@article{epos195,
          volume = {101},
          number = {1},
           month = {July},
          author = {Ilya Zaliapin and Andrei Gabrielov and Vladimir Keilis-Borok and Henry Wong},
           title = {Clustering Analysis of Seismicity and Aftershock Identification},
       publisher = {The American Physical Society},
         journal = {Physical Review Letters},
            year = {2008},
             url = {https://episodesplatform.eu/eprints/195/},
        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)] based on the space-time-magnitude nearest-neighbor distance {\ensuremath{\eta}} between earthquakes. We show that for a homogeneous Poisson marked point field with exponential marks, the distance {\ensuremath{\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 {\ensuremath{\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.}
}