principles and applications of microearthquake networks

158 6. Methods of Data Analysis
6.5 Quantification of Earthquakes
As pointed out by Kanamori (1978b), it is not a simple matter to find a
single measure of the size of an earthquake, because earthquakes result
from complex physical processes. In the previous section, we described
the Richter magnitude scale and its extensions. Since Richter magnitude is
defined empirically, it is desirable to relate it to the physical processes of
earthquakes. In the past 30 years, considerable advances have been made
in relating parameters describing an earthquake source with observed
ground motion. Readers are referred to an excellent treatise on quantitative
methods in seismology by Aki and Richards (1980).
6.5.1. Quantitative Models of Earthquakes
Reid's elastic rebound theory (Reid, 1910) suggests that earthquakes
originate from spontaneous slippage on active faults after a long period of
elastic strain accumulation. Faults may be considered as the slip surfaces
across which discontinuous displacement occurs in the earth, and the
faulting process may be modeled mathematically as a shear dislocation in
an elastic medium (see Savage, 1978, for a review). A shear dislocation
(i.e., slip) is equivalent to a double-couple body force (Maruyama, 1963;
Burridge and Knopoff, 1964). The scaling parameter of each component
couple of a double-couple body force is its moment. Using the equivalence
between slip and body forces, Aki (1966) introduced the seismic
moment Mo as
(6.45) Mo = pL4D(A) clA = pnA
where p is the shear modulus of the medium, A is the area of the slipped
surface or source area, and D is the slip D(A) averaged over the area A.
Hence the seismic moment of an earthquake is a direct measure of the
strength of an earthquake caused by fault slip. If an earthquake occurs
with surface faulting, we may estimate its rupture length Land its average
slip 0. The source area A may be approximated by Lh, where h is the
focal depth. A reasonable estimate for 1 is 3 x 10" dynedcm'. With these
quantities, we can estimate the seismic moment using Eq. (6.45). For
more discussion on seismic moment, readers may refer to Brune ( 1976),
and Aki and Richards (1980).
From dislocation theory, the seismic moment can be related to the
far-field seismic displacement recorded by seismographs. For example,
Hanks and Wyss (1972) showed how to determine seismic source param-