EARTHQUAKE FREQUENCY AND MOMENT MAGNITUDE RELATIONS FOR MAINSHOCKS, FORESHOCKS AND AFTERSHOCKS - THEORETICAL B-VALUES

The Gutenberg-Richter relation, log n = a - b M, where n is the cumula tive number of earthquakes greater than the magnitude, M and a and b a re constants determined empirically is discussed using a mathematical model of adult and the moment magnitude, M-W. A simple power law of M- 0 = k n(l) which relates the earthquake moment, M-0 and frequency, n w as discussed and the meanings of constants k and l were derived. The r elation of M-0 = Delta sigma (LA) using the stress drop, Delta sigma, fault length, L and area of a fault plane, A, gives M-0 = Delta sigma L-3 and M-0 = Delta sigma hL(2) for two cases of A = L-2 and A = Lh, r espectively, where the depth of the brittle-ductile transition layer; h = 2 x 10(4) m and Delta sigma = 5 x 10(6) N/m(2) are assumed. The fr equency-magnitude relation is obtained considering different rupture m echanisms of earthquakes. Deviation of the empirical Gutenberg-Richter relation at a large magnitude is interpreted. as the effect of the se ismogenic layer in earth interior. Theoretical analysis from assumptio n of different rupture mechanisms indicated varied b vales for small a nd large events, as well as the different types of earthquakes. Mainsh ocks gave b of 1.0 and 0.75, respectively for small and large events. The b values of 0.75 and 0.50 for aftershocks and 0.50 and 0.375 for f oreshocks were also obtained Some results from both statistic calibrat ion of earthquake catalogue and experiments were in agreement with our predicted values.