Moment‐magnitude relations in theory and practice

Abstract

The observation that motivates this study is the difference in c values in moment‐magnitude relations of the form log MO = cML + 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 MO ‐ ML plane and the relatively large number of ML<5 earthquakes in the central California data set. With the prescription that the far‐field shear waves from which ML is taken be finite‐duration, band‐limited, white Gaussian noise in acceleration, we can estimate ML as a function of MO alone, by fixing the arms stress drop at 100 bars and ƒmax at 15 Hz. These model calculations fit available California moment‐magnitude data for 0≲ML≲7,1017≲MO≲1028 dyne cm with striking accuracy. This range in source strength is entire: earthquakes with MO≥1028 dyne cm are unlikely to occur in California, and earthquakes with ML<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 arms stress drop of 100 bars (to a factor of 2 or so) is a stable and pervasive feature of all (ML≳2 1/2) California earthquakes whose spectral corner frequency lies in the “visible” bandwidth, ƒ0≤ƒmax.