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Truncated exponential frequency-magnitude relationship in earthquake statistics

ISTITUTO DI GEOFISICA MINERARIA PALERMO UNIVERSITY, C.SO. CALATAFIMI 260, PALERMO, Italy

Abstract

The following doubly truncated exponential probability density distribution

where M₀ is the threshold magnitude value, and ß is a parameter, is proposed for the earthquake occurrence. The relation (a) has been obtained carrying out a simple model based on a number of assumptions, among which the more characterizing is the existence of a maximum regional finite magnitude value M_p. This assumption, derived by an evidence recognized by most seismologists, allows a simple explanation of the known behavior of the experimental cumulative frequency-magnitude graphs.

In order to estimate ß and M_p the moments method is suggested, which also represents a maximum likelihood method for ß estimation.

Finally, some results of application of the model to six seismic regions are presented.

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