Empirically the rate of earthquakes = magnitude M is well fit by the Gutenberg-Richter relationship, logN=a-bM (1) where N is the number of earthquakes = M over a given time period, a is the number of M = 0 earthquakes over the same period, and b is a parameter that determines the ratio of larger to smaller earthquakes (Ishimoto and Iida 1939; Gutenberg and Richter 1944).