Spatial features of earthquake clusters investigated by different approaches

Earthquake clustering is a prominent feature of seismic catalogs, both in time and space. Several methodologies for earthquake cluster identification have been proposed in the literature with at least a twofold scope: (1) characterization of the clustering features and their possible relation to physical properties of the crust; (2) declustering of earthquake catalogs which, by removing events temporally and spatially dependent on the mainshocks, allows for spatio-temporal analysis of the background seismicity. Nevertheless the application of different (de)clustering methods may lead to diverse classifications of earthquakes into main events and secondary events; consequently, the definition of mainshock is not univocal, but strictly related to the different physical/statistical assumptions underlying each method. Therefore we consider different declustering techniques to investigate classification similarities which might provide strong support for some clustering features, and classification differences which might highlight strength and lack of the clustering methods. The comparative analysis of earthquake clusters is carried out for a sequence of earthquakes occurred in North-Eastern Italy, as reported in OGS catalog since 1977. In this area only low-to-moderate magnitude events have been recorded during the last decades, despite its high seismic hazard attested by at least eight historical destructive earthquakes occurred since 1348, the most recent one being the 1976 May 6 M6.4 earthquake, located in the Julian Prealps. Hence, a further aim of the clustering analysis is to provide a quantitative basis to understand the role of moderate size earthquakes in the framework of regional seismicity. Two clustering techniques are applied: the nearest-neighbor approach (Zaliapin and Ben-Zion, 2013) and the stochastic declustering approach (Zhuang et al., 2004). Both methods can be satisfactorily applied to decompose the seismic catalog into background seismicity and individual sequences (clusters) of earthquakes; moreover, they are data-driven and allow studying the internal structure of the clusters. The nearest-neighbor (NN) approach is based on the nearest-neighbor distance of events in the space-time-energy domain (Baiesi and Paczuski, 2004), where the distance between event i and event j is the product of (1) their inter-occurrence time, (2) their hypocentral distance up to the fractal dimension of the earthquake hypocentre distribution, and (3) the frequency of the magnitude of event i as given by the Gutenberg-Richter law. The histogram of the distances between every pair of events i and j clearly shows a bimodal distribution that can be approximated as a mixture of two Gaussian distributions, one associated with the Poissonian background activity and the other with the clustered populations. The nearest-neighbor method has only two parameters, fractal dimension d and b-value, that are robustly identified by the Unified Scaling Law for Earthquakes (USLE) method (Peresan and Gentili, 2018). The stochastic declustering approach (SD) is based on the space-time epidemic-type aftershock sequence (ETAS) model (Ogata, 1998), a branching point process controlled by a hazard function conditional on the observation history: background earthquakes independently occur at constant Poisson rate, triggering other events with a spatio-temporal decay modelled by the Omori-Utsu law. By the thinning simulation procedure for point processes, the probability that an event at any time t is independent or triggered by previous earthquakes is calculated. Based on these probabilities, the whole process stochastically splits into key sub-processes: the background process (i.e. the declustered catalog), and the cluster processes triggered by each background event. The estimation of ETAS parameters is an iterative algorithm that simultaneously estimates the background rate by a variable kernel method, the model parameters by the maximum likelihood method, and the branching structure obtained by the thinning procedure (Zhuang et al., 2002). A preliminary comparison of results from the two methods shows that the cluster structures produced by NN and SD approaches have comparable trend in terms of spatial extent of seismic clusters. The detected clusters can be represented as topological trees. For large sequences, trees obtained from the SD method show a more complex internal structure than trees obtained by the NN method. The greater complexity might reflect the basic features of the SD method, in particular the multilevel triggering property of the ETAS model for which each event is able to generate offspring. Based on the internal structure of the trees detected by NN method, two geographical areas can be recognized. Specifically, burst-like sequences are associated with the north-western part and swarm-like sequences with the south-eastern part of the study region. The territorial heterogeneity of earthquakes clustering is in good agreement with spatial variability of scaling parameters identified by the USLE method, the fractal dimension in particular.