Back to the future: old methods for new estimation and test of the Gutenberg–Richter b-value for catalogues with variable completeness

Abstract

SUMMARYIn this short paper we show how to use the classical maximum likelihood estimation procedure for the b-value of the Gutenberg–Richter law for catalogues with different levels of completeness. With a simple correction, that is subtracting the relative completeness level to each magnitude, it becomes possible to use the classical approach. Moreover, this correction allows to adopt the testing procedures, initially made for catalogues with a single level of completeness, for catalogues with different levels of completeness too.