Multidimensional earthquake frequency distributions consistent with Non-Extensive statistical physics: The interdependence of magnitude, interevent time and interevent distance in North California

Abstract

It is now accepted that the active tectonic grain comprises a self-organized complex system, therefore its expression (seismicity) should be manifested in the temporal and spatial statistics of energy release rates, and exhibit memory due to long-range interactions in a fractal-like space-time. Such attributes can be properly understood in terms of Non-Extensive Statistical Physics. In addition to energy release rates expressed by the magnitude M, measures of the temporal and spatial interactions are the time (Δt) and hypocentral distance (Δd)  between consecutive events. Recent work indicated that if the distributions of M, Δt and    Δd are independent so that the joint probability p(M, Δ  t, Δd)  factorizes as p(M) p(  Δt) p(  Δd),  earthquake frequency is related to M, Δt and    Δd by well defined power-laws consistent with NESP. The present work applies these concepts to investigate the self-organization and temporal/spatial dynamics of North Californian seismicity. The results indicate that the statistical behaviour of seismicity in this area is consistent with NESP predictions and has attributes of universality, as its holds for a very broad range of spatial, temporal and magnitude scales. They also indicate that the expression of the regional active tectonic grain comprises a mixture of processes significantly dependent on Δd, which include near (<100km) and far (>400km) field interactions.