of an earthquake, and
between
P
d
and the peak ground velocity (
PGV
) at the site of observation. In 2007,
seven local earthquakes in southern California with
4
:
0
M
L
4
:
7
have triggered
the calculation of
M
w
and
PGV
by the
EEW
algorithm. While the mean values of es-
timated parameters were in the expected range, the scatter was large, in particular for
the smallest events. During the same time period the
EEW
algorithm produced a large
number of false triggers due to low trigger thresholds. To improve the real-time per-
formance of the onsite approach, we have developed a new trigger criterion that is
based on combinations of observed
τ
c
and
P
d
values. This new criterion removes
97% of previous false triggers and leads to a significant reduction of the scatter in
magnitude estimates for small earthquakes.
Introduction
Earthquake early warning (
EEW
) systems make use of
differences between the propagation speed of seismic and
electromagnetic waves and issue warnings, if necessary, to
potential users before strong shaking at the user sites occurs.
The maximal warning time of an
EEW
system is generally
defined as the time span between the
P
-wave detection at the
first triggered
EEW
sensor and the arrival of high-amplitude
S
or surface waves at the user site. As these time periods usu-
ally are extremely short,
EEW
systems must recognize the
severity of expected ground motions within a few seconds.
Based on this information, suitable actions for the damage
reduction can be triggered and executed (Harben, 1991;
Goltz, 2002).
EEW
systems face two major challenges: (1) they have
to be highly reliable, which means that both missed and false
alerts need to be avoided; (2) the warning times should be as
large as possible. About six
EEW
systems are presently in
operation or in testing: in Japan (Nakamura, 1988; Kamigai-
chi, 2004; Horiuchi
et al.
, 2005; Tsukada
et al.
, 2007), in
Taiwan (Wu and Teng, 2002; Wu and Kanamori 2005a,b),
in California (Allen and Kanamori, 2003; Kanamori, 2005;
Allen, 2007; Cua and Heaton, 2007; Wu
et al.
, 2007; Wur-
man
et al.
, 2007), in Mexico (Espinosa-Aranda
et al.
, 1995),
in Romania (Wenzel
et al.
, 1999; Böse
et al.
, 2007), and in
Turkey (Erdik
et al.
, 2003; Böse
et al.
, 2008). Many of these
systems are operated for research purposes and do not trigger
any actions so far.
EEW
systems are either designed for (1) regional or for
(2) onsite warning. Regional warning systems that are based
on networks of seismic stations usually yield stable but late
estimates of seismic source parameters and therewith warn-
ings. Onsite warning systems, in contrast, are based on single
sensor observations and allow for fast but usually less reli-
able estimates (Kanamori, 2005).
The California Integrated Seismic Network (
CISN
) has
developed an infrastructure that allows for testing
EEW
al-
gorithms in a real-time environment, with the objective to
(1) evaluate their performance in the rapid assessment of
earthquakes, as well as to (2) examine the steps required to
develop a pilot
EEW
system in California (Hauksson
et al.
,
2006). The
CISN
infrastructure consists of both hardware and
software systems. The latter has been jointly developed by
the California Institute of Technology (Caltech), the U.S.
Geological Survey (
USGS
), and University of California,
Berkeley, building on the existing software systems by the
CISN
and the Advanced National Seismic System (
ANSS
).
Three
EEW
algorithms are currently tested within the
CISN
: ElarmS (Allen and Kanamori, 2003; Allen, 2007;
897
Bulletin of the Seismological Society of America, Vol. 99, No. 2A, pp. 897
905, April 2009, doi: 10.1785/0120080034
Wurman
et al.
, 2007), the Virtual Seismologist (Cua and
Heaton, 2007), and the
τ
c
P
d
algorithm (Kanamori, 2005;
Wu
et al.
, 2007). The two first algorithms are regional (net-
work based) warning approaches, while the
τ
c
P
d
algorithm
belongs to the group of onsite (single sensor based) warning
methods (Kanamori, 2005).
In this study, we focus on the real-time performance
of the
τ
c
P
d
algorithm in southern California. About 130
broadband stations (100 samples per second velocity data)
of the Southern California Seismic Network (
SCSN
) as part
of the
CISN
are presently used for the
EEW
testing (Fig. 1).
All of the data are transmitted via digital communications
(Hauksson
et al.
, 2001). Between 1 January 2007 and 31 De-
cember 2007, about 80 local earthquakes in southern Cali-
fornia with
M
L
3
:
0
were reported, including the nine
largest earthquakes with
4
:
0
M
L
4
:
7
(see the Data and
Resources section). Of course, small- and moderate-sized
earthquakes with
M<
6
:
0
will usually not cause damage
and, therefore, do not require early warnings. However, it
is necessary to use the more frequent small events for testing
and calibration of
EEW
algorithms and systems, because
large earthquakes occur rarely.
The difficulty in using small- and moderate-sized earth-
quakes for testing the single station-based warning algo-
rithms is caused by the usually low signal-to-noise (
S/N
)
ratios of the seismograms, especially in the early
P
phase.
To use these small earthquakes for testing, we need to set
the trigger thresholds at the stations at a low level. As a con-
sequence, however, we run the risk of a large number of false
triggers produced by noise and teleseismic earthquakes. In
this article, we describe a trigger criterion suitable for onsite
warning that automatically recognizes and removes the ma-
jority of false triggers and that helps to stabilize the magni-
tude estimates for small- and moderate-sized earthquakes.
Although this problem is not serious for large earthquakes,
a better triggering algorithm developed for small to moderate
earthquakes will be useful for improving the overall perfor-
mance of
EEW
for large earthquakes, too.
Figure
1.
Distribution of broadband sensors of the Caltech/
USGS SCSN
used for
EEW
testing in southern California (triangles). Stars
mark the epicentres of nine local earthquakes (
4
:
0
M
L
4
:
7
) analyzed in this study. Details are given in Table 1.
898
Short Note
The
τ
c
P
d
Algorithm
One of the major elements of
EEW
is the rapid and reli-
able determination of earthquake magnitudes. To determine
the size of an earthquake, it is important to find out whether
the earthquake rupture has stopped or keeps growing. This is
generally reflected in the period of the initial ground motion.
Kanamori (2005) extended the method of Nakamura (1988)
and Allen and Kanamori (2003) to determine a period param-
eter
τ
c
from the initial few seconds of
P
waves.
τ
c
is defined
as
τ
c

