Environmental Engineering Reference
In-Depth Information
of all possible magnitudes, at all significant distances from the site of interest, as a proba-
bility by taking into account their frequency of occurrence (Thenhaus and Campbell, 2003).
Statistical Analysis and Recurrence Equations
Limiting Factors
Prediction of an event for a given location during investigations is usually based on statisti-
cal analysis of recorded historical events, but the limitations in the accuracy of such predic-
tions must be recognized. It is known where earthquakes are likely to occur from recorded
history, but it must be considered that major events can occur in areas where they would be
totally unexpected. New Madrid and Charleston, for example, are essentially singular events.
Comparing the span of modern history and its recorded events with the span of even
recent geologic history results in the realization that data are meager as a basis for accu-
rate prediction. For example, activity can be cyclic. A region can apparently go through
several centuries without seismic activity and then enter a period with numerous events.
The Anatolian zone of Turkey, with 2000 years of recorded events, now is an active seis-
mic area, although it has had periods of inactivity for as long as 250 years (Bollinger,
1976). By comparison, the history of significant population in the United States is scarcely
250 years, not adequately long for effective predictions.
On a historical basis, records of events are closely related to population density and area
development, especially for events of moderate to low magnitudes felt over limited areas.
General Recurrence Relationships
Occurrence frequency of shocks of any given magnitude for the world in general and
most of the limited areas that have been studied is roughly about 8 to 10 times that for
shocks about one magnitude higher. The relationship (Richter, 1958; Lomnitz, 1974) can be
represented by
log 10 N
a
bM
(11.12)
where N is the number of shocks of magnitude M or greater per unit of time, a, b are con-
stants for a given area based on statistical analysis of recorded data,
a
log 10 N (0), or the logarithm of the number of earthquakes greater than M
0 for a
given time period, given in units of earthquakes per year and
b
F ( M )]/ M } where F ( M ) is the cumulative probability distributionof earth-
quake magnitudes.
On a semi-log plot for 5.5
log 10 {[1
8.5, Equation 11.12 plots as a straight line for number of
events against M . Studies by the Japan Meteorological Society found a drop off in the num-
ber of events above M
M
7.5. Data were for the period of 1885 to 1990 (Scawthorn, 2003).
Recurrence relation is also found expressed in terms of I o as
log N
α β
I o
(11.13)
where N is the annual number of earthquakes with epicentral intensities equal to or
greater than I o and
are the empirical constants which describe the decay rate of occur-
rence with increasing epicentral intensity in a manner similar to a and b in Equation 11.12
(Christian et al., 1978).
α
,
β
Some Regional Relationships
Recurrence equations have been developed for various regions expressing the number of
earthquakes per year ( N ) in terms of the maximum magnitude M or MM intensity I , for
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