Declustering algorithms and network theory for the topological inspection of earthquake sequences

The complexity of earthquake sequences is investigated by two declustering methods: the "nearest-neighbor" method (NN), which is based on nearest-neighbor distances between events in space-time-energy domain, and the stochastic declustering method (SD), which is based on the space-time ETAS (epidemic-type aftershock sequence) model, a branching point process defined by a hazard function conditional on the observation history. Both methods are data-driven and can be satisfactorily applied to decompose the seismic catalog into background seismicity and sequences of clustered earthquakes; in addition, they allow studying the internal structure of the identified sequences (or several probable realizations of it, in the case of SD method) since they provide the connections between events forming each cluster. A comparative analysis of the identified sequences is performed by exploiting graphical tools and quantitative methods from network theory. The aim is of characterizing the topological structure of the clusters and highlighting common features that emerge from both declustering methods. As a case study, we consider the seismic sequences occurred in Northeastern Italy and reported in the local bulletins, compiled at the National Institute of Oceanography and Experimental Geophysics (OGS) since 1977. Fig.1 shows the subset of earthquakes occurred in the years 1998-1999 and the results from the application of the two declustering algorithms. The background and clustered components are consistently identified by the two methods. Still, the SD method tends to include in clusters few events that are quite far in time clusters, but very close in space (red dots in Fig. 1c, top panel); on the other side, the NN method tends to associate some events that are pretty distant from the mainshock epicenter, but very close in time (red dots in Fig. 1c, low panel). Nonetheless, the trees obtained from SD display a more complex internal structure than the trees obtained from NN, a difference that can be explained by the multilevel triggering model associated with the SD method.