Three functional forms for earthquake occurrence relations are compared, and slip rate constraints on each are derived. Constrained occurrence relations referred to total fault area, to rupture area of the maximum magnitude earthquake, and to a particular site along the fault and are presented and discussed. The slip rate constraints provide a means to estimate Mmax from occurrence rates of small magnitude earthquakes, or a means to estimate the threshold of observations in a qualitative earthquake catalog, as well as a means to estimate occurrence rates when Mmax is obtained from other considerations. This paper shows examples of these three types of applications.
The relations considered are: N1(M) is such that the cumulative occurrence rate of earthquakes with magnitude greater than M is an exponential function truncated at Mmax; N2(M) is such that the corresponding incremental occurrence rate is a truncated exponential function; and N3(M) is such that the corresponding incremental occurrence rate is an exponential function plus a constant which causes the rate to go to zero at Mmax. A speculative model for the magnitudes of the earthquakes at Pallett Creek observed by Sieh (1978a) suggests that N2(M) is more appropriate than N1(M) or N3(M) for these earthquakes.