[1] The power law decay of the aftershocks rate is observed only after a characteristic time scale c. The dependence of c on the mainshock magnitude M M and on the lower cut-off magnitude M I is well established. By considering ten sequences recorded in the California Catalog we show that the aftershock number distribution becomes independent of both M M and M I if time is rescaled by an appropriate time scale fixed by the difference M M À M I . This result is interpreted within a more general dynamical scaling hypothesis recently formulated, relating time differences to magnitude differences. The above hypothesis gives predictions in good agreement with the recent findings by Peng et al. (2007). Citation: Lippiello, E., M. Bottiglieri, C. Godano, and L. de Arcangelis (2007), Dynamical scaling and generalized Omori law, Geophys. Res. Lett., 34, L23301,

The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features have been questioned and some criticisms have been raised. We investigate the existence of universal scaling properties by analyzing a Californian catalog and by means of numerical simulations of an epidemic-type model. We show that the interevent time distribution exhibits a universal behavior over the entire temporal range if four characteristic times are taken into account. The above analysis allows us to identify the scaling form leading to universal behavior and explains the observed deviations. Furthermore, it provides a tool to identify the dependence on the mainshock magnitude of the c parameter that fixes the onset of the power law decay in the Omori law.

[1] We propose a fast method able to discriminate between Poissonian independent earthquakes and aftershocks. The method is based on the evaluation of the variability coefficient, defined as the ratio between the standard deviation and the average value of the interoccurrence time between two successive earthquakes. We apply this technique to the California and a properly constructed synthetic catalogue in order to estimate the level of background seismicity and identify seismic sequences. We then investigate the spatiotemporal organization of aftershocks focusing on the distributions of interevent times and interevent distances between two successive events. We find evidence for the existence of a characteristic spatial length scale, related to the size of the aftershock zone, whereas no typical timescale is detected.

We consider long-time recorded seismic signals of Stromboli volcano to determine the inter-time distribution function of the Strombolian explosion-quakes. We show that it is Poissonian. Hence, the apparently observed periodic recurrence of the explosions is actually described by the constant rate of a Poisson process. Moreover, combining a diffusive model with the experimental inter-time distribution, we can determine the size distributions of the bubbles and infer the observed slug sizes.

The clustered occurrence of earthquakes is viewed as an intermittent phenomenon, interpreting the clusters of events as chaotic bursts combined to the Poissonian occurrence of background seismicity. In particular, we suggest that it can be interpreted as an example of on-off intermittency. This kind of intermittency is parameter driven and exhibits certain universal statistical properties. The study of a Californian catalogue allows to interpret earthquake occurrence as an on-off intermittent phenomenon. Our results suggest the existence of a branching mechanism in earthquake occurrence well explained by epidemic type models.

We present a study of the earthquake intertime distribution D(Δt) for a California catalog in temporal periods of short duration T. We compare experimental results with theoretical predictions and analytical approximate solutions. For the majority of intervals, rescaling intertimes by the average rate leads to collapse of the distributions D(Δt) on a universal curve, whose functional form is well fitted by a Gamma distribution. The remaining intervals, exhibiting a more complex D(Δt), are all characterized by the presence of large shocks. These results can be understood in terms of the relevance of the ratio between the characteristic time c in the Omori law and T: Intervals with Gamma-like behavior are indeed characterized by a vanishing c/T. The above features are also investigated by means of numerical simulations of the Epidemic Type Aftershock Sequence (ETAS) model. This study shows that collapse of D(Δt) is also observed in numerical catalogs; however, the fit with a Gamma distribution is possible only assuming that c depends on the main-shock magnitude m. This result confirms that the dependence of c on m, previously observed for m>6 main shocks, extends also to small m>2.

[1] Stochastic branching models provide a good description of some aspects of the temporal organization in seismicity. Generally, they assume that magnitudes are independent of history, as in the widely used Epidemic Type Aftershock Sequence (ETAS) model. Here, we consider a recent epidemic-like model where time-magnitude and magnitude-magnitude correlations are introduced via a dynamical scaling (DS) hypothesis, namely, the magnitude difference between earthquakes fixes the time scale for correlations. We also consider a variation of the ETAS model where the c parameter of the Omori law is not fixed but depends on the parent magnitude. We develop a novel procedure to maximize the log likelihood of the different models. This method is based on a Monte Carlo sampling in the parameter space with a variable step size during the evolution to converge to the given accuracy. The log likelihood indicates that the DS model provides the best fit for the major California sequences and the whole catalog, setting as lower magnitude thresholds M c ≥ 3.5. For M c = 3, the best fit is obtained by a model with c depending on both the parent magnitude and goes into M c as in the generalized Omori law. The better performance of the DS model with respect to the ETAS model is attributed to correlations in magnitudes.Citation: Bottiglieri, M., E. Lippiello, C. Godano, and L. de Arcangelis (2011), Comparison of branching models for seismicity and likelihood maximization through simulated annealing,

S U M M A R YIndependent component analysis (ICA) is a recent and well-known technique used to separate mixtures of signals. This technique has been applied to the ground deformation time-series recorded at the permanent GPS network of the Osservatorio Vesuviano-INGV in order to characterize the deformation background level in the Neapolitan volcanic area. The analysis revealed the presence of five independent periodic signals common at all the GPS stations; some of them are interpreted as effects of earth tides. The residual signal at each station represent the local ground deformation. Unfortunately the ICA cannot provide the absolute amplitude of the components, indeed we are not able to obtain a residual amplitude at each station. Then we used a stationarity analysis in order to investigate the eventual presence of local transient deformations. The ICA technique combined with the stationarity analysis has shown to be a very interesting tool for individuating ground deformation trends and could be very useful in volcanic areas monitoring.