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The probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are properly rescaled. In this work, we aim to discover if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the Mw 6.1 L’Aquila earthquake that occurred on 6 April 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of Mw 6 and 6.5, respectively, and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: q-exponential, q-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis.

The main purpose of this paper was to, for the first time, analyse the spatiotemporal features of the background seismicity of Northern Algeria and its vicinity, as identified by different declustering methods (specifically: the Gardner and Knopoff, Gruenthal, Uhrhammer, Reasenberg, Nearest Neighbour, and Stochastic Declustering methods). Each declustering method identifies a different declustered catalogue, namely a different subset of the earthquake catalogue that represents the background seismicity, which is usually expected to be a realisation of a homogeneous Poisson process over time, though not necessarily in space. In this study, a statistical analysis was performed to assess whether the background seismicity identified by each declustering method has the spatiotemporal properties typical of such a Poisson process. The main statistical tools of the analysis were the coefficient of variation, the Allan factor, the Markov-modulated Poisson process (also named switched Poisson process with multiple states), the Morisita index, and the L–function. The results obtained for Northern Algeria showed that, in all cases, temporal correlation and spatial clustering were reduced, but not totally eliminated in the declustered catalogues, especially at long time scales. We found that the Stochastic Declustering and Gruenthal methods were the most successful methods in reducing time correlation. For each declustered catalogue, the switched Poisson process with multiple states outperformed the uniform Poisson model, and it was selected as the best model to describe the background seismicity in time. Moreover, for all declustered catalogues, the spatially inhomogeneous Poisson process did not fit properly the spatial distribution of earthquake epicentres. Hence, the assumption of stationary and homogeneous Poisson process, widely used in seismic hazard assessment, was not met by the investigated catalogue, independently from the adopted declustering method. Accounting for the spatiotemporal features of the background seismicity identified in this study is, therefore, a key element towards effective seismic hazard assessment and earthquake forecasting in Algeria and the surrounding area.