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Due to the complexity of the generator process of seismic events, we study under several aspects the interaction structure between earthquake events using recently developed spatio-temporal statistical techniques and models. Using these advanced statistical tools, we aim to characterise the global and local scale cluster behaviour of the Easter Sicily seismicity considering the catalogue data since 2006, when the Italian National Seismic Network was upgraded and earthquake location was sensibly improved. Firstly, we characterise the global complex spatiotemporal interaction structure with the space-time ETAS model where background seismicity is estimated non-parametrically, while triggered seismicity is estimated by MLE. After identifying seismic sequences by a clustering technique, we characterise their spatial and spatio-temporal interaction structures using other advanced point process models. For the characterisation of the spatial interactions, a version of hybrid of Gibbs point process models is proposed as method to describe the multiscale interaction structure of several seismic sequences accounting for both the attractive and repulsive nature of data. Furthermore, we consider log-Gaussian Cox processes (LGCP), that are relatively tractable class of empirical models for describing spatio-temporal correlated phenomena. Several parametric formulation of spatio-temporal LGCP are estimated, by the minimum contrast procedure, assuming both separable and non-separable parametric specification of the correlation function of the underlying Gaussian Random Field.

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