principles and applications of microearthquake networks

6.4. Estirnatioti of Etrrthquake Mugnitude 157
authors, e.g., Hori (1973), Real and Teng (1973), Herrmann (1975), Bakun
and Lindh (19771, Griscom and Arabasz (1979), Johnson (1979), and
Suteau and Whitcomb (1979). Duration magnitude M, for a given station
is usually given in the form
(6.44) M, = a, + a2 log 7 + a,A + a,h
where T is signal duration in seconds, A is epicentral distance in kilometers,
h is focal depth in kilometers, and cil, a,, u3 and a4 are empirical
constants. These constants usually are determined by correlating signal
duration with Richter magnitude for a set of selected earthquakes and
taking epicentral distance and focal depth into account.
It is important to note that different authors may define signal duration
differently. In practice, total duration of the seismic signal of an earthquake
is difficult to measure. Lee el CJI. (1972) defined signal duration to
be the time interval in seconds between the onset of the first P-wave and
the point where the seismic signal (peak-to-peak amplitude) no longer
exceeds 1 cm as it appears on a Geotech Develocorder viewer with 20x
magnification. This definition is arbitrary, but it is easy to apply, and
duration measurements are reproducible by different readers. Since the
background seismic noise is about 0.5 cm (peak-to-peak), this definition is
equivalent to a cutoff point where the signal amplitude is approximately
twice that of the noise. Because magnitude is a rough estimate of the size
of an earthquake, the definition of signal duration is not very critical.
However, it should be consistent and reproducible for a given microearthquake
network. For a given earthquake, signal duration should be measured
for as many stations as possible. In practice, a sample of 6 to 10
stations is adequate if the chosen stations surround the earthquake epicenter
and if stations known to record anomalously long or short durations
are ignored. Duration magnitude is then computed for each station, and
the average of the station magnitudes is taken to be the earthquake magnitude.
Using signal duration to estimate earthquake magnitude has become a
common practice in microearthquake networks, as evidenced by recent
surveys of magnitude practice (Adams, 1977; Lee and Wetmiller, 1978). In
addition, studies to improve determination of magnitudes of local earthquakes
have been carried out. For example, Johnson (1979, Chapter 2)
presented a robust method of magnitude estimation based on the decay of
coda amplitudes using digital seismic traces; Suteau and Whitcomb (1979)
studied relationships between local magnitude, seismic moment, coda
amplitudes, and signal duration.