Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling $J\left(r\right)\sim r^{-(d+\sigma )}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $\sigma$ controls the algebraic growth in time of the characteristic domain size $L\left(t\right), L\left(t\right)\sim t^{1/z}$, with growth exponent $z=1+\sigma$ for $\sigma <1$ and $z=2$ for $\sigma >1$. These results hold for quenches to a nonzero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely, we find that in this case the growth exponent takes the value $z=4/3$, independently of $\sigma$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.

SUMMARY: The epidemic type aftershock sequence (ETAS) model provides a good description of the post-seismic spatio-temporal clustering of seismicity and is also able to capture some features of the increase of seismic activity caused by foreshocks. Recent results, however, have shown that the number of foreshocks observed in instrumental catalogues is significantly much larger than the one predicted by the ETAS model. Here we show that it is possible to keep an epidemic description of post-seismic activity and, at the same time, to incorporate pre-seismic temporal clustering, related to foreshocks. Taking also into-account the short-term incompleteness of instrumental catalogues, we present a model which achieves very good description of the southern California seismicity both on the aftershock and on the foreshock side. Our results indicate that the existence of a preparatory phase anticipating main shocks represents the most plausible explanation for the occurrence of foreshocks.

Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and creeping regions as two blocks connected elastically, subject to different friction laws. We show analytically that, upon introduction of variability in the fault plane’s static friction threshold, a nontrivial stick‐slip dynamics ensues. In particular, we support the hypothesis (Perfettini and Avouac, 2004) that the aftershock occurrence rate is proportional to the afterslip rate, up to a corrective factor that is also computed. Thus, the Omori law originates from the afterslip’s logarithmic evolution in the velocity‐strengthening region. We confirm these analytical results with numerical simulations, generating synthetic catalogs with statistical features in good agreement with instrumental catalogs. In particular, we recover the Gutenberg–Richter law with a realistic $b$‐value (⁠$b≃1$⁠) when Coulomb stress thresholds obey a power‐law distribution.

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%.

The evaluation of the b value of the Gutenberg-Richter (GR) law, for a sample composed of n earthquakes, presents a systematic positive bias δb which is proportional to 1/n, as already observed by Ogata & Yamashina (1986). In this study we show how to incorporate in δb the bias introduced by deviations from the GR law. More precisely we show that δb is proportional to the square of the variability coefficient CV, defined as the ratio between the standard deviation of the magnitude distribution and its mean value. When the magnitude distribution follows the GR law CV = 1 and this allows us to introduce a new graphical procedure, based on the dependence of b on n, which allows us to identify the incompleteness magnitude m_c as the threshold magnitude leading to CV = 1. The method is tested on synthetic catalogs and it is applied to estimate m_c in Southern California, Japan and New Zealand.