2
π
=

r
p
where
r

R
τ
0
0
_
u
2

t

dt

=

R
τ
0
0
u
2

t

dt

,
u

t

is the ground-motion displacement, and
τ
0
is the duration
of the record used. In a series of studies (Wu and Kanamori,
2005a,b; Wu
et al.
, 2006, 2007; Wu and Kanamori, 2008a,b)
τ
0
is set at 3 sec. Wu
et al.
(2007) systematically studied
the records from earthquakes in southern California to ex-
plore the usefulness of
τ
c
for
EEW
purposes. They found that
the moment magnitude
M
est
of an earthquake can be esti-
mated from
M
est

4
:
218
log
10

τ
c

6
:
166

σ
M
est
;
(1)
with the standard deviation
σ
M
est

0
:
385
.
Another important element in
EEW
is the estimation of
the strength of
S
-wave shaking. Wu and Kanamori (2005b)
showed that the maximum amplitude of the high-pass filtered
vertical displacement during the initial 3 sec of the
P
wave,
P
d
, can be used to estimate the peak ground velocity (
PGV
)at
the same site. Based on 780 earthquake records from Japan,
Taiwan, and southern California at epicentral distances of
less than 30 km, Wu and Kanamori (2008a) established an
empirical relationship for estimating peak ground velocity
PGV
est
from
P
d
with the equation
log
10

PGV
est

0
:
920
log
10

P
d

1
:
642

σ
PGV
est
(2)
(
PGV
est
is in centimeters per second and
P
d
is in centi-
meters), where
σ
PGV
est

