Is the seismic moment-frequency relation universal?

Abstract

We evaluate the seismic moment-frequency relation for the Harvard catalogue in the period 1977-1994. This catalogue is composed of about 12 000 earthquakes. After selection of events in terms of depth and energy, we retain about 8000 data points. We estimate two parameters of the seismic moment distribution: the power exponent β and the cut-off value M(m). The method used is a least-squares linear fit on a log-log scale performed over a range selected on the basis of the standard deviation from the histogram. The analysis is carried out for different subdivisions of the Earth in square grids of different sizes. Neither parameter exhibits a dependence on cell size, suggesting the universality of their values and the interpretation of the existence of a cut-off as a finite size effect linked to a finite catalogue length. The variations of the parameters are investigated as a function of time (duration of the catalogue) and versus the number of events used for building up the distribution. Again, β and M(m) do not depend on time, but M(m) depends on the number of events, reaching a stable value for N ~ 1000. The only significant change in the parameters is observed for different values of M(Oupper) in the catalogue, revealing the existence of universality classes.