  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.
