Magnitude-dependent epidemic-type aftershock sequences model for earthquakes
We propose a version of the pure temporal epidemic type aftershock sequences (ETAS) model: the ETAS model with correlated magnitudes. As for the standard case, we assume the Gutenberg-Richter law to be the probability density for the magnitudes of the background events. Instead, the magnitude of the triggered shocks is assumed to be probabilistically dependent on that of the relative mother events. This probabilistic dependence is motivated by some recent works in the literature and by the results of a statistical analysis made on some seismic catalogs [Spassiani and Sebastiani, J. Geophys.