Implications of a conservation law for the distribution of earthquake sizes

Abstract

We investigate the implications that a sum rule for the average velocity of a geological fault has on the distribution of earthquake sizes. Under general conditions the exponent B of the Gutenberg-Richter law for the distribution of small seismic moments is shown to obey BB≊1. (b) The large events do not fall in the scaling region; in this case we are able to derive a relationship between the exponents relating their frequency and seismic moment to the total size of the system. (c) The large earthquakes also show scaling behavior but with a different exponent B’; then the sum rule implies that B’>1.