Entropy, energy, and proximity to criticality in global earthquake populations

Abstract

We examine the question of proximity of the global earthquake population to the critical point characterised by the energy E and entropy S based on annual frequency data from the Harvard CMT catalogue. The results are compared with a theoretical model corresponding to a Boltzmann probability density distribution of the form p(E) ∝ E−B−1e−E/θ. The data are consistent with the model predictions for fluctuations in the characteristic energy θ at constant B value, of the form S∼B〈lnE〉. This approximation is valid for large θ, relative to the maximum possible event size, confirming that the Earth is perpetually in a near‐critical state, reminiscent of self‐organized criticality. However, the results also show fluctuations of ±10% in entropy that may be more consistent with the notion of intermittent criticality. A more precise definition of the two paradigms, and a similar analysis of numerical models, are both needed to distinguish between these competing models.