Journal of Seismology 6: 125–134, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. 125 On the methods to identify clustering properties in sequences of seismic time-occurrences L. Telesca 1,∗ , V. Cuomo 1 , V. Lapenna 1 & M. Macchiato 2 1 Istituto di Metodologie Avanzate di Analisi Ambientale,CNR, Tito Scalo (PZ), Italy; 2 Dipartimento di Scienze Fisiche, Universit` a Federico II, Naples, Italy ( ∗ )Author for correspondence: tel: +39-971-427206, fax: +39-971- 427222, e-mail: ltelesca@imaaa.pz.cnr.it) Received 4 July 2000; accepted in revised form 18 May 2001 Key words: clustering, fractal tools, seismicity Abstract In recent years there has been deep development in the use of techniques to analyse the statistical properties of point process time series. Furthermore many efforts have been made to establish robust methods to identify time clustering structures in the temporal distribution of seismic events. In this paper we intend to give a systematic review of some common used techniques to characterise the temporal properties of an earthquake sequence; we also present new methods, commonly used in other scientific fields, to reveal time clustering structures in a seismic sequence and to clearly identify non-poissonian behaviours at different time scales. An application of these methods has been performed on the seismicity of Irpinia-Basilicata area (Southern Italy). Introduction Understanding the time dynamics of a seismic pro- cess is one of the fundamental problem in seismology. This problem is strictly connected to seismic hazard analysis (Boschi et al., 1995): knowing the statistical distribution ruling event occurrence improves the cap- ability of reliably evaluating the probability of future earthquake occurrences. The seismic activity model- ing has been performed using several distributions, among which the poissonian distribution was the most extensively used, since, in many cases, for large events a simple discrete Poisson distribution provides a close fit. But it is well known that earthquake occurrence exhibits a strong degree of correlation between events of the same sequence. Omori (1895) and successively Utsu (1970) observed that the number of aftershocks decreases in time as a power-law (t+c) −p , with p lar- ger than 1.0. Kagan and Jackson (1991) showed that earthquake sequences are characterised by time clus- tering properties with both short and long time scales. The temporal clustering of the seismic sequences is widely observed in many seismic catalogues (Smal- ley et al., 1987; Kagan and Jackson, 1991; Bodri, 1993; Trifu and Radulian, 1994; Bittner et al., 1996; Lapenna et al.; 1998a; Lapenna et al., 1998b; Telesca et al. 1999). Several methods have been used to evidence time clustering properties of earthquake sequences. An ex- tensively used method to identify clustered or pois- sonian behaviours in earthquake occurrence time se- quences is the coefficient of variation (C V ) of earth- quake interevent time (τ ) as a ratio of the standard deviation (σ τ ) to the average time (<τ>); a com- pletely random Poisson occurrence has a coefficient of variation equal to one, while it is larger than one for clustered earthquakes (Davis et al., 1989; Kagan and Jackson, 1991; Boschi et al., 1995). Fractal and multifractal approaches have been developed to re- veal time clustering properties of seismic sequences by means of the estimation of the fractal dimension of earthquake interoccurrence time sequences, using the correlation integral method (Godano et al., 1997; De Rubeis et al., 1997); the slope (D t ) of the correla- tion integral of time distribution of earthquakes versus the interevent time in log-log scales gives information about the nature of the seismic process: a low value of D t means that events are very clustered. Regarding