Wednesday, March 3, 2010

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.

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