Everything you always wanted to know about b-value* (*but were afraid to ask)

The b-value of the Gutenberg-Richter law is one of the most widely studied parameters regarding the distribution of earthquakes’ magnitude. The estimation of such a parameter and its uncertainty is critical, and it may become complex in the case of seismic catalogs with a non-uniform magnitude of completeness, or when different shapes of the Gutenberg-Richter relation (e.g. the tapered one) are adopted. Here we review recent results on the b-value estimation, also in the case of catalogs with multiple completeness levels, including the application of the weighted likelihood methodology, a method particularly suitable for spatial b-value mapping and for studying its temporal variations. These new techniques are applied to both global and regional seismic catalogs, in order to unveil the peculiarities of the b-value.