Earthquake Clustering and Declustering

Once clustering on regional scales has been removed, the times of large earthquakes on a global scale are statistically compatible with the hypothesis that events arise from a homogeneous Poisson process: There is little statistical evidence for global clustering of large events. In the other direction, there is strong statistical evidence that window-declustered catalogs of Southern California seismicity do not follow a homogeneous temporal Poisson process. The conventional chi-square test for Poisson temporal behavior based on counting the number of windows that contain various numbers of events has serious shortcomings, some of which can be circumvented by conditioning and using randomization to determine (conditional) p-values, and some of which require a completely different approach. I will present a new randomization test for clustering in space and time, and a new temporal declustering method based on deleting the smallest number of events so that those that remain pass tests for Poisson occurrence. This work is joint with Peter Shearer and, separately, Brad Luen.