Related papers: Elementary theory of earthquake source relaxation
The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent…
We prove ergodicity of a point process earthquake model combining the classical stress release model for primary shocks with the Hawkes model for aftershocks.
The empirical Bath's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we show that the…
In this work the distribution of inter-occurrence times between earthquakes in aftershock sequences is analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the…
In the standard rebound theory of earthquakes, elastic deformation energy is progressively stored in the crust until a threshold is reached at which it is suddenly released in an earthquake. We review three important paradoxes, the strain…
Earthquake cycles are studied by taking into account the interactions among slip, fluid pressure, temperature, and porosity on the fault planes, which are known to play a crucial role in earthquake dynamics. The spring-block model with a…
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…
We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of…
The essence of the cumulative effect of a round-the-world seismic echo is that the echo can serve as a trigger for a second tremors in the epicentral zone of the earthquake that gave rise to the echo. According to the classification of…
The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the…
Earthquakes are indeed triggered by fault dislocations, but whether this process alone can produce the actual earthquake energy released by the mainshock has long been questioned. Therefore, exploring the true source of energy that causes…
We show that Bak et al.'s unified scaling law cannot be trivially explained by a single Omori aftershock sequence. On the contrary, the spatial heterogeneity of seismicity plays a fundamental role in the unified scaling law, which implies…
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…
The physics of earthquake triggering together with simple assumptions of self-similarity impose the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude md of completeness…
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching…
Fault ruptures of regular earthquakes typically grow in a self-similar manner, where the radiated energy is proportional to the seismic moment. Their proportionality factor, termed as scaled energy, has been conventionally described as the…
Coulomb-stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress field changes, and places with positive increases are brought closer to failure.…
Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on…
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…
We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit…