Clustering Analysis of Seismicity and Aftershock Identification

Abstract

We introduce a statistical methodology for clustering analysis of seismicity in the time-space-energy domain and use it to establish the existence of two statistically distinct populations of earthquakes: clustered and nonclustered. This result can be used, in particular, for nonparametric aftershock identification. The proposed approach expands the analysis of Baiesi and Paczuski [Phys. Rev. E 69, 066106 (2004)10.1103/PhysRevE.69.066106] based on the space-time-magnitude nearest-neighbor distance eta between earthquakes. We show that for a homogeneous Poisson marked point field with exponential marks, the distance eta has the Weibull distribution, which bridges our results with classical correlation analysis for point fields. The joint 2D distribution of spatial and temporal components of eta is used to identify the clustered part of a point field. The proposed technique is applied to several seismicity models and to the observed seismicity of southern California.

A tentative model for the explanation of Båth law using the order parameter of seismicity in natural time

“…As it was shown in Zaliapin and Ben-Zion (2013a), Zaliapin et al (2008) and Zaliapin and Ben-Zion (2015), earthquake catalogues show a bimodal joint distribution of ðlog 10 T; log 10 RÞ. One mode corresponds to the background events-like events in a Poisson process-while the other corresponds to the clustered events with n ij \10 À5 , i.e.…”

“…One mode corresponds to the background events-like events in a Poisson process-while the other corresponds to the clustered events with n ij \10 À5 , i.e. events closer in time and space to their parents than expected in a Poisson process Ben-Zion 2013a, 2015;Zaliapin et al 2008). Figure 6 depicts this bimodal distribution for the Global CMT catalogue.…”

“…The nearest-neighbour, which is called the parent, can be the parent of multiple events which are called offsprings. We should note that each possible parent-offspring pair is assigned a corresponding distance n but the nearestneighbour is defined as the pair with minimum n ij (Zaliapin et al 2008;Zaliapin and Ben-Zion 2013a). Normalizing the time and space distances by the magnitude of the parent, we have (Zaliapin et al 2008;Zaliapin and Ben-Zion 2015) …”

“…where T is referred to (Zaliapin et al 2008;Zaliapin and Ben-Zion 2015) as the rescaled time and R as the rescaled distance. We selected b ¼ 1, d ¼ 1:6 and p ¼ 0:5 (Zaliapin et al 2008;Zaliapin and Ben-Zion 2015).…”

“…In this case, we consider the definition of aftershocks suggested in Zaliapin et al (2008) which uses the nearestneighbour distance: For each earthquake i in a catalogue, we consider its occurrence time t i , latitude u i (in radians), longitude h i (in radians) and magnitude m i . For a pair of earthquakes i and j, the time-space-magnitude distance is defined (Baiesi and Paczuski 2004) as…”