Bulletin of the Seismological Society of America, Vol. 83, No. 1, pp. 264-268, February 1993
SHOR T NO TES
LOCATING EARTHQUAKES WITH AMPLITUDE:
APPLICATION TO REAL-TIME SEISMOLOGY
BY HIROO KANAMORI
Earthquakes are traditionally located using travel times. However, since the
ground-motion amplitude generally decays with the distance from the source, it
should also be possible to locate earthquakes using amplitude data. Amplitudes
are affected by m a n y factors other than the distance, so that we do not expect to
be able to locate the epicenter, the location of the initial rupture, very accurately
with amplitude data. However, locating earthquakes with amplitudes has its
own merits: (1) For postearthquake emergency services, it is often more important to know the spatial distribution of strong-motion parameters such as peak
acceleration and peak velocity than the rupture initiation point itself (National
Research Council, 1991). This is especially true for thrust earthquakes (e.g.,
1971 San Fernando earthquake; 1987 Whittier Narrows earthquake) or events
with large rupture zones. (2) The amplitudes are usually much easier to
determine than the arrival times, especially for events with complex rupture
patterns or with immediate foreshocks in which event association can be
difficult. For application to real-time earthquake information systems such as
CUBE ( C a l t e c h / U S G S Broadcast of Earthquakes; Kanamori et al., 1991), the
amplitude method could provide a quick and robust w a y to send useful information for emergency operations. Here, we report a few examples and propose a
method for future implementation in a CUBE-type system.
We use peak acceleration as the amplitude parameter. However, use of other
parameters such as peak velocity and CAV (EPRI, 1991) is equally possible. For
simplicity, we use the peak acceleration-distance relation developed by Joyner
and Boore (1981) to fit the observed data. This relation is given by
log A = - 1 . 0 2 + 0.249M - log(d 2 + 7.32) 1/2 - 0.00255(d z + 7.32) 1/2, (1)
where A is the peak horizontal acceleration in g, M is magnitude, and d is the
closest distance to the surface projection of the fault rupture in kin. In our
application, d is interpreted as the distance between the site and the "strongmotion centroid" (SMC) that is to be determined from the amplitude data. Since
d is defined differently from Joyner and Boore (1981), the meaning of the
magnitude M is also different.
We fit the observed peak acceleration data with equation (1) and determine
M, latitude (~b), and longitude (A) of the SMC. Equation (1) is nonlinear with
respect to 4) and A. We scan the model p a r a m e t e r space (M, ~b, A) to determine
the approximate location of the global minimum of the error function. Then we
use the values of M, ¢, and • at that location as the first approximation to
determine the final solution using the method of least-squares. This procedure
is especially important for spotting an event located outside the network.
We tested this method using the data for the 1989 Loma Prieta, 1991 Sierra
Madre, 1992 J o s h u a Tree, 1992 Landers, and 1992 Big Bear earthquakes. The
data used and the results are summarized in Table 1. Figure l a shows the
264
SHORT
NOTES
265
TABLE 1
DETERMINATION OF STRONG-MOTION CENTROID WITH PEAK ACCELERATION
Data Set
M
Latitude
(°)
Longitude
(°)
RMS
(% of g)
1992 L a n d e r s E a r t h q u a k e ( M w = 7.3, ¢ = 34.22 °, A = - 116.43 °)
TERRAscope
TERRAscope
All d a t a (76) t
Prediction by
Prediction by
(6)*
+ S C S N F B A (13)
7.93
7.98
8.86
34.46
34.38
34.57
- 116.90
- 116.61
- 116.45
TERRAscope
Ts + FBA
0.37
2.5
