On the influence of time and space correlations on the next earthquake magnitude

A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence of magnitude correlations. The standard approach generally assumes that magnitudes are independent and therefore in principle unpredictable. Here we show the existence of clustering in magnitude: earthquakes occur with higher probability close in time, space and magnitude to previous events. More precisely, the next earthquake tends to have a magnitude similar but smaller than the previous one. A dynamical scaling relation between magnitude, time and space distances reproduces the complex pattern of magnitude, spatial and temporal correlations observed in experimental seismic catalogs.