ESTIMATION OF THE GUTENBERG-RICHTER RELATION ALLOWING FOR INDIVIDUAL EARTHQUAKE MAGNITUDE UNCERTAINTIES

For the estimation of seismicity parameters in the Gutenberg-Richter r elation, a method is presented which tables account of individual eart hquake magnitude uncertainties and rounding intervals. The magnitude o f each earthquake is regarded as a continuous distribution. The method corners bias due to magnitude uncertainties in estimates of the a-val ue and due to variation in magnitude uncertainties in estimates of the b-value. It extends a method presented by Tinti and Mulargia for cons tant magnitude variance. The method is demonstrated on simulated data and is used to examine activity rates and b-values estimated from the New Zealand earthquake catalogue for the period 1987-1992.