0
:
326
.
For the real-time testing of the
τ
c
P
d
method within the
SCSN
, we have implemented the algorithm in an UNIX en-
vironment. We have chosen a modular design, so that mod-
ules can be easily changed, replaced, and/or added by new
modules in order to improve the overall capabilities of the
system. The processing steps are as follows: (1) retrieve ve-
locity data from the
SCSN
(or the waveform storage); (2) set
the baseline at zero by using average values continuously
determined from the real-time data streams in intervals of
60 sec, and apply gain correction; (3) convert velocity to dis-
placement by recursive integration; apply high-pass Butter-
worth filter (
>
0
:
075
Hz); (4) calculate
τ
c
and
P
d
from the
initial 3 sec of waveform data.
To pick the seismic
P
phase we use a modification of an
algorithm proposed by Allen (1978) in a combination with a
simple
P=S
wave discriminator, which is based on the ratios
of horizontal to vertical ground motions. To avoid false trig-
gers, the system used station-dependent
P
d
thresholds for
triggering. The thresholds ranged between 0.00004 and
0.0644 cm with an average of 0.0057 cm.
Data
For the time from 1 January 2007 to 31 December 2007,
the
SCSN
reports 79 local earthquakes with
M
L
3
:
0
for
southern California (see the Data and Resources section).
P
d
thresholds were exceeded for 40 of these events, trigger-
ing a total of 269 stations. During the same time period the
system produced some thousand false triggers due to the gen-
erally low trigger thresholds set for initial testing.
Seven out of the nine earthquakes with
4
:
0
M
L
4
:
7
(Fig. 1) were detected by the
EEW
algorithm; during events
number 14330056 and 10285533, the
EEW
algorithm was
not running. The number of reporting stations varied be-
tween 3 and 41 (Table 1). Averaged over the estimates from
all reporting stations for all the seven events, the mean error
of magnitudes
M
est
, estimated from period parameter
τ
c
in
equation (1), is 0.5 units (Table 1). The magnitudes were usu-
ally slightly overestimated. The scatter of estimates is con-
siderable, in particular for the smaller events with
M
L
<
4
:
5
.
Table
1
Local Earthquakes in Southern California with
4
:
0
M
L
4
:
7
in 2007 Used for EEW Testing
Station-Dependent
P
d
Thresholds
New
τ
c
P
d
Trigger Criterion
Event Identification
Number
Date; Time
(yyyy/mm/dd; hh:mm:ss UTC)
Latitude
(°)
Longitude
(°)
Depth
(km)
M
L
Number of Reporting
Stations
M
est
Number of Reporting
Stations
M
est
10275733
2007/09/02; 17:29:14.790 33.7322

