The effect of the magnitude uncertainty on the b value

Since the magnitude is usually not the same from one catalog to another for the same earthquake, the calculated b value will change with different catalogs. Big b error is usually introduced when the magnitudes of the events are not well measured. For this reason, based on the uncertainty of the observed magnitude, i.e., the "apparent" magnitude, the frequency-magnitude relation (Gutenberg-Richter relation) was estimated by assuming the normal distribution of the apparent magnitude around the "true" one. The number of the events with same "true" magnitude was recalculated according to this distribution. The error of the b value obtained with the "true" magnitude is largely reduced by taking into account the distribution of the "apparent" one. In order to show the advantage of the present method, the b values in the three zones in China are calculated with both ordinary and present method. Furthermore, in consideration of the magnitude saturation of the large events, the data set was divided into two pats on M=7.0. Results obtained by the method presented in this paper are of higher precision than those with ordinary method.