Thursday, March 4, 2010

Limiting Value for g and Nonequilibrium

Both fits for Northern and Southern California have nearly the same value for the constant term in the form assumed for the gain or ratio of the successive values of the number of earthquakes in the histogram intervals. As the magnitude increase the gains level out and approachs a limiting value. The two fits indicate a value of 0.786 ± 0.011. If there is a distribution for earthquakes we would expect all fits to have a value close to this.

One of the problems with the fits is that we may not be dealing with equilibrium distributions. Most of the smaller earthquakes in Southern California can be interpreted as aftershocks. The aftershocks follow Omori's Law and tend to persist for long times after a major earthquake slowly decreasing in magnitude. We cannot expect all the energy released by an earthquake to be dissipated as heat or dispersed as seismic waves. Some of it is redistributed in the area around the main shock and it takes a while before conditions return to normal. This may be a form of Nonequilibrium Thermodynamics.

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