**RATE
OF SEISMICITY
**[c6, p171]

The average rate
of earthquake activity within the San Andreas system can be estimated from the
Gutenberg-Richter frequency-magnitude relation log N=a-bM, where N is the cumulative
number of events of magnitude equal to or greater than M during a given time
period. For the 77 events along the fault system with summary magnitudes M>=6
since 1852, this relation well describes the population with a=5-3/4 and b=1
(
Figure 6.14). Comparable results are obtained for subsets of M=6 events, such as the
instrumental period (1898-1989).

It is useful to compare these results from the historical record with the frequency-magnitude relation determined from systematic
microearthquake observations. If the historical rate of activity applies today and the frequency-magnitude relation for microearthquakes (M>=3) is described by the same relation, then about 5,600
M>=2 events should be observed each year. This prediction exceeds the number of events observed during the interval 1980-87 by about a factor of 2 (see chap. 5) and suggests that a
somewhat smaller value of b = 0.93 may be more appropriate for the extended magnitude range.

For the catalog as a whole, the rate of earthquake occurrence is well
described by a Poisson process, in which the probability of finding one or more events in any interval of t years is P=1-e(lambda)t, where (lambda) is the average rate of earthquake occurrence. It
follows from the observed frequency-magnitude relation that the odds of having at least one M>=6 event per year are 0.43. There 15 also an even chance of at least one M>=6 event within any 15-month
interval, one M>=7 within any 12-1/2-year interval, or one M>=8 within any 125-year interval.

The rate of earthquake activity along the plate boundary can also be usefully compared with plate-motion estimates derived from plate-tectonic theory. Current estimates of the relative velocity
across the North American-Pacific plate boundary, determined from the spreading rate in the Gulf of California of 5 cm/yr (DeMets and others, 1987), imply an annual seismic-moment rate of 2 x 1026
dyne-cm/yr for a 10-km-thick brittle crust, equivalent to a single **M**=6.8 earthquake. Earthquakes of this size occur far less often, and the principal seismic contribution to the plate motion
comes from infrequent large events. The erroneous notion that the smaller events substantially contribute to the total is demonstrably false, as shown by summing the contributions of all the
earthquakes below some magnitude. The innumerable events of **M**=<6 occurring each year contribute less than 10 percent to the total seismic-strain release.

Within the San Andreas fault system, the total seismic-moment release since 1852 corresponds to 70 percent of the total North American-Pacific plate motion predicted by plate-tectonic models. This proportion is somewhat inflated because not all of the earthquakes act to transmit slip along the plate boundary; for example, the 1952 Kern County earthquake, the third largest in historic time, directly accommodated little plate-parallel motion. Although aseismic displacements account for some of the deficit, notably along the central, creeping section of the San Andreas fault, deformation occurring elsewhere, notably within the Basin and Range, contributes substantially to the relative motion between the North American and Pacific plates.