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.

A Fit for Northern California Earthquake Data 2000 - 2009

Lately I've been working on a fit to some earthquake data for Northern California for the last decade from the Northern California Earthquake Data Center (NCEDC) which includes data contributed by the USGS's Northern California Seismic Network and the Berkeley Seismological Laboratory. I included more terms in the fit and got a slightly better result when compared with the fit for Southern California but one has to wonder if the initial curvature at M 0.0 is due to fluctuations or is an true representation of the distribution. Most likely some of both. The total number of earthquakes included in the fit was 202,614 and the peak for the fit was at M 1.0013. The fluctuations below M 2.0 were again larger than expected for 3σ bounds assuming σ = √(Nfit).

The ratio, g, of number of earthquakes for successive intervals of the histogram shows some differences from that for the data for Southern California earthquakes. There is an initial dip which would indicate a lower slope and a "plateau" at M 2.0 which corresponds to higher numbers in the histogram. The slope of the curve at higher magnitude is not quite as linear as was the case for Southern California. Also note the simpler form used for g above. It didn't affect the fit at all and one can easily convert between the two forms. The orignal formula was a modified version of the diode equation.

Omori's Law

I suppose everyone has heard about the M 8.8 earthquake that occurred early Saturday morning in Chili. That was an unusually strong earthquake and there have been a large number of aftershocks most between M 5.5 and M 6.2 in the last few days. Omori's Law states that the number of aftershocks decreases in an inverse proportion to the time after the main strike. The magnitudes slowly decrease too and will eventually return to normal but it may be a few months before this happens.

The victims of an earthquake take the blunt of what happens but in a disaster of such magnitude they need the help of their neighbors, the country as a whole and the international community. If we can't prevent earthquakes from happening we need to have assistance programs in place and the means to get aid to those in need. Here are some efforts in place:

International Strategy for Disaster Reduction

Global Platform for Disaster Risk Reduction

Pan American Health Organization