Testing self-organized criticality in the crust using entropy: A regionalized study of the CMT global earthquake catalogue

[1] We test the notion of self-organized criticality (SOC) and the proximity to the critical point in the brittle crust. If the system were strictly critical, we would expect an infinite correlation length with minimal temporal or spatial predictability. An alternative view is that the Earth is in a self-organized subcritical (SOSC) state with a finite and systematically fluctuating correlation length. This would imply a system that is sufficiently near-critical to maintain power law scaling relations over a finite scale range, but can intermittently reach criticality in the form of a single large earthquake when the correlation length becomes effectively infinite over the scale of the observed region. Here we address the question of proximity to criticality from the viewpoint of statistical physics by describing a regionalized study equivalent to the ensemble approach in thermodynamics. Flinn-Engdahl regionalization of global seismicity is used to calculate the expectation of the logarithm of energy [lnE] and entropy S from centroid moment tensor (CMT) data for different seismic regions. We compare a phase diagram for S and [lnE] from the data with an analytical statistical mechanical solution and find that they are in good agreement. The analysis shows systematic spatial heterogeneity in entropy that is associated with the tectonic deformation style. Oceanic ridges are seen to be low entropy ( relatively ordered), and subduction zones have higher entropy ( less ordered) with collision-zones scattered at the two extremes. Statistically resolvable phase variations in the system as a whole point toward it being better described as subcritical in the spatial ensemble.