principles and applications of microearthquake networks

6.5. Qua 11 ti3 ca tiot I of Earth qua kes 159
eters using body-wave spectra. The seismic moment Mo may be determined
by
(6.46) Mo = (fio/$oCh)4npRc3
where is the long-period limit of the displacement spectrum of either P
or S waves, $od is a function accounting for the body-wave radiation pattern,
p is the density of the medium, R is a function accounting for
spreading of body waves, and L’ is the body-wave velocity, Similarly,
seismic moment can also be determined from surface waves or coda
waves (e.g., Aki, 1966, 1969). Thus, if seismic moment is determined from
seismograms and if we assume the source area to be the aftershock area,
then we can estimate the average slip D from Eq. (6.45).
Actually, seismic moment is only one of the three parameters that can
be determined from a study of seismic wave spectra. For example, Hanks
and Thatcher (1972) showed how various seismic source parameters are
related if one accepts Brune’s (1970) source model. The far-field displacement
spectrum is assumed to be described by three spectral parameters.
These parameters are (1) the long-period spectral level ao, (2) the
spectral corner frequency fo, and (3) the parameter E which controls the
high-frequency (f > fo) decay of spectral amplitudes. They can be extracted
from a log-log plot of the seismic wave spectrum (spectral level
vs frequencyf). If we further assume that the physical interpretation of
these spectral parameters as given by Brune (1970) is correct, then the
source dimension I’ for a circular fault is given by
(6.47) r = 2.34c/2nfo
where u and fo are seismic velocity and corner frequency, respectively.
The stress drop ACT is given by
(6.48) ACT = 7M,,/16r3
Similar formulas for strike-slip and dip-slip faults have been summarized
by Kanamori and Anderson (1975, pp. 1074-1075).
The stress drop ACT is an important parameter and is defined as the
difference between the initial stress C T before ~ an earthquake and the final
stress C T ~ after the earthquake
(6.49) ACT = g o - (TI
The mean stress (T is defined as
(6.50) 6 = &(go + CTJ
and is related to the change in the strain energy AW before and after an
earthquake by (Kanamori and Anderson, 1975, p. 1075)