C. Godano

Universality in solar flare and earthquake occurrence

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analyzing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely, both problems exhibit the same distributions of sizes, interoccurrence times, and the same temporal clustering: We find after flare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism.

Influence of time and space correlations on earthquake magnitude

A crucial point in the debate on the feasibility of earthquake predictions is the dependence of an earthquake magnitude from past seismicity. Indeed, while clustering in time and space is widely accepted, much more questionable is the existence of magnitude correlations. The standard approach generally assumes that magnitudes are independent and therefore in principle unpredictable. Here we show the existence of clustering in magnitude: earthquakes occur with higher probability close in time, space, and magnitude to previous events. More precisely, the next earthquake tends to have a magnitude similar but smaller than the previous one. A dynamical scaling relation between magnitude, time, and space distances reproduces the complex pattern of magnitude, spatial, and temporal correlations observed in experimental seismic catalogs.

Role of Static Stress Diffusion in the Spatiotemporal Organization of Aftershocks

We investigate the spatial distribution of aftershocks, and we find that aftershock linear density exhibits a maximum that depends on the main shock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and the fractal dimensionality of epicenters clearly indicate triggering by static stress. The nonmonotonic behavior of the linear density and its dependence on the main shock magnitude can be interpreted in terms of diffusion of static stress. This is supported by the power law growth with exponent H approximately 0.5 of the average main-aftershock distance. Implementing static stress diffusion within a stochastic model for aftershock occurrence, we are able to reproduce aftershock linear density spatial decay, its dependence on the main shock magnitude, and its evolution in time.

Spatial organization of foreshocks as a tool to forecast large earthquakes

An increase in the number of smaller magnitude events, retrospectively named foreshocks, is often observed before large earthquakes. We show that the linear density probability of earthquakes occurring before and after small or intermediate mainshocks displays a symmetrical behavior, indicating that the size of the area fractured during the mainshock is encoded in the foreshock spatial organization. This observation can be used to discriminate spatial clustering due to foreshocks from the one induced by aftershocks and is implemented in an alarm-based model to forecast m > 6 earthquakes. A retrospective study of the last 19 years Southern California catalog shows that the daily occurrence probability presents isolated peaks closely located in time and space to the epicenters of five of the six m > 6 earthquakes. We find daily probabilities as high as 25% (in cells of size 0.04 × 0.04deg2), with significant probability gains with respect to standard models.

Multiple-Time Scaling and Universal Behavior of the Earthquake Interevent Time Distribution

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.

Memory in self-organized criticality

Self-organized criticality (SOC) successfully describes power law behaviour of size distribution in many natural phenomena. However, it does not consider time correlations between events and therefore it is unable to reproduce the time occurrence behaviour, namely the inter-event time distribution, extremely relevant for many problems. We present a SOC model with memory: events are nucleated not only as a consequence of the instantaneous value of the local field with respect to the firing threshold, but on the basis of the whole history of the system. We apply the model to the study of earthquake occurrence and we obtain, without any parameter tuning, excellent agreement with inter-event time and magnitude distributions from the Southern California Catalog.

Unjamming Dynamics: The Micromechanics of a Seismic Fault Model

The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional molecular dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow us to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.

Statistics of slipping event sizes in granular seismic fault models

We investigate a recently introduced seismic fault model where granular particles simulate fault gouge, performing a detailed analysis of the size distribution of slipping events. We show that the model reproduces the Gutenberg-Richter law characterising real seismic occurrence, independently of model parameters. The effect of system size, elastic constant of the external drive, thickness of the gouge, frictional and mechanical properties of the particles are considered. The distribution is also characterised by a bump at large slips, whose characteristic size is solely controlled by the ratio of the drive elastic constant and the system size. Large slips become less probable in the absence of fault gouge and tend to disappear for stiff drives.

A low magnitude seismic sequence near Isernia (Molise, central Italy) in January 1986

Following the increase in seismic activity which occurred near Isernia (Molise, Central Italy) in January 1986, a digital seismic network of four stations with three-component, short-period seismometers, was installed in the area by the Osservatorio Vesuviano. The temporary network had an average station spacing of about 8–10 km and, in combination with permanent local seismic stations, allowed the accurate determination of earthquake locations during an operating period of about one month. Among the 1517 detected earthquakes, 170 events were selected with standard errors on epicentre and depth not greater than respectively 0.5 and 1.5 km. The most frequent focal depths ranged between 4 and 8 km, while the epicentres distribution covered a small area NE of Isernia of about 10 km2. A main rupture zone could not be clearly identified from the spatial distribution of the earthquakes, suggesting a rupture mechanism involving heterogeneous materials. The activity was characterized by low energy levels, the largest earthquake, on January 18, 1986, havingMD=4.0. The time sequence of events and pattern of seismic energy release revealed a strong temporal clustering of events, similar to the behaviour commonly associated with seismic swarms.

Parameter Estimation in the ETAS Model: Approximations and Novel Methods

Abstract Branching processes provide an accurate description of earthquake occurrence in the short term (days to a few weeks). Yet, the implementation of these models is not usually straightforward because of the difficulties in estimating the parameters. Indeed, log‐likelihood estimation involves a spatial integral that cannot be analytically evaluated and is difficult to implement in numerical codes. Here we present a novel technique that allows for an accurate, stable, and relatively fast parameter inversion procedure. We study the efficiency of this technique using synthetic epidemic‐type aftershock sequence catalogs with a set of parameters known a priori . Results show the efficiency of the novel technique and illustrate the limits of recently proposed approximations.