Estimating the Completeness Magnitude mc and the b-Values in a Snap

Abstract

A good estimation of the b-value is crucial for the earthquake hazard assessment. Its evaluation can be strongly affected by an incorrect estimation of the completeness magnitude mc because a too small mc will reflect into a small b-value, whereas a too large mc will imply a larger standard deviation due to the reduction of the magnitude interval. Several methods for the estimation of mc exist, however its evaluation is very delicate and requires some critical decision making in most cases. Here we present a new, very rapid and simple method for mc estimation. It is based on the observation that the Gutenberg-Richter distribution is an exponential one only for magnitudes larger than mc. As a consequence, the average magnitude ma value should increase linearly with a threshold magnitude mth. The departures from such linear behavior, allows a correct estimation of mc, whereas the linearity of the of ma versus mth allows a correct estimation of the b-value.