Statistical analysis of triggered seismicity in the Kresna region of SW Bulgaria (1904) and the Umbria-Marche region of central Italy (1997)

A version of the restricted trigger model is used to analyse the temporal behaviour of some aftershock sequences. The conditional intensity function of the model is similar to that of the Epidemic Type Aftershock-Sequence (ETAS) model with the restriction that only the aftershocks of magnitude bigger than or equal to some threshold $M_{tr}$ can trigger secondary events. For this reason we have named the model Restricted Epidemic Type Aftershock-Sequence (RETAS) model. Varying the triggering threshold we examine the variants of the RETAS model which range from the Modified Omori Formula (MOF) to the ETAS model, including such models as limit cases. In this way we have a quite large set of models in which to seek the model that fits best an aftershock sequence bringing out the specific features of the seismotectonic region struck by the crisis. We have applied the RETAS model to the analysis of two aftershock sequences: The first is formed by the events which followed the strong earthquake of M = 7.8 which occurred in Kresna, SW Bulgaria, in 1904. The second includes three main shocks and a large swarm of minor shocks following the quake of 26 September 1997 in the Umbria-Marche region, central Italy. The MOF provides the best fit to the sequence in Kresna; that leads to the thought that just the stress field changes due to the very strong main shock generate the whole sequence. On the contrary the complex behaviour of the seismic sequence in Umbria-Marche appears when we make the threshold magnitude vary. Setting the cut-off magnitude M_0 = 2.9 the best fit is provided by the ETAS model, while if we raise the threshold magnitude M_0 = 3.6 and set M_tr = 5.0, the RETAS model turns out to be the best model. In fact observing the time distribution of this reduced data set it appears more evident that especially the strong secondary events are followed by a cluster of aftershocks.