principles and applications of microearthquake networks

216 8. Applications for Earthquake Prediction
tain seismic waves, seismic wave spectrum, focal depth, and orientation
of the principal stress axes. The goal is to find some precursors that can
discriminate between background earthquakes and foreshock activity. Although
some earlier studies used data from regional networks, they have
produced encouraging results and have suggested directions for more detailed
investigations. Thus, a major reason to establish a microearthquake
network is to provide the necessary data for studying earthquake precursors.
8.3.1. Changes in b-Slope
As discussed in Section 1.1.2, the frequency of earthquakes as a function
of magnitude may be represented by the Gutenberg-Richter relation
(8.1) log N = - bM
where N is the number of earthquakes of magnitude M or greater, and a
and b are numerical constants. The parameter b is often referred to as
b-slope, and it describes the rate of increase of earthquakes as magnitude
decreases. Studies in many areas of the world have shown that the
6-slope values usually are within the range of 0.6-1.2. This range corresponds
to an increase in the number of earthquakes of 4 to 16 times for
each decrease of magnitude by one unit.
For a given sample of earthquake magnitude data, if we plot N versus
M, then the 6-slope may be estimated from the slope of the least squares
line fitted through the data points. Alternatively, the b-slope may be
computed by Utsu’s formula (Utsu, 1965) in a form given by Aki (1965)
(8.2) h = log(e)/(M - Mmin)
where log(e) = 0.4343. &! is the average magnitude, and Mmin is the
minimum magnitude in a given sample of data. Aki (1965) showed that Eq.
(8.2) was the maximum likelihood estimate of the b-slope and derived
confidence limits for this estimate. As pointed out by Hamilton (1967), Eq.
(8.2) may be written as
(8.3)
Therefore, the nature of the frequency-magnitude relation is measured
equivalently by b or &f (Wyss and Lee, 1973). Readers interested in a
more detailed discussion of b-slope and its significance in earthquake
statistics are referred to Utsu (1971). We now summarize a few examples
of b-slope studies as they relate directly to earthquake prediction.
Suyehiro et nl. (1964) calculated b-slopes from foreshock and aftershock
activity associated with a magnitude 3.3 earthquake on January 22,