Calculating California seismicity rates

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). Thus to characterize the seismicity rate, N, and risk in a given region we need to solve for the values of a and b. Here we are concerned with solving for the long term average values of these parameters for the state of California. My primary data source is a catalog of 1850-2006 M = 4.0 seismicity compiled with Tianqing Cao (Appendix H). Because earthquakes outside of the state can influence California I consider both earthquakes within the state and within 100 km of the state border (Figure 1).