Space-time correlation of earthquakes

Seismicity is a complex process featuring non-trivial space-time correlations in which several forms of scale invariance have been identified. A frequently used method to detect scale-invariant features is the correlation integral, which leads to the definition of a correlation dimension separately in space and time. In this paper, we generalize this method with the definition of a space-time combined correlation integral. This approach allows us to analyse medium-strong seismicity as a point process, without any distinction among main, after or background shocks. The analyses performed on the catalogue of worldwide seismicity and the corresponding reshuffled version strongly suggest that earthquakes of medium-large magnitude are time clustered inside specific space-time regions. On the basis of this feature, we recognize a space-time domain statistically characterized by sequences' behaviour and a domain of temporal randomness. Then, focusing on the spatial distribution of hypocentres, we find another domain confined to short distances and characterized by a relatively high degree of spatial correlation. This spatial domain slowly increases with time: we interpret this as the 'afterevent' zone representing the set of all subsequent events located very near (about 30 km) to each reference earthquake and embedded on specific seismogenic structures such as faults planes.