117
:
4770
12.60 4.7
19
4
:
2

0
:
8
44
4
:
3

0
:
6
14312160
2007/08/09; 07:58:49.590 34.2995

118
:
6195
7.58 4.6
19
4
:
8

0
:
5
31
4
:
8

0
:
4
14285168
2007/04/15; 22:57:26.720 32.6923

116
:
0565
8.01 4.3
3
4
:
8

0
:
5
5
5
:
0

0
:
3
14330056
2007/10/24; 12:22:48.770 35.8380

117
:
6847
4.50 4.3
——
9
4
:
5

0
:
5
10230869
2007/02/09; 03:33:44.070 33.2113

116
:
1480
12.00 4.2
41
4
:
4

1
:
1
13
3
:
9

0
:
5
10285533
2007/10/16; 08:53:44.120 34.3853

117
:
6347
8.06 4.2
——
20
4
:
2

0
:
4
14295640
2007/06/02; 05:11:26.470 33.8718

116
:
2118
4.83 4.2
15
4
:
3

1
:
4
11
3
:
9

0
:
2
14282008
2007/03/30; 09:09:35.830 36.0277

117
:
7753
0.35 4.0
10
5
:
4

0
:
4
1
4.6
10295849
2007/12/19; 12:14:09.590 34.1555

116
:
9820
10.22 4.0
16
4
:
6

1
:
4
15
4
:
2

0
:
4
For most events the number of reporting stations increases after application of the new
τ
c
P
d
trigger criterion (compared to the previously used station-
dependent
P
d
thresholds) while the mean errors and standard deviations of estimated magnitudes
M
est
decrease (see the Data and Resources section).
Short Note
899
Analyses of the corresponding distributions (Fig. 2) reveal
that the standard deviations of
M
est
range from 0.5 to 1.4
magnitude units. Note that the scatter is mainly due to the
records with poor
S/N
ratios, station drift, et cetera, rather
than due to a failure of the
τ
c
P
d
algorithm itself. For the
analyzed magnitude range
4
:
0
M
4
:
7
we assume
M
L
M
w
(Clinton
et al.
, 2006).
The
τ
c
P
d
Trigger Criterion
To improve the real-time performance of the
τ
c
P
d
al-
gorithm, in particular for small- and moderate-sized events,
we modified the previously used trigger algorithm based on
station-dependent
P
d
thresholds with the aim (1) to decrease
the number of false triggers, that is, triggers that cannot be
Figure
2.
Histograms for the estimated magnitudes
M
est
for the events in Table 1 obtained from the application of station-dependent
P
d
thresholds. Stars on the
x
axis show the magnitudes determined by
SCSN
. Note the high scatter in
M
est
in particular for earthquakes with
M
L
4
:
5
. During two events, 14330056 and 10285533, the
EEW
algorithm was not running.
900
Short Note
associated with any local earthquakes, (2) to reduce the scat-
ter in
M
est
, that is, to automatically recognize earthquake rec-
ords with poor
S/N
ratios, and (3) to increase the number of
reporting stations with high
S/N
ratios that, however, did not
pass the previously set
P
d
thresholds. The new trigger cri-
terion is based on
τ
c
-dependent and therewith magnitude-
dependent
P
d
thresholds. We call it
τ
c
P
d
trigger criterion.
The
τ
c
P
d
trigger criterion uses an empirical attenuation
relation for
PGV
determined by G. Cua and T. Heaton (un-
published manuscript, 2008) based on earthquake records
from southern California and the Next Generation Attenua-
tion (
NGA
) strong-motion database. This relation is valid
for earthquakes in the magnitude range
2
:
0
<M
8
:
0
and
rupture-to-site distances
r
200
km. The relationship gives
PGV
as a function of
r
with the magnitude as a parameter.
Using equations (1) and (2), we transform the function to
a relation between
P
d
and
r
with
τ
c
as a parameter (see
the Appendix), schematically shown in Figure 3 (left-hand
panel). We then assume that only earthquakes within a cer-
tain distance range
r
min
r
r
max
are relevant to
EEW
at a
specific site. As shown in Figure 3 (left-hand panel), ampli-
tude
P
d
has limiting values
P
0
d;
max
and
P
0
d;
min
, corresponding
to
r
min
and
r
max
, respectively. To illustrate the dependence of
P
d
on the period parameter, we plot in Figure 3 (right-hand
panel)
P
0
d;
min
(filled circles) and
P
0
d;
max
(filled triangles) as a
function of
τ
c
. If we consider the uncertainties in the
τ
c
M
est
relation (equation 1), the
P
d
PGV
est
relation (equation 2),
and the empirical attenuation relation for
PGV
(G. Cua and
T. Heaton, unpublished manuscript, 2008), we obtain
P
d
thresholds
P
00
d;
min
and
P
00
d;
max
, as indicated by the two dashed
curves in the right-hand panel of Figure 3 (see the Appendix
for a more detailed explanation).
We formulate the
τ
c
P
d
trigger criterion as follows: for
a given period parameter
τ
c
(
0
:
2
τ
c
) and for a given dis-
placement amplitude
P
d
(
P
d
>P
d;
thres
), both determined
from the initial 3 sec of the
P
waveform data at a given sta-
tion, we characterize the quality of the corresponding trigger
by a parameter
Q
, which is defined by
Q
8
<
:
1
:
0
;
if

P
d
P
d;
thres

and

P
d
P
0
d;
min

and

P
d
P
0
d;
max

;
0
:
5
;
if

P
d
P
d;
thres

and
f
P
d
P
00
d;
min

and

P
d
P
0
d;
min

or

P
d
P
0
d;
max

and

P
d
P
00
d;
max
g
;
0
:
0
;
else.
(3)
In the first case,
P
d
is between
P
0
d;
min
and
P
0
d;
max
(region Ia in
Fig. 3, right-hand panel) and the corresponding trigger was
likely caused by a local earthquake within
r
min
r
r
max
.
We judge the detected event is with good data quality and
a high
S/N
ratio and assign
Q

1
:
0
. In the second case,
the value of the observed
τ
c
P
d
pair is between
P
0
d;
min
and
P
00
d;
min
or between
P
0
d;
max
and
P
00
d;
max
(region Ib in Fig. 3,
right-hand panel). We judge the detected event to be asso-
ciated with moderate data quality and assign
Q

