Influence length and space-time correlation between earthquakes

Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade process, each event produces aftershocks. A definitive method to assess any connection between two earthquakes separated in time and distance does not exist. Here we propose a novel method of data analysis that, based on the space-time combined generalization of the correlation integral leads to a self-consistent visualization and analysis of both spatial and temporal correlations. When analyzing global seismicity we discovered a universal relation linking the spatial Influence Length of a given earthquake to the time elapsed from the event itself. Following an event, time correlations (i.e. causality effects) exist in a region that shrinks over time, suggesting a long-range dissipating stress transfer. A different process is acting in the short-range where events are randomly set, evidencing a sub-diffusive growth of the seismogenic zone.