Probabilistic identification of earthquake clusters using rescaled nearest neighbour distance networks

Despite the widely recognized importance of the spatio-temporal clustering of earthquakes, there are few robust methods for identifying clusters of causally related earthquakes. Recently, it has been proposed that earthquakes can be linked to their nearest neighbour events using a rescaled distance that depends on space, time and magnitude. These nearest neighbour links may correspond either to causally related event pairs within a clustered sequence or a non-causal relationship between independent events in different sequences. The frequency distribution of these rescaled nearest neighbour distances is consistent with a two-component mixture model where one component models random background events and the other models causally related clusters of events. To distinguish between these populations, a binary threshold has commonly been used to separate the clustered and background events. This has an obvious weakness in that it ignores the overlap of the two distributions and therefore all uncertainty in the event pair classification. It is also restricted so far to treating the two modes as normal distributions. Here we develop a new probabilistic clustering framework using a Markov Chain Monte Carlo mixture modelling approach which allows overlap and enables us to quantify uncertainty in event linkage. We test three hypotheses for the underlying component distributions. The normal and gamma distributions fail to fit the tails of the observed mixture distribution in a well-behaved way. In contrast, the Weibull mixture model is well-behaved in the tail, and provides a better fit to the data. We demonstrate this using catalogues from Southern California, Japan, Italy and New Zealand. We also demonstrate how this new approach can be used to create probabilistic cluster networks allowing investigation of cluster structure and the spatial, temporal and magnitude distributions of different types of clustering and highlight difficulties in applying simple metrics for cluster discrimination.