Information theory and the earthquake frequency-magnitude distribution

Abstract A new frequency-magnitude relation consistent with an average magnitude 〈 m 〉 and an average seismic moment 〈 M o 〉 in the magnitude range ( m c , ω) is derived using the principles of information theory. The resulting density distribution n ( m ) dm = C exp{−λ 1 m − λ 2 M o ( m )} dm can be interpreted as a Boltzmann distribution of possible energy transitions scaled by a geometric factor, depending on how such transitions may occur on a fault plane. It gives a better fit to available frequency data on the Central Mediterranean area than other distributions which can only successfully model part of the magnitude range. The technique offers a direct method of including long-term geological information from plate models or observed fault movement in order to extrapolate seismicity statistics beyond the instrumental and historical eras. This approach is found to be in reasonable agreement with southern Californian frequency data—the resulting distribution being consistent with a geologically estimated recurrence time for the major events on the southern locked portion of the San Andreas fault.