Reconciling the irreconcilable: window-based versus stochastic declustering algorithms

Short-term earthquake clustering is one of the most essential features of seismicity. Clusters are identified using various techniques, generally deterministic and based on spatiotemporal windowing. Conversely, the leading approach in short-term earthquake forecasting has a probabilistic view of clustering, usually based on the epidemic type aftershock sequence (ETAS) models. The effectiveness of the deterministic techniques and whether or not to prefer a probabilistic approach is often debated in the literature: sharp cutoffs or randomness degree? In this study, we contribute to the debate by "measuring"(inferring) seismic clusters, identified by two different deterministic window-based techniques, in terms of the ETAS probabilities associated with any event in the clusters, to investigate the consistency between deterministic and probabilistic approaches. Inference is performed by considering, for each event in an identified cluster, the corresponding probability of being independent and the expected number of triggered events according to ETAS. Results show no substantial differences between the two deterministic cluster identification procedures, and an overall consistency between the identified clusters and the relative events' ETAS probabilities. A consistency between probabilistic and deterministic declustering approaches is also important for seismic hazard analyses, where the latter approach is routinely used for its simplicity.