Moment‐magnitude relations in theory and practice

The observation that motivates this study is the difference in c values in moment‐magnitude relations of the form log M O = cM L + d between central and southern California. This difference is not at all related to geographical area; rather, it results from positive curvature in the log M O ‐ M L plane and the relatively large number of M L <5 earthquakes in the central California data set. With the prescription that the far‐field shear waves from which M L is taken be finite‐duration, band‐limited, white Gaussian noise in acceleration, we can estimate M L as a function of M O alone, by fixing the a rms stress drop at 100 bars and ƒ max at 15 Hz. These model calculations fit available California moment‐magnitude data for 0≲ M L ≲7,10 17 ≲ M O ≲10 28 dyne cm with striking accuracy. This range in source strength is entire: earthquakes with M O ≥10 28 dyne cm are unlikely to occur in California, and earthquakes with M L <0 cannot be recorded in California, at least under ordinary conditions of recording earthquakes at ordinary hypocentral depths. More fundamentally, the remarkably good fit of model to data implies that the a rms stress drop of 100 bars (to a factor of 2 or so) is a stable and pervasive feature of all ( M L ≳2 1/2) California earthquakes whose spectral corner frequency lies in the “visible” bandwidth, ƒ 0 ≤ƒ max .