A new version of the ETAS model for seismic events with correlated magnitudes

The distribution of the magnitudes of seismic events is generally assumed to be independent on past seismicity. However, by considering events in causal relation, for example, mother-daughter, it seems natural to assume that the magnitude of a daughter event is conditionally dependent on one of the corresponding mother events. In order to find experimental evidence supporting this hypothesis, we analyze different catalogs, both real and simulated, in two different ways. From each catalog, we obtain the law of the magnitude of the triggered events by kernel density. The results obtained show that the distribution density of the magnitude of the triggered events varies with the magnitude of their corresponding mother events. As the intuition suggests, an increase of the magnitude of the mother events induces an increase of the probability of having “high” values of the magnitude of the triggered events. In addition, we see a statistically significant increasing linear dependence of the magnitude means.