## 1. Introduction

[2] Geophysical processes are featured by complex behavior that often is characterized by self-similarity, which suggests that their dynamics may be interpreted as due to many components interacting over a wide range of time or space scales [*Ashkenazy et al.*, 2003]. Earthquakes are a typical example of complex phenomena, where power-law statistics characterize the distribution of spatial, temporal and energy parameters. The existence of power-laws describing the main characteristics of a seismic process qualifies earthquakes as a good example of fractal systems.

[3] In particular, tectonic processes are generally considered to display fractal properties in time. The interevent intervals (times between two successive seismic events) follow a Poissonian distribution for completely random seismic sequences, while they are generally power-law distributed for time-clusterized sequences [*Telesca et al.*, 2001]. But the probability density function of the interevent intervals is only one window into a process, because it yields only first-order information and it reveals none about the correlation properties [*Turcott et al.*, 1994]. Therefore, time-fractal second-order methods are necessary to investigate the temporal fluctuations of seismic sequences more deeply. The use of statistics like the Allan Factor [*Allan*, 1966], the Fano Factor [*Lowen and Teich*, 1995], and the Detrended Fluctuation Analysis (DFA) [*Peng et al.*, 1995] has provided additional insight into the time dynamics of seismicity. All these measures lead to the determination of a scaling exponent, estimated by a linear fitting procedure performed on the power-law statistics plotted in log-log scales. Such scaling exponent informs about the dynamical properties of an earthquake sequence, in terms of its correlation structures and its memory phenomena and several studies have been performed aiming at the: (1) discrimination between Poissonian and clusterized sequences, (2) spatial variability of time-clustering behavior, and (3) magnitude-variability of the property of time-clusterization [*Telesca et al.*, 2003]. Furthermore, the numerical value of the scaling exponent allows us to determine quantitatively the strength of the temporal fluctuations of seismicity.

[4] In the present study, the scaling analysis was performed on the series of earthquakes that occurred in Umbria-Marche, central Italy. This area was struck by a strong earthquake occurred on September 26, 1997, with a duration magnitude of 5.8 (this event will be indicated as EQ0 hereafter). After that, the Umbria-Marche region, central Italy, was deeply studied and many investigations have been performed regarding its geodynamical features [*Boncio and Lavecchia*, 2000; *Calamita et al.*, 2000], active tectonics [*Galadini et al.*, 1999; *Cinti et al.*, 2000], spatio-temporal seismic distribution [*Ripepe et al.*, 2000; *Di Giovambattista and Tyupkin*, 2000], and induced geophysical effects [*Esposito et al.*, 2000]. This area is characterized by a well-documented historical and instrumental seismicity, mainly confined within the upper part of the crust (<16 km) [*Lavecchia et al.*, 1994].