The observation that motivates this study is the difference in c values in moment-magnitude relations of the form log M₀ = 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 M₀ - 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 M₀ alone, by fixing the arms stress drop at 100 bars and f_max at 15 Hz. These model calculations fit available California moment-magnitude data for 0 ≲ M_L ≲ 7, 10¹⁷ ≲ M₀ ≲ 10²⁸ dyne cm with striking accuracy. This range in source strength is entire: earthquakes with M₀ ≥ 1028 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, f₀ ≤ f_max.