Related papers: A model for complex aftershock sequences
The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay ~1/t^{1+\theta} of seismicity after an earthquake) and…
Aftershock sequences are of particular interest in seismic research since they may condition seismic activity in a given region over long time spans. While they are typically identified with periods of enhanced seismic activity after a…
When materials are loaded below their short-term strength over extended periods, a slow time-dependent process known as creep deformation takes place. During creep deformation, the structural properties of a material evolve as a function of…
The paper is based on the report read by the author on October 24, 2018 at the meeting of the Scientific Council of the Institute of Earth Physics of the Russian Academy of Sciences. The report was dedicated to the 150th anniversary of the…
We study the dynamical aspects of a statistical-mechanical model for fracture of heterogeneous media: the fiber bundle model with various interaction range. Although the model does not include any thermal activation process, the system…
The deactivation coefficient has been introduced for the source that cools down after the mainshock of the earthquake. The deactivation coefficient satisfies two conditions. First, it can be computed from observed aftershock frequency data…
The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been…
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical…
According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of…
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…
The recently proposed discrete scale invariance and its associated log-periodicity are an elaboration of the concept of scale invariance in which the system is scale invariant only under powers of specific values of the magnification…
After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number…
We consider two statistical regularities that were used to explain Omori's law of the aftershock rate decay: the Levy and Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behavior influenced by…
We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the…
The power law of aftershock evolution was proposed by Hirano in 1924 and introduced by Utsu into seismology in the second half of the last century. The Hirano-Utsu law is widely used in studying the relaxation of earthquake source after the…
Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock,…
The earthquake source after the main shock can theoretically be represented as a black box without an entrance. At the output, there is a signal in the form of aftershocks, the frequency of which decreases on average with time according to…
The statistical properties of avalanches in a dissipative particulate system under slow shear are investigated using molecular dynamics simulations. It is found that the magnitude-frequency distribution obeys the Gutenberg-Richter law only…
The elementary theory of relaxation of the source cooling down after the main shock of an earthquake is presented axiomatically. The names of the objects under study are given and the relationships between them are determined. A new basic…
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the…