0
:
5
.In
the third case (regions IIa or IIb in Fig. 3, right-hand panel),
the trigger was likely caused by a distant earthquake
(
r>r
max
), an earthquake with poor
S/N
ratio, or by noise.
In this case we assign
Q

0
:
0
.If
Q
0
:
5
,
M
est
and
PGV
est
are computed. If
Q

0
:
0
, the trigger is ignored.
Results
The
τ
c
P
d
diagram in Figure 4 shows the distribution of
triggers produced by the onsite warning algorithm in south-
ern California in 2007: correct triggers, associated with local
earthquakes, are marked by dots and false triggers by x
s. In
order to extend the range of magnitudes, we also included
431 records of 27 Californian earthquakes with
4
:
2
M
7
:
3
studied by Wu
et al.
(2007). We apply the
τ
c
P
d
trigger criterion with
r
min

1
km,
r
max

100
km, and
P
d;
thres

0
:
0005
cm (which is about ten times smaller than
the average value of the previously set station-dependent
P
d
thresholds) to these data.
As predicted, triggers caused by earthquakes tend to
cluster between
P
0
d;
min
and
P
0
d;
max
(Fig. 4). Only a few of
them lie between
P
0
d;
min
and
P
00
d;
min
or
P
0
d;
max
and
P
00
d;
max
, re-
spectively. False triggers, in contrast, tend to cluster outside
these areas: they usually have high
τ
c
and low to moderate
P
d
values. Applying the new
τ
c
P
d
criterion to all triggers
produced by the
EEW
algorithm in 2007, allows removing
97% of the former false triggers. Also, the number of earth-
quake triggers, which were earlier rejected due to the pre-
viously used station-dependent
P
d
thresholds, is increased.
For instance, the number of reporting stations increases by
25 for the 2 September 2007
M
L
4.7 Elsinore earthquake,
and by 12 for the 9 August 2007
M
L
4.6 Chatsworth earth-
quake (Table 1). For two events, 14330056 and 10285533,
during which the
EEW
algorithm was not running, we obtain
from archived data estimates from 9 and 20 reporting sta-
tions, respectively. For event 14282008 the observed ground
motion passes the new
τ
c
P
d
trigger criterion at only one
close station.
Another positive effect is that the new
τ
c
P
d
trigger cri-
terion significantly reduces the scatter of
M
est
. Figure 5
shows the recalculated levels of
M
est
for the earthquakes pre-
viously analyzed in Figure 2, which had been obtained from
the station-dependent
P
d
thresholds. Averaged over the es-
Short Note
901
timates of all triggered stations for the nine events, the mean
prediction error of
M
est
is 0.3 magnitude units. The standard
deviations of estimates range between 0.2 and 0.6 magnitude
units (Table 1).
Discussion and Conclusions
The
τ
c
P
d
onsite warning algorithm developed by Ka-
namori (2005) and Wu
et al.
(2007) has been implemented
within the
SCSN
and tested for about 1 yr in a real-time en-
vironment. Although no large events that would require early
warning occurred during 2007, the
EEW
algorithm processed
seven local earthquakes with
4
:
0
M
L
4
:
7
. The high scat-
ter in the estimated magnitudes for these small events can be
significantly reduced after the application of a new
τ
c
P
d
trigger algorithm presented in this article. This criterion es-
sentially removes all triggers that were likely caused by dis-
tant earthquakes, noise, or events with poor
S/N
ratios. At
the same time the criterion allows reducing the number of
false triggers by 97%, compared to the earlier used station-
dependent
P
d
thresholds.
The earthquake 14282008 occurred 6 km east of Coso
Junction, an area known for the frequent occurrence of
earthquake swarms. The event was preceded by more than
20 foreshocks and followed by more than 30 aftershocks
within a 5 min period (see the Data and Resources section).
A small foreshock that occured 48 sec before the mainshock
caused high-background noise level at the majority of close
EEW
stations before and during the arrival of the seismic
P
phase from the mainshock. Although such foreshocks are rel-
atively rare, the real-time identification of such events will
pose a major challenge in developing future
EEW
systems.
Mass-recentering of the sensors by the network opera-
tors can produce both large
τ
c
and
P
d
values within the areas
Ia and Ib in Figure 3, right-hand panel, and, thus, can cause
false triggers. We are developing capabilities in the
EEW
al-
gorithm to automatically recognize these events by, for in-
stance, evaluating the bias level of the signal. In the future,
we plan joint analysis of waveforms from the colocated
broadband and strong-motion instruments, which can be
used for the elimination of calibration steps.
Figure
3.
Illustration of the
τ
c
P
d
trigger criterion. Left-hand panel: Attenuation relations for
P
d
as a function of site-to-rupture distance
r
and period parameter
τ
c
;
τ
c
increases from bottom to top. The assumption that only earthquakes within a certain distance range
r
min
r
r
max
are relevant to
EEW
at a specific site sets a constraint on the range of expected amplitudes
P
d
associated with
r
min
,
P
0
d;
max
, and
r
max
,
P
0
d;
min
. Right-hand panel: For continuous values of
τ
c
we obtain nonlinear discriminant functions (solid curves). Earthquakes with
r
min
r
r
max
and high
S/N
ratios are expected to produce
τ
c
P
d
pairs within area Ia, while noisy data and distant earthquakes will generate
τ
c
P
d
combinations in region IIa. Spiky noise will be mapped onto region IIb. For
EEW
we shall only consider triggers that produce
τ
c
P
d
pairs
within regions Ia and Ib. Region Ib accounts for the uncertainties of the underlying relations.
c
τ
Figure
4.
τ
c
P
d
diagram for earthquakes (
4
:
2
M
7
:
3
;Wu
et al.
, 2007) and false triggers in southern California. The majority
of triggers produced by earthquakes (dots) can be clearly separated
from false triggers (x
s) by the discriminant functions of the
τ
c
P
d
trigger criterion (solid and dashed curves). For improved clarity we
plot only false triggers produced during one month.
902
Short Note
To consider the increasing areas of impacts by large
earthquakes for which warnings are needed, one may possi-
bly expect a dependency of
r
max
on magnitude and, thus, on
τ
c
. The current
τ
c
P
d
trigger criterion has been determined
from an attenuation relation for
PGV
at rock sites. Thus, for
stations built on soft soils, the impact of site effects might be
significant. We tested if the usage of station-dependent mag-
nitude corrections and
V
S
30
-dependent
PGV
corrections, as
used within the
SCSN
, can help to reduce the scattering of
the data in Figure 4. However, because
P
and
S
waves are
affected differently by site conditions, site corrections for
τ
c
magnitude and
P
d
PGV
relations in equations (1) and (2) are
complex, and common
P
or
S
correction factors cannot be
applied. Unfortunately, because of a lack of data, the current
database does not allow for a reliable analysis of correction
terms separately for each
SCSN
station.
Figure
5.
Histograms for the estimated magnitudes
M
est
for the events in Table 1 obtained after the application of the new
τ
c
P
d
trigger
criterion. Stars on the
x
axis show the magnitudes determined by
SCSN
. The scatter of
M
est
is significantly reduced if compared with the
estimates in Figure 2 because records with poor
S/N
are removed by the new criterion.
Short Note
903
The current early warning system tested in southern
California uses a time window of
τ
0

