principles and applications of microearthquake networks

6.4. Es tim a tiori of’ Eli rtli qu n lie Mag ti itu de 155
average all the station magnitudes to obtain the local magnitude ML for the
earthquake.
6.4.2. Extension to Other Magnitudes
In the 1940s, B. Gutenberg and C. F. Richter extended the local magnitude
scale to include more distant earthquakes. Gutenberg (1945a) defined
the surface-wave magnitude M, as
(6.40) Ms = log A - log Ao(Ao)
where A is the maximum combined horizontal ground amplitude in micrometers
for surface waves with a period of 20 sec, and (-log A,,) is
tabulated as a function of epicentral distance h in degrees in a similar
manner to that for local magnitude (Richter, 1958, pp. 345-347).
A difficulty in using the surface-wave magnitude scale is that it can be
applied only to shallow earthquakes that generate observable surface
waves. Gutenberg (1945b) thus defined the body-wave magnitude mb to be
(6.41) mIj = log(A/T) -fCA, h)
where A/T is the amplitude-to-period ratio in micrometers per second,
and f(A. h) is a calibration function of epicentral distance A and focal
depth h. In practice, the determination of earthquake magnitude M (either
body-wave or surface-wave) may be generalized to the form (Bath, 1973,
pp. 11&118):
(6.42) M = log(A/T) + C1 lOg(A) + C2
where C, and C2 are constants. A summary on magnitude scales may be
found in Duda and Nuttli (1974).
6.4.3. Estimating Magnitude for Microearthquakes
Because Wood-Anderson instruments seldom give useful records for
earthquakes with magnitude less than 2, we need a convenient method for
estimating magnitude of local earthquakes recorded by microearthquake
networks with high-gain instruments. One approach (e.g., Brune and Allen,
1967; Eaton et al., 1970b) is to calculate the ground motion from the
recorded maximum amplitude, and from this compute the response expected
from a Wood-Anderson seismograph. As Richter (1958, p. 345)
pointed out, the maximum amplitude on the Wood-Anderson record may
not correspond to the wave with maximum amplitude on a different instrument’s
record. This problem can, in principle, be solved by converting
the entire seismogram to its Wood- Anderson equivalent and determining