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

Abstract

[1] 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 ÀBÀ1 e ÀE/q . The data are consistent with the model predictions for fluctuations in the characteristic energy q at constant B value, of the form S$BhlnEi. This approximation is valid for large q, 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.

Generalized statistical mechanics approaches to earthquakes and tectonics

“…BG statistical mechanics has been applied to earthquake physics in a series of works, which address the theory as a variational principle for deriving the large-scale properties of earthquake populations [11,75] or to investigate the thermodynamic state of the crust [76][77][78]. One of the first studies that applied statistical mechanics to earthquakes was that of Berrill & Davis [79].…”

Long-term seismogenesis and self-organized criticality

“…Nor can the times occupied be readily compared, since although starts suddenly, AMR is emergent. In the lead-up to a major earthquake, the three-stage faulting model can be both compared and contrasted with the well-known asperity model (Kanamori, 1981). Both models attribute the delay in major fracture on a fault to some kind of non-uniformity.…”

“…In statistical mechanics, this is attributed to a correlation process that evolves towards increasingly large wavelengths. Evidence of the AMR precursor developing over an area of diameter several times the major fault-length has been found in a number of cases (Jaumé and Sykes, 1999;Bowman et al, 1998).…”

“…By transforming from magnitude to energy or moment, the relation becomes a power law, and is thus typical of relations signifying fractality in a wide variety of phenomena. Kagan (1999) has studied global sets of earthquakes and found Eq.…”

“…The realization that self-organised criticality (SOC) applies to earthquakes (Bak and Tang, 1989;Ito and Matsuzaki, 1990), as well as to other prominent natural phenomena, has provided new guidelines for research into the process by which individual earthquakes are generated. For nearly a century the idea underlying such research has been the elastic rebound hypothesis of Reid (1910).…”