Statistical mechanics of earthquakes: the temporal and spatial ensembles
Abstract
Many far-from-equilibrium complex systems converge to steady-state solutions with a well-defined distribution of energetic microstates and macroscopic Boltzmann fluctuations in the system Hamiltonian. This implies that conventional tools of canonical-ensemble statistical mechanics may be applied, for example to questions such as 'how close is the system to the critical point'. Here we analyse the temporal and spatial variability of entropy S and energy E for the global catalogue for scalar moment (assumed proportional to radiated energy), in order to address this question in an objective and repeatable way. We compare the results to analytical solutions for S, <E>, and <lnE>, based on a distribution of energetic microstates that maximises S, subject to the constraints of finite <E> and <lnE>. The latter constraint results from the fact that in this problem the energetic microstates are degenerate. We split the global CMT catalogue up into a temporal ensemble of annual variations in S, <E> and <lnE>, and a spatial ensemble based on the Flinn-Engdahl zoning scheme. The temporal results show fluctuations that cannot be distinguished from the critical point, defined when dS/d<lnE>=B, the slope of the power-law component of the frequency-energy distribution. The spatial fluctuations show significant deviations from this criterion, with a statistically-significant curvature indicative of a significant sampling of the phase space around the critical point. Ocean ridge systems exhibit systematically low S, whereas subduction zones tend to have high S. Zones of continental collision show a much greater range of fluctuations about the phase diagram, but all plot on the predicted trend. We infer that the global data show no time-dependent component that can be distinguished from random Boltzmann fluctuations. The spatial variability does show fluctuations above this level, implying significant spatial fluctuations around (below) the critical point.
- Publication:
-
EGS - AGU - EUG Joint Assembly
- Pub Date:
- April 2003
- Bibcode:
- 2003EAEJA.....1157M