Mean Field Threshold Systems and Phase Dynamics: An Application to Earthquake Fault Systems

Earthquake dynamics are considered to be one example of a strongly correlated, high dimensional driven threshold system(Burridge and Knopoff, 1967). Such driven meanfield threshold systems demonstrate complex observable space-time patterns of behavior that are difficult to understand or predict without knowledge of the underlying dynamics, which are typically unobservable. Here we describe a new method based on the application of phase dynamics to historic seismicity to analyze and forecast the space-time patterns of activity in these systems (Tiampo et al, 2002). This technique characterizes the seismicity by normalizing to the background rate, in order to define a coarse-grained measure of the spatio-temporal clustering. Application to earthquake data from a typical, seismically active region, southern California, shows that the method provide considerable insight and information regarding the underlying physical process and temporal dynamics of the earthquake fault system.