3
sec length to de-
termine the early warning parameters
τ
c
and
P
d
. As pointed
out by Rydelek and Horiuchi (2006) or Rydelek
et al.
(2007),
this time window might possibly be too short for the deter-
mination of magnitudes larger than 6.5, because of the long
rupture durations of large earthquakes. The available data in-
dicate that it is possible to recognize from this 3 sec time
window if
M
w
6
:
5
or
M
w
>
6
:
5
(Kanamori, 2005). We
chose the 3 sec length as a compromise between knowing
it is a large magnitude earthquake and not waiting too long
to evaluate the available data. Additional research needs to be
undertaken to verify if a 3 sec long window is optimal, which
may include the approach of threshold warning as recently
proposed in Wu and Kanamori (2008b). However, the trigger
criterion used in this study is not affected by the duration of
the time window used.
Of course, small- and moderate-sized earthquakes with
M<
6
:
0
as analyzed in this study will usually not cause
damage to buildings, equipment, or humans. For the auto-
matic recognition of large earthquakes Wu and Kanamori
(2005a,b, 2008a,b) and Wu
et al.
(2006, 2007) propose to
test whether the criterion
τ
c
>
1
sec and
P
d
>
0
:
5
cm is ful-
filled. These large events will likely not be affected by the
problem of poor
S/N
ratios addressed in this study. However,
it is necessary to use the more frequent small events for test-
ing and calibration of
EEW
algorithms because large earth-
quakes are rare. Thus, the lessons learned from this study of
small earthquakes will form the basis for future enhance-
ments of
EEW
algorithms and understanding of their robust-
ness in real-time applications.
Data and Resources
Waveform data used in this study (Table 1) are taken
from the Southern California Earthquake Data Center (www
.data.scec.org, last accessed March 2008). Figure 1 was
made using the Generic Mapping Tools version 4.2.1 (Wes-
sel and Smith, 1998; www.soest.hawaii.edu/gmt, last ac-
cessed March 2008).
Acknowledgments
This work is funded through Contract Number 06HQAG0149 from
USGS
/
ANSS
to the California Institute of Technology (Caltech). The South-
ern California Seismic Network (
SCSN
) and the Southern California Earth-
quake Data Center (
SCEDC
) are funded through contracts with
USGS
/
ANSS
,
the California Office of Emergency Services (
OES
), and the Southern Cali-
fornia Earthquake Center (
SCEC
). This is Contribution Number 10000 of the
SeismoLab, Geological and Planetary Sciences at Caltech.
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Appendix
Mathematical Description of the Trigger Criterion
The reformulation of the empirical attenuation rela-
tion for
PGV
established by G. Cua and T. Heaton (unpub-
lished manuscript, 2008) in terms of displacement amplitude
P
d
gives
P
0
d;
min