3.2
5.1
1992 Big B e a r E a r t h q u a k e ( M w = 6.4, ~b = 34.21 °, A = - 116.83 °)
TERRAscope
TERRAscope
All d a t a (23) t
Prediction by
Prediction by
(6)
+ S C S N F B A (12)
6.00
6.67
7.63
34.09
34.04
34.22
- 116.96
- 116.90
- 116.82
TERRAscope
Ts ÷ FBA
0.11
1.29
4.3
10.5
9.4
1992 J o s h u a T r e e E a r t h q u a k e (Mw = 6.1, ¢ = 33.94 °, A = - 1 1 6 . 3 4 °)
TERRAscope
TERRAscope
All d a t a (31) t
P r e d i c t i o n by
P r e d i c t i o n by
(6)
+ S C S N F B A (11)
5.81
6.24
7.39
34.08
34.14
33.97
- 116.33
- 116.21
- 116.27
TERRAscope
Ts + FBA
0.14
0.37
6.05
13.44
1991 S i e r r a M a d r e E a r t h q u a k e ( M ~ = 5.5, ~b = 34.26 °, A = - 118.00 °)
T E R R A s c o p e (6)
T E R R A s c o p e ÷ S C S N F B A (10)
All d a t a (101) t
Prediction by TERRAscope
Prediction by Ts + FBA
4.63
5.41
5.98
34.02
34.13
34.19
- 118.04
- 118.07
- 118.05
0.12
4.3
3.6
1989 L o m a P r i e t a E a r t h q u a k e ( M w = 6.9, ¢ = 37.04 °, A = - 121.88 °)
All d a t a (129) 5
8.21
36.97
- 121.84
10.0
* N u m b e r s i n t h e p a r e n t h e s e s i n d i c a t e t h e n u m b e r of s t a t i o n s u s e d .
CTERRAscope, S C S N FBA, a n d C D M G s t a t i o n s .
*TERRAscope, S C S N FBA, C D M G , a n d U S G S s t a t i o n s .
1992 Landers
(a
35
(b)
"
lg92
Landers
Earthqueke
Computed
:::::::::::::::::::::::::: ::i:::::::: :: : :! :!:::::! ::t:::;!:): ::i
•
-117
1oo
Distance, k m
-116
FIG. 1. (a) T h e e p i c e n t e r (star) a n d t h e s t r o n g - m o t i o n c e n t r o i d (SMC, + s y m b o l ) of t h e 1992
L a n d e r s e a r t h q u a k e , d e t e r m i n e d w i t h d a t a f r o m T E R R A s c o p e , T E R R A s c o p e ÷ S C S N , a n d all t h e
s t a t i o n s i n c l u d i n g t h o s e of t h e C a l i f o r n i a Division of M i n e s a n d Geology. T h e c o n t o u r l i n e s i n d i c a t e
t h e e r r o r s w h e n only T E R R A s c o p e s t a t i o n s a r e u s e d . (b) T h e fit of e q u a t i o n (1) w i t h t h e d a t a w h e n
all t h e d a t a a r e u s e d .
266
SHORT NOTES
results for the 1992 Landers earthquake. The contour lines show the topography of the error function, when only TERRAscope data are used. Figure lb
shows the fit with the data. Figures 2a to d show the results for the other
events. Contour lines are not shown in these figures to avoid clutter. As shown
in Figure 1, the SMC determined from the amplitude data is, in general, very
close to the epicenter determined from travel times. Even when only six
TERRAscope stations are used, the SMC is located fairly close to the epicenter.
For the Landers earthquake, the SMC location using all the data is about
40 km north of the epicenter, which is reasonable considering the 70-km fault
extending north from the epicenter.
1992 Big Bear
34.5 ~ a )
1992 Joshua Tree
34.5
(b)
TERR.~cope+SCSN
+
"J~TERRAscope
84
\
33.5 ~
-117.5
~
33.5
-I 17
-116.5
-116.5
-116
1991 Sierra ]~adre
34.5
(c)
'
~
37.5
1989 Loma P r i e t a
TERRAsco'Jope+SCSN
34
33.5
-118.5
--~-TERRAseope
37
,
-118
\
-113'.5
36.E
-122
-121.5
FIG. 2. (a) The epicenter (star) a n d the strong-motion centroid (SMC, + symbol) of the 1992 Big
Bear e a r t h q u a k e determined with the data from TERRAscope, TERRAscope + SCSN, and all the
stations including those of the California Division of Mines and Geology. (b) Same as (a). The 1992
J o s h u a Tree earthquake. (c) Same as (a). The 1991 Sierra Madre E a r t h q u a k e . (d) The epicenter
(star) and the strong-motion centroid (SMC, + symbol) of the 1989 Loma Prieta earthquake, determined with data from the stations of the California Division of Mines a n d Geology a n d the U.S.
