Statistical Analysis of Triggered Seismicity in the Kresna Region of SW Bulgaria (1904) and the Umbria-Marche Region of Central Italy (1997)

Abstract

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.

Seismicity Changes Detection During the Seismic Sequences Evolution as Evidence of Stress Changes

“…Gospodinov and Rotondi (2006) offer the Restricted Epidemic Type Aftershock Sequence (RETAS) model, which is based on the assumption that not all events in a sample but only aftershocks with magnitudes larger than or equal to a threshold M th can induce secondary seismicity. Then the conditional intensity function for the model is formulated as: (4) Varying M th between the cut-off magnitude M o and the main shock magnitude M i , different versions of RETAS are examined, between ETAS and MOF models, considering these two models as limit cases.…”

“…Aiming to reveal the evolution pattern of two seismic sequences that took place in the Greek territory, the first one in the vicinity of Skyros Island, in 2001, and the second one along the west coast of Lefkada Island, in 2003, the aftershocks' temporal behaviour is examined based upon the application of Gospodinov and Rotondi (2006) software. This includes the selection of the appropriate statistical model, among MOF (Utsu, 1969), ETAS (Ogata, 1988) and RETAS and the data elaboration based upon the selected model.…”

Modelling the Energy Release Process of Aftershocks

“…Multiple strong events and complex aftershock se quences led Ogata (1988) to the formulation of the Epidemic Type Aftershock-Sequence (ETAS) by which each aftershock can trigger its own secondary events. Gospodinov and Rotondi (2006) proposed the RETAS model, which is based on the assumption th at only aftershocks with magnitudes larger than or equal to a threshold Mth can induce secondary se ismicity. It has the advantage that it includes the MOF and the ETAS models as limit cases.…”

“…Researchers often study the temporal or spatio-temporal relaxation patterns after a strong earthquake by elaborating adequate stochastic models of aftershock occurrences (Ogata, 1988(Ogata, , 1998Ogata et al, 2003;Gospodinov and Rotondi, 2006). Much fewer papers consider the energy distribution of aftershocks, most often exploring their recurrence law.…”

Evidence of Precursory Patterns in Aggregated Time Series

“…Several versions of ETAS modeling have been developed aiming at better explaining observed seismicity. Gospodinov and Rotondi (2006) for example suggested the Restricted ETAS model (RETAS), where only earthquakes above a cut-off magnitude (which can be higher than mc) can produce their own aftershocks. Implicit in all these models is that all events can be considered as foreshocks, mainshocks and aftershocks .…”