principles and applications of microearthquake networks

160 6. Methods of Data Analysis
(6.5 1) AW = ADU
The radiated seismic energy E, is
(6.52) E,=q.lW
where q is the seismic efficiency. 7 is less than 1 because only part of the
strain energy change is released as radiated seismic energy.
Kanamori and Anderson (1975) discussed the theoretical basis of some
empirical relations in seismology. They showed that for large earthquakes
the surface-wave magnitude Ms is related to rupture length L by
(6.53) M, - log L2
and the seismic moment Mo by
(6.54) Mo - L"
Thus we have
(6.55) log M O - $M,
which is empirically observed. Gutenberg and Richter ( 1956) related the
surface-wave magnitude M, to the seismic energy E, empirically by
(6.56)
log E, = 1.5iM, + 11.8
Kanamori and Anderson (1975, p. 1086) showed that
(6.57) E, - L3
and by using Eq. (6.53), we have
(6.58) log 45, - +Ms
which agrees with the Gutenberg-Richter relation given in Eq. (6.56).
6.5.2. Applications to Microearthquake Networks
The preceding subsection shows that seismic moment is a fundamental
quantity. The ML and M, magnitude scales as originally defined by Richter
and Gutenberg can be related to seismic moment approximately. Indeed,
Hanks and Kanamori ( 1979) proposed a moment-magnitude scale by
defining
(6.59)
M = "1 .? og MrJ - 10.7
This moment-magnitude scale is consistent with ML in the range 3-6, with
M, in the range 5-8, and with M, introduced by Kanamori ( 1977) for great
earthquakes (M 2 8). Because the duration magnitude scale MD is usually