Incorporating spatial properties in the statistical analysis

Abstract

In addition to the inter-event time T measuring the stasis time between successive earthquake events, we define the inter-event occurrence radius R
to study the spatial relationship between earthquake events. The value of R between two earthquake events is a simple Euclidean distance between their epicenters. Statistics of R reveal two discernible peaks R_short ≈ 11 km and R_long ≈ 1200 km corresponding to the characteristic values of correlated and uncorrelated events. Setting a threshold R_short < R_thres < R_long, we separate successive events into two groups: Return times of successive events whose R ≤ R_thres are recorded as Tin, and those whose R>R_thres are recorded as T_out. We find significant differences in the statistics of T_in and T_out, suggesting non-uniformity in earthquake statistics. Finally, we find that an intermediate value R^∗ ≈ 111 km best separates the correlated and uncorrelated events in the time series.