b-EST—universal estimation of the Gutenberg–Richter b value, with a MATLAB/Python toolbox

The b value, the scaling exponent of the Gutenberg–Richter law, is a widely investigated parameter in statistical seismology, quantifying the relative proportion of small and large earthquakes in a seismic catalog. Despite its simple definition, an accurate and reliable estimation is not straightforward due to some methodological limitations (e.g., assumptions behind their derivation) and to catalog incompleteness. Different methods have been proposed during the last six decades for measuring the b value. Among them, the b-positive approach, using the positive difference of consecutive magnitudes, enables the mitigation of the so-called short-term incompleteness. In this article, we review these methods, showing that all the approaches converge to a universal formula if the magnitudes of earthquakes are properly standardized and selected. We also review b value estimations by establishing methodological consistency through comparison with extensive simulations. Moreover, we provide bEST, a novel MATLAB/ Python tool for a multimethodological assessment of the b value.