Ergodicity in Natural Fault Systems

— Attempts to understand the physics of earthquakes over the past decade generally have focused on applying methods and theories developed based upon phase transitions, materials science, and percolation theory to a variety of numerical simulations of extended fault networks. This recent work suggests that fault systems can be interpreted as mean-field threshold systems in metastable equilibrium (Rundle et al., 1995; Klein et al., 1997; Ferguson et al., 1999), and that these results strongly support the view that seismic activity is highly correlated across many space and time scales within large volumes of the earth’s crust (Rundle et al., 2000; Tiampo et al., 2002). In these systems, the time averaged elastic energy of the system fluctuates around a constant value for some period of time and is punctuated by major events that reorder the system before it settles into another metastable energy well. One way to measure the stability of such a system is to check a quantity called the Thirumalai-Mountain (TM) energy metric (Thirumalai and Mountain, 1993; Klein et al., 1996). In particular, using this metric, we show that the actual California fault system is ergodic in space and time for the period in question, punctuated by the occurrence of large earthquakes, and that, for individual events in the system, there are correlated regions that are a subset of the larger fault network.