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We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks…

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to…

Sequences of aftershocks following Omori's empirical law are observed after most major earthquakes, as well as in laboratory-scale fault-mimicking experiments. Nevertheless, the origin of this memory effect is still unclear. In this letter,…

The presented paper is devoted to the search for mathematical basis for describing the aftershock evolution of strong earthquakes. We consider the experimental facts and heuristic arguments that allow to make a choice and to focus on the…

Static and dynamic stress changes in the Earth's crust induced by an earthquake typically trigger other earthquakes. Identifying such aftershocks is an important step in seismic hazard assessment but has remained challenging, especially in…

Omori Law describes the evolution of the aftershocks of a strong earthquake. Established at the end of the century before last, it is characterized by the beauty of its form, quite definite clarity, as a result of which it still attracts…

The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law…

The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ~ 1/(t_c-t)^p' of the time to the mainshock occurring at t_c. Here, we show that this…

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…

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,…

Aftershocks of aftershocks - and their aftershock cascades - substantially contribute to the increased seismicity rate and the associated elevated seismic hazard after the occurrence of a large earthquake. Current state-of-the-art…

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event.…

Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade…

Non-inertial afterslip has been inferred to occur following large earthquakes. An explanation for this slow slip phenomenon is that coseismically generated stresses induce sliding on parts of a fault surface with velocity-strengthening…

We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the…

The decay rate of aftershocks is commonly very well described by the modified Omori law, $n(t) \propto t^{-p}$, where n(t) is the number of aftershocks per unit time, t is the time after the main shock, and p is a constant in the range…

Here we focus on a basic statistical measure of earthquake catalogs that has not been studied before, the asymmetry of interevent time series (e.g., reflecting the tendency to have more aftershocks than spontaneous earthquakes). We define…

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…

We present a simple model of earthquakes on a pre-existing hierarchical fault network. The system self-organizes on long time scales in a stationary state with a power law Gutenberg-Richter distribution of earthquake sizes. The largest…

We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of…