On the nature and dynamics of the seismogenetic systems of North California, USA: An analysis based on Non-Extensive Statistical Physics

We examine the nature of the seismogenetic system in North California, USA, by searching for evidence of complexity and non-extensivity in the earthquake record. We attempt to determine whether earthquakes are generated by a self-excited Poisson process, in which case they obey Boltzmann-Gibbs thermodynamics, or by a Critical process, in which long-range interactions in non-equilibrium states are expected (correlation) and the thermodynamics deviate from the Boltzmann-Gibbs formalism. Emphasis is given to background seismicity since it is generally agreed that aftershock sequences comprise correlated sets. We use the complete and homogeneous earthquake catalogue published by the North California Earthquake Data Centre, in which aftershocks are either included, or have been removed by a stochastic declustering procedure. We examine multivariate cumulative frequency distributions of earthquake magnitudes, interevent time and interevent distance in the context of Non-Extensive Statistical Physics, which is a generalization of extensive Boltzmann-Gibbs thermodynamics to non-equilibrating (non-extensive) systems. Our results indicate that the seismogenetic systems of North California are generally sub-extensive complex and non-Poissonian. The background seismicity exhibits long-range interaction as evidenced by the overall increase of correlation observed by declustering the earthquake catalogues, as well as by the high correlation observed for earthquakes separated by long interevent distances. It is also important to emphasize that two subsystems with rather different properties appear to exist. The correlation observed along the Sierra Nevada Range - Walker Lane is quasi-stationary and indicates a Self-Organized Critical fault system. Conversely, the north segment of the San Andreas Fault exhibits changes in the level of correlation with reference to the large Loma Prieta event of 1989 and thus has attributes of Critical Point behaviour albeit without acceleration of seismic release rates. SOC appears to be a likely explanation of complexity mechanisms but since there are other ways by which complexity may emerge, additional work is required before assertive conclusions can be drawn.