Thursday, January 21, 2010

An Extension of the Empirical Formula

The formula for the expected number of earthquakes in the histogram intervals can be extended to other cases. The simple rate law assumed below can be used to derive a general expression for the proportional factor, N0, if the time period, ΔT, and the interval width, ΔM, are known. The value for R0 can found if the other values are known for one histogram.

R0 = 2.033 x 10^8 per year assuming the interval if from M to M+ΔM.

If instead the interval is from M-ΔM/2 to M+ΔM/2, i. e., M is a central value, the following formulas should be used and again R0 = 2.033 x 10^8 per year.

The fit in the last blog assumed that M was a central value so the second formula is required to find R0.

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