Proximity to Criticality: Statistical Mechanics, Numerical Models and Natural Earthquake Data
Abstract
Complex driven threshold systems often produce statistical fluctuations that are very similar to those of equilibrium systems, with Boltzmann fluctuations in energy that can be used formally to define an entropy S and a 'temperature term' T. In this spirit we develop a mean field formulation for the frequency-magnitude distribution of earthquakes. Based on the results of numerical models for earthquakes as a complex system (averaged over several cycles), we assume a positive correlation between the distribution of potential strain energy U in the internal system and the radiated seismic energy E. The model predicts a functional relationship between S and <lnE> that can be used to answer the question: 'How close is the system to the critical point?'. We examine this question for temporal and spatial ensembles using CMT data. The answer for the temporal ensemble (annual data) is that the fluctuations represented by the earthquakes are indistinguishable from self-organised criticality, with a linear relationship between S and <logE>, but no correlation between S and <E>. Similarly <lnE> and <E> are not strongly correlated because <lnE> is determined most by intermediate-sized events on the Gutenberg-Richter trend, and <E> is dominated by the largest events. However, the spatial ensemble (with regions as defined in the Flinn-Engdahl scheme) show a systematic curvature in the plot of S v <lnE> consistent with an intermittently (but still near-critical) critical point system.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2003
- Bibcode:
- 2003AGUFMNG32A..06A
- Keywords:
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- 3220 Nonlinear dynamics;
- 7209 Earthquake dynamics and mechanics;
- 7223 Seismic hazard assessment and prediction;
- 7230 Seismicity and seismotectonics