Geological Survey.
SHORT NOTES
267
An important application of this method is real-time estimation of strong
motions. If some strong-motion data are available in near real-time, we can
locate the SMC with this method quickly and then estimate strong-motion
distribution using equation (1). To illustrate this, we performed the following
experiment. In southern California, six TERRAscope stations provide near-real
time ground-motion data. Also, several accelerographs are installed in the
Southern California Seismic Network (SCSN), from which near real-time data
are available through analog telemetry. Using the peak acceleration data for the
1992 Landers earthquake obtained from the six TERRAscope stations, we
located the SMC (Fig. la), estimated the peak accelerations at all other strongmotion instrument sites of SCSN and the California Division of Mines and
Geology (CDMG), and compared them with the observed. Figure 3 shows the
results. Even if only six sparse TERRAscope stations are used, we can predict
strong motions over a large area of southern California very well. The strong
motion sites of SCSN and CDMG cover the area that includes San Bernardino,
Riverside, Palmdale, and Los Angeles. The RMS (root-mean-square) error is
5.1% of g. This result suggests that if a sufficiently large number (e.g., 30) of
telemetered stations are available, we can make good real-time estimations
of strong ground motions. As mentioned earlier, the method uses only amplitude
data and is very simple to implement in a real-time seismic system.
When more real-time data become available, further considerations may be
given to: (1) strong-motion parameters other than peak acceleration, (2) noncircular distribution of strong-motion parameters for elongated sources, (3) station
corrections, and (4) nonlinear site response.
The values of M listed in Table 1 differ significantly from those assigned to
these earthquakes. This difference is largely due to the difference in the
definition of d. Since the geometry and size of the fault plane are unknown
immediately after the occurrence of an earthquake, we cannot use d defined by
1992
Landers
(Prediction
Earthquake
by
TERRAscope
o
Observed
•
Computed
only)
100
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Distance,
km
FIG. 3. Comparison of the observed peak accelerations with those predicted with only
TERRAscope data.
268
SHORT NOTES
Joyner and Boore (1981). Thus, M in Table 1 should be regarded as a scaling
constant and should not be given much significance. For most strong-motion
applications, however, what is really needed are strong-motion parameters,
rather than the earthquake magnitude. In a way, our method side-steps the
ordinary seismological parameters such as the magnitude, depth, mechanism,
and rupture directivity, which are not necessarily the parameter of immediate
interest for emergency services.
ACKNOWLEDGMENTS
Discussions during the Seismological Laboratory coffee break with Don Anderson, Jim Mori,
David Wald, and Tom Heaton motivated this study. This research was conducted under the CUBE
project and the TERRAscope project, which is supported by the L. K. Whittier and Arco Foundations. Contribution No. 5199, Division of Geological and Planetary Sciences, California Institute of
Technology, Pasadena, California.
REFERENCES
EPRI (1991). Standardization of the cumulative absolute velocity, EPRI TR-100082 (Tier 1),
Palo Alto, California, Electric Power Research Institute, prepared by Yankee Atomic Electric
Company.
Joyner, W. B. and D. M. Boore (1981). Peak horizontal acceleration and velocity from strong-motion
records including records from the 1979 Imperial Valley, California, earthquake, Bull. Seism.
Soc. Am. 71, 2011-2038.
Kanamori, H., E. Hauksson, and T. Heaton (1991). TERRAscope and CUBE project at Caltech, Eos
72, 564.
National Research Council (1991). Real-Time Earthquake Monitoring, Early Warning and Rapid
Response, National Academy Press, Washington, D.C., 1-52.
SEISMOLOGICALLABORATORY
CALIFORNIAINSTITUTEOF TECHNOLOGY
PASADENA, CALIFORNIA91125
Manuscript received 18 August 1992