10

log
10
f
10
aM
est

b

R
max

C

M
est

0

d
log
10

R
max

C

M
est

0

e
f
g
1
:
642

=
0
:
92

(A1)
and
P
0
d;
max

10

log
10
f
10
aM
est

b

R
min

C

M
est

0

d
log
10

R
min

C

M
est
0
e
f
g
1
:
642

=
0
:
92

;
(A2)
with
a

0
:
86
,
b

0
:
000558
,
d

1
:
37
,
e

2
:
58
,
R
min


r
2
min

9
p
,R
max


r
2
max

9
p
, and
C

M
est

0

c
1
exp

c
2

M
est

5

arctan

M
est

5

π
=
2

, with
c
1

0
:
84
and
c
2

0
:
98
. The parameter
f
in equations (A1)
and (A2) makes the conversion from root mean square hor-
izontal
PGV
to maximum horizontal
PGV
. Following G. Cua
(personal communication, 2008), we set
f

1
:
1
.
Accounting for the uncertainties of all relations involved
in equations (A1) and (A2) we obtain, in addition
P
00
d;
min

10

log
10
f
10
a

M
est

σ
M
est

b

R
max

C

M
est

00

d
log
10

R
max

C

M
est

00

e

σ
IM
f
g
1
:
642

σ
PGV

=
0
:
92

;
(A3)
and
P
00
d;
max

10

log
10
f
10
a

M
est

σ
M
est

b

R
min

C

M
est

000

d
log
10

R
min

C

M
est

000

e

σ
IM
f
g
1
:
642

σ
PGV

=
0
:
92

;
(A4)
with
C

M
est

00

c
1
exp

c
2

M
est

σ
M
est

5

×

arctan

M
est

σ
M
est

5

π
=
2

;
and
C

M
est

000

c
1
exp

c
2

M
est

σ
M
est

5

×

arctan

M
est

σ
M
est

5

π
=
2

;
respectively. The standard deviations
σ
M
est
and
σ
PGV
est
are
determined in equations (1) and (2), and
σ
IM

0
:
28
(for
rock sites; G. Cua and T. Heaton, unpublished manu-
script, 2008).
Seismological Laboratory
California Institute of Technology
1200 E. California Boulevard
Mail Code 252-21
Pasadena, California 91125
mboese@gps.caltech.edu
hauksson@gps.caltech.edu
solanki@gps.caltech.edu
hiroo@gps.caltech.edu
heaton@gps.caltech.edu
(M.B., E.H., K.S., H.K., T.H.H.)
Department of Geosciences
National Taiwan University
Taipei, Taiwan
drymwu@ntu.edu.tw
(Y.-M.W.)
Manuscript received 18 April 2008
Short Note
905