Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes

Past studies that attempted to quantify the spatio-temporal organization of seismicity have defined the conditions by which an event and those that follow it can be related in space and/or time. In this work, we use the simplest measures of spatio-temporal separation: the interevent distances R and interevent times T between pairs of successive events. We observe that after a characteristic value R*, the distributions of R begin to follow that of a randomly shuffled sequence, suggesting that events separated by R > R* are more likely to be uncorrelated events generated independent of one another. Interestingly, the conditional T distributions for short-distance (long-distance) events, R <= R* (R > R*), peak at correspondingly short (long) T values, signifying the spatio-temporal clustering (separation) of correlated (independent) events. By considering different threshold magnitudes within a range that ensures substantial catalogue completeness, invariant quantities related to the spatial and temporal spacing of correlated events and the rate of generation of independent events emerge naturally.