Ergodic dynamics in a natural threshold system

Numerical simulations suggest that certain driven, dissipative mean-field threshold systems, including earthquake models, can be characterized by statistical properties often associated with ergodic dynamics, in the same sense as stochastic Brownian motion. We applied a fluctuation metric proposed by Thirumalai and Mountain [Phys. Rev. E 47, 479 (1993)]] for statistically stationary systems and find that the natural earthquake fault system in California demonstrates similar ergodic dynamics.     

Nonlinear network dynamics on earthquake fault systems

Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.     

New approach to Gutenberg-Richter scaling

We introduce a new model for an earthquake fault system that is composed of noninteracting simple lattice models with different levels of damage denoted by q. The undamaged lattice models (q=0) have Gutenberg-Richter scaling with a cumulative exponent β=1/2, whereas the damaged models do not have well defined scaling. However, if we consider the "fault system" consisting of all models, damaged and undamaged, we get excellent scaling with the exponent depending on the relative frequency with which faults with a particular amount of damage occur in the fault system. This paradigm combines the idea that Gutenberg-Richter scaling is associated with an underlying critical point with the notion that the structure of a fault system also affects the statistical distribution of earthquakes. In addition, it provides a framework in which the variation, from one tectonic region to another, of the scaling exponent, or b value, can be understood.     

Space-time clustering and correlations of major earthquakes

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that the occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering.     

Analysis of complex networks associated to seismic clusters near the Itoiz reservoir dam

On September 18, 2004, a 4.6 mbLg earthquake occurred in the western Pyrenees, with an epicenter located approximately 4 km from the Itoiz reservoir dam. We study the aftershock sequence of this earthquake and compare it with others that occurred in the same area in order to evaluate whether this might be a case of reservoir induced seismicity triggered by impounding of water. In order to do so, we first decluster the catalog by means of a link algorithm whose distance is based on the ETAS model. We then analyze the different clusters obtained in terms of their fractal dimension and the properties of the complex network formed by the individual earthquakes belonging to these clusters. We conclude that there are properties of the cluster representing the September 18, 2004 earthquake that are distinctively different from the properties of other clusters found in the same region. This could be an indicator of a different seismic source, potentially produced by the Itoiz dam impoundment.     

Tests for specific nonparametric relations between two distribution functions with applications

Let (X,Y) be a random vector and let G and H be the marginal distributions of X and Y, respectively. In this paper, we propose two tests, one of Kolmogorov‐Smirnov type and the other of Wilcoxon type, for the null hypothesis Ψ(G) = H against the alternative Ψ(G) < H, where Ψ() is a function such that Ψ(G) is a distribution function. The tests are based on the empirical distribution functions of the observations on X and Y, which are dependent. We obtain their asymptotic null distributions. A suspected relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values, and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.