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DEPARTMENT OF EARTHQUAKE AND PLANETARY SCIENCES MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139
Abstract
The frequency of occurrence of earthquakes with different seismic moments is expressed in terms of the rate of slip on a fault and to the largest seismic moment likely to occur in the region. Beginning from the Gutenberg-Richter empirical expression relating the relative recurrence of events with different magnitudes and using another empirical relation between magnitude and seismic moment, the relative number of events with seismic moment greater than or equal to Mo is given by N(Mo) = 
Mo–ß. ß can be determined from parameters in these empirical expressions. From average rates of slip on faults, this expression can be used to give the recurrence rates for events of different seismic moment: = (1–ß)Mo
/Momax1–ß where Momax is the maximum possible seismic moment in a region, and Mo is the average rate of occurrence of the seismic moment. On a fault of area A, with shear modulus µ, and long-term average rate of slip 
, Mo = µA. A similar expression can be given for for regions where deformation is distributed over a broad area without a major throughgoing fault. Using rates of convergence at island arcs determined from plate motions for the last 5 m.y., the calculated frequency of occurrence of earthquakes with large seismic moments agrees well with the historic record. At present, uncertainties in the requisite parameters and in assumptions on which the recurrence relation is based, however, make such an approach only marginally better than reliance on the historic record alone. With more data constraining ß, the largest possible seismic moments, the role of fault creep, and long-term rates of slip or deformation, however, this approach to seismic risk should be a more reliable predictor of recurrence rates than the existing historic record. As an example, the formulas are applied to the southeastern Caribbean.
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