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Sensors 2008, 8
An earthquake excites both P and S waves. The S wave carries the major destructive energy, and
the smaller amplitude P wave precedes the S wave by the time equal to the 70% of the P-wave travel
time to the station. The initial portion of the P wave, despite its small and nondestructive amplitude,
carries the information of the earthquake size, and estimation of the earthquake size from the P wave
provides information about the strength of shaking to be brought by the following S wave. Using P
wave information to estimate the strength of S wave destructive shaking is a principal concept of EEW.
One of the major elements of EEW is to determine the earthquake magnitude rapidly and reliably.
To determine the size of an earthquake, it is important to determine whether the earthquake rupture has
stopped or keeps growing which is generally reflected in the period of the initial motion. Small and
large events generally cause short and long period initial motions, respectively.
developed by Nakamura (1988) attempts to use the period averaged over some time window.
Kanamori (2005) used the following procedure which is modified from the method used by Nakamura
(1988). The ground-motion displacement, ( )
are used to compute the following ratio r by
where the integration is taken over the time interval
previous studies (Wu and Kananmori, 2005a, 2005b, 2007; Wu et al., 2006; 2007),
Using Parseval's theorem,
where ˆ ( )
u f is the frequency spectrum of ( )
Thus,
can be used as a parameter representing the average period of the initial portion of the P wave.
approximately represents the P wave pulse width which increases with the magnitude and can be used
to estimate the event magnitude.
Another important element of EEW is to estimate the strength of S wave shaking at a site from the
initial P waves at the same site. Wu and Kanamori (2005a) showed that the maximum amplitude of a
high-pass filtered vertical displacement during the initial 3 sec of the P wave, Pd can be used to
u t , and velocity, ( )
τ
∫
0
2
u t dt
( )
r
=
0
τ
∫
0
u t dt
2
( )
0
(0, )
2
∞
∫
π
2
f u f
2
ˆ
df
4
( )
r
=
0
2
∞
∫
ˆ ( )
u f
df
0
u t , and
f
π
1
2
τ
=
=
c
r
2
f
u t , from the vertical component record
τ
after the onset of P wave. In a series of
0
π
=
4
2
f
2
2
is the average of
f weighted by
4
The method
(1)
τ is set at 3 s.
0
(2)
2
2
ˆ ( )
u f
(3)
τ
c
.
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