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We analyze 21 aftershock sequences of California to test for evidence of space-time diffusion. Aftershock diffusion may result from stress diffusion and is also predicted by any mechanism of stress weakening. Here, we test an alternative…

We propose a new physically-based ``multifractal stress activation'' model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on…

Very often damage and fracture in heterogeneous materials exhibit bursty dynamics made of successive impulse-like events which form characteristic aftershock sequences obeying specific scaling laws initially derived in seismology:…

Recently, simple differential models of aftershocks have attracted increased attention of researchers at the Institute of Physics of the Earth, Russian Academy of Sciences for their remarkable properties. The shortened Bernoulli equation…

A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to…

According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends…

This paper is devoted to the study of the interaction between two distinct forms of non-stationary processes, which we will refer to as non-stationarity of first and second kind. The non-stationarity of first kind is caused by…

The aftershock sequence of the devastating Japan earthquake of March 2011 is analyzed for the presence of periodicities at the Earth tide periods. We use spectral analysis as well as a time-domain method KORRECT developed earlier to detect…

Recently, the physics of aftershocks has been enriched by three new problems. We will conditionally call them dynamic, inverse, and morphological problems. Dynamic problem is to search for the cumulative effect of a round-the-world seismic…

Earthquakes are rupture-like processes that propagate along tectonic faults and cause seismic waves. The propagation speed and final area of the rupture, which determine an earthquake's potential impact, are directly related to the nature…

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…

130 years ago, Omori formulated the first law of earthquake physics. The essence of the law is that the frequency of aftershocks decreases hyperbolically over time. 100 years ago, Hirano doubted the universality of Omori law and proposed a…

Earthquakes rank among the most destructive manifestations of the Earth's dynamics. Can they be predicted? This is often the first question students ask. To answer that right away: no, at present it is not possible to anticipate the date,…

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…

Physics-based and statistic-based models for describing seismic occurrence are two sides of the same coin. In this article we compare the temporal organization of events obtained in a spring-block model for the seismic fault with the one…

This paper is devoted to the theory of aftershocks. The history of discovery of the Omori law is briefly described, the initial formulation of the law is given in the form of an algebraic formula describing the decrease in the frequency of…

Slow-slip phenomena, including afterslips and silent earthquakes, are studied using a one-dimensional Burridge--Knopoff model that obeys the rate-and-state dependent friction law. By varying only a few model parameters, this simple model…

A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence…

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly referred…

We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time,…