ON THE VARIATION OF B-VALUES WITH EARTHQUAKE SIZE

We investigate the effect on Gutenberg and Richter's parameter b of the saturation of moment-magnitude relationships caused by source finiteness. Any conventional magnitude scale measured at a constant period features a saturation which results in a stepwise increase in the slope of the log10 moment-magnitude relationship. We predict that this leads to an increase in b value with earthquake size. This is in addition to the effect of the physical saturation of the transverse dimension of the fault, previously described in the literature. A number of scaling models are used to predict the behavior of b with increasing magnitude, in the case of both the 20 s surface-wave magnitude M(s), and the 1s body-wave magnitude m(b). We show in particular that a b value of unity can be expected only in a range of earthquake size where the relevant magnitude has already started to saturate: it should be the exception, not the rule, and cannot be extended to a wide range of magnitudes, except at the cost of significant curvature in the frequency-magnitude curve. The widely reported b = 1 stems from the common practice of using a heterogeneous magnitude scale, e.g. M(s) for large events and m(b) for smaller ones.