Related papers: Seismic quiescence and b-value decrease before lar…
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box…
Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumours, or…
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…
A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies. A stochastic model is proposed for…
Spatio-temporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. Particular attention is paid to clarifying how the statistical…
The recently introduced Minimalist Model [Vazquez- Prada et al., 2002] of characteristic earthquakes provides a simple representation of the seismicity originated in a sin- gle fault. Here, we first characterize the properties of this model…
The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude…
The Carlson-Langer model is a deterministic model of earthquakes. There were many investigations of this model, but its complicated spatio-temporal dynamics is not yet completely understood. We again study the model equation numerically,…
Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes, either with or without the viscosity term, are studied by means of numerical computer simulations. The continuum limit of the model is…
We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree.Vacant sites become occupied at rate 1. Further, each site is hit by…
Earthquakes vary in size over many orders of magnitude, yet the scaling of the earthquake energy budget remains enigmatic. We propose that fundamentally different "small-slip" and "large-slip" fracture processes govern earthquakes. We…
Precise real time estimates of earthquake magnitude and location are essential for early warning and rapid response. While recently multiple deep learning approaches for fast assessment of earthquakes have been proposed, they usually rely…
The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the…
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus…
The exact mechanisms leading to an earthquake are not fully understood and the space-time structural features are non-trivial. Previous studies suggest the seismicity of very low intensity earthquakes, known as micro-earthquakes, may…
Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate…
We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of…
Natural earthquake fault systems are highly non-homogeneous. The inhomogeneities occur be- cause the earth is made of a variety of materials which hold and dissipate stress differently. In this work, we study scaling in earthquake fault…
We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…