Forecasting of the first hour aftershocks by means of the perceived magnitude.

The majority of strong earthquakes takes place a few hours after a mainshock, promoting the interest for a real time post-seismic forecasting, which is, however, very inefficient because of the incompleteness of available catalogs. Here we present a novel method that uses, as only information, the ground velocity recorded during the first 30 min after the mainshock and does not require that signals are transferred and elaborated by operational units. The method considers the logarithm of the mainshock ground velocity, its peak value defined as the perceived magnitude and the subsequent temporal decay. We conduct a forecast test on the nine M  ≥ 6 mainshocks that have occurred since 2013 in the Aegean area. We are able to forecast the number of aftershocks recorded during the first 3 days after each mainshock with an accuracy smaller than 18% in all cases but one with an accuracy of 36%.

Induced and endogenous acoustic oscillations in granular faults.

The frictional properties of disordered systems are affected by external perturbations. These perturbations usually weaken the system by reducing the macroscopic friction coefficient. This friction reduction is of particular interest in the case of disordered systems composed of granular particles confined between two plates, as this is a simple model of seismic fault. Indeed, in the geophysical context frictional weakening could explain the unexpected weakness of some faults, as well as earthquake remote triggering. In this manuscript, we review recent results concerning the response of confined granular systems to external perturbations, considering the different mechanisms by which the perturbation could weaken a system, the relevance of the frictional reduction to earthquakes, as well as discussing the intriguing scenario whereby the weakening is not monotonic in the perturbation frequency, so that a re-entrant transition is observed, as the system first enters a fluidized state and then returns to a frictional state.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Controlled Viscosity in Dense Granular Materials.

We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency, we observe a reentrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture.

Synchronized oscillations and acoustic fluidization in confined granular materials.

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency.

Scaling laws in earthquake occurrence: Disorder, viscosity, and finite size effects in Olami-Feder-Christensen models.

The relation between seismic moment and fractured area is crucial to earthquake hazard analysis. Experimental catalogs show multiple scaling behaviors, with some controversy concerning the exponent value in the large earthquake regime. Here, we show that the original Olami, Feder, and Christensen model does not capture experimental findings. Taking into account heterogeneous friction, the viscoelastic nature of faults, together with finite size effects, we are able to reproduce the different scaling regimes of field observations. We provide an explanation for the origin of the two crossovers between scaling regimes, which are shown to be controlled both by the geometry and the bulk dynamics.

Mechanical origin of aftershocks.

Aftershocks are the most striking evidence of earthquake interactions and the physical mechanisms at the origin of their occurrence are still intensively debated. Novel insights stem from recent results on the influence of the faulting style on the aftershock organisation in magnitude and time. Our study shows that the size of the aftershock zone depends on the fault geometry. We find that positive correlations among parameters controlling aftershock occurrence in time, energy and space are a stable feature of seismicity independently of magnitude range and geographic areas. We explain the ensemble of experimental findings by means of a description of the Earth Crust as an heterogeneous elastic medium coupled with a Maxwell viscoelastic asthenosphere. Our results show that heterogeneous stress distribution in an elastic layer combined with a coupling to a viscous flow are sufficient ingredients to describe the physics of aftershock triggering.

Dynamic Weakening by Acoustic Fluidization during Stick-Slip Motion.

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.

Non-monotonic dependence of the friction coefficient on heterogeneous stiffness.

The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on loading conditions, the real area of contact along the interfaces and the confining pressure. Here we show, by means of numerical simulations of a 2D Burridge-Knopoff model with a simple local friction law, that the macroscopic friction coefficient depends non-monotonically on the bulk elasticity of the system. This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction. We rationalize these results by means of an energetic balance argument.

Nonequilibrium fluctuation-dissipation theorem and heat production.

We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium "effective temperature." Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by adenosine triphosphate hydrolysis illustrate these points.

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 × 0.04deg(2)), with significant probability gains with respect to standard models.

Solid-on-solid single-block dynamics under mechanical vibration.

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena are not well understood. Here we address these questions focusing on a simple spring-block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows us to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion, we identify the conditions under which friction is suppressed and/or recovered, and we evidence the critical role played by surface modulations and by the properties of the confining force.

Crossover in growth law and violation of superuniversality in the random-field Ising model.

We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.

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.

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.

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.

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.

Off-equilibrium response function in the one-dimensional random-field Ising model.

A thorough numerical investigation of the slow dynamics in the d=1 random-field Ising model in the limit of an infinite ferromagnetic coupling is presented in this paper. Crossovers from the preasymptotic pure regime to the asymptotic Sinai regime are investigated for the average domain size, the autocorrelation function, and staggered magnetization. By switching on an additional small random field at the time t(w) the linear off-equilibrium response function is obtained, which displays as well the crossover from the nontrivial behavior of the d=1 pure Ising model to the asymptotic behavior where it vanishes identically.

Interface fluctuations, bulk fluctuations, and dimensionality in the off-equilibrium response of coarsening systems.

The relationship between statics and dynamics proposed by Franz, Mezard, Parisi, and Peliti (FMPP) for slowly relaxing systems [Phys. Rev. Lett. 81, 1758 (1998)] is investigated in the framework of nondisordered coarsening systems. Separating the bulk from interface response we find that for statics to be retrievable from dynamics the interface contribution must be asymptotically negligible. How fast this happens depends on dimensionality. There exists a critical dimensionality above that the interface response vanishes like the interface density and below that it vanishes more slowly. At d=1 the interface response does not vanish leading to the violation of the FMPP scheme. This behavior is explained in terms of the competition between curvature-driven and field-driven interface motion.

Fluctuation dissipation ratio in the one-dimensional kinetic ising model

The exact relation between the response function R(t,t(')) and the two time correlation function C(t,t(')) is derived analytically in the one-dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio X(t,t(')) is found to depend on time through C(t,t(')) in the time region where scaling C(t,t('))=f(t/t(')) holds. The crossover from the nontrivial form X[C(t,t('))] to X(t,t(')) identical with1 takes place as the waiting time t(w) is increased from below to above the equilibration time t(eq).