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After the main shock of an earthquake, a stream of aftershocks that does not subside for a long time is usually observed. Fusakichi Omori found that the frequency of aftershocks decreases hyperbolically with time. It has recently been…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
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…
Together with the Gutenberg-Richter distribution of earthquake magnitudes, Omori's law is the best established empirical characterization of earthquake sequences and states that the number of smaller earthquakes per unit time triggered by a…
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…
In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not…
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…
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…
A part of the seismic time series, in which the Omori law for temporal pattern of aftershocks holds, is refereed to as the Omori regime. Here the properties of correlation between earthquake events both inside and outside of the Omori…
The analysis of the classical and mirror triads of the sequence of earthquakes has been carried out in order to find the equations of evolution of foreshocks and aftershocks. The differential equation with cubic (quadratic) nonlinearity has…
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period…
Inspired by spring-block models, we elaborate a "minimal" physical model of earthquakes which reproduces two main empirical seismological laws, the Gutenberg-Richter law and the Omori aftershock law. Our new point is to demonstrate that the…
The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence…
If we assume that earthquakes are chaotic, and influenced locally then chaos theory suggests that there should be a temporal association between earthquakes in a local region that should be revealed with statistical examination. To date no…
As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, known as the Epidemic-Type Aftershock Sequence…
The paper is devoted to comparing two approaches to the study of aftershocks. The methodological foundations of the traditional approach were laid many years ago. A new approach has emerged relatively recently. The two approaches differ…
The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g.…
The elementary theory of aftershocks, being relatively simple mathematically, belongs to the basics of earthquake physics. The paper briefly outlines the concepts and ideas of the theory, provides equations for the relaxation of the source…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and…