principles and applications of microearthquake networks

6.5. Quantificatioii of Earthquakes 161
tied to Richter’s local magnitude M,, one would expect that this
moment-magnitude scale is also consistent with MD in the range of 0-3.
However, this consistency is yet to be confirmed.
Many present-day microearthquake networks are not yet sufficiently
equipped and calibrated for spectral analysis of recorded ground motion.
In the past, special broadband instruments with high dynamic range recording
have been constructed by various research groups for spectral
analysis of local earthquakes (e.g., Tsujiura, 1966, 1978; Tucker and
Brune, 1973: Johnson and McEvilly, 1974; Bakun et d., 1976; Helmberger
and Johnson, 1977; Rautian et lil., 1978). Alternatively, one uses accelerograms
from strong motion instruments (e.g., Anderson and
Fletcher, 1976; Boatwright, 1978). Several authors have used recordings
from microearthquake networks for spectral studies (e.g., Douglas et ul.,
1970; Douglas and Ryall, 1972; Bakun and Lindh, 1977: Bakun et al.,
1978b). In addition, O’Neill and Healy ( 1973) proposed a simple method of
estimating source dimensions and stress drops of small earthquakes using
P-wave rise time recorded by microearthquake networks.
In order to determine earthquake source parameters from seismograms,
it is necessary in general to have broadband, on-scale records in digital
form. If such records were available, D. J. Andrews (written communication,
1979) suggested that it would be desirable to determine the following
two integrals:
(6.60)
where u is ground displacement, 14 is ground velocity, t is time, and the
integrals are over the time duration of each seismic phase or over the
entire record. At distances much greater than the source dimension, both
displacement and velocity of ground motion return to zero after the passage
of the seismic waves. Thus the two integrals given by Eq. (6.60) are
the two simplest nonvanishing integrals of the ground motion. The integral
A is the long-period spectral level Ro and is related to seismic moment by
Eq. (6.46). The integral B is proportional to the energy that is propagated
to the station. If the spectrum of ground motion follows the simple Brune
( 1970) model with F = 1. the corner frequency fo is related to the integrals
A and B by
(6.61 1
Whereas the numerical coefficient may be different in other models, the
quantity Z31’3/A2’3. having dimension of time-’, can be expected to be a
robust measure of a characteristic frequency. Andrews believes that this
procedure is better than the traditional method of finding corner frequency