To b or not to b? - Is There Value in b Value Research?

In 1935 Richter proposed measuring the log of amplitude to assess the intrinsic size, or magnitde, of earthquakes; not long after Ishimoto, Iida, and Gutenberg observed that the distribution of log-number vs magnitude had an approximately straight-line form. The slope of this relationship is the b value, or, if scalar moment is used rather than magnitude, the beta value. Subsequently b and beta have been used routinely to describe the size distribution of earthquake groups. There is a truly enormous literature which concerns how to best to measure b and beta and purports to explain their mechanical significance. But, there are problems. First, magnitudes and moments are themselves unreliable; reported values for individual events are highly variable, and systematic errors depend strongly on event size, on the method of measurement, and on geographic region. Second, the log-number/log-moment relationship is seldom really straight, and so its slope depends on the size range chosen. Both these difficulties mean that the true accuracy in measurements of b or beta is seldom better than 0.1 or 0.2, reducing the utility of b and beta for predicting occurrence rates for large events. In general, most investigations overinterpret the significance of b and beta, especially since there is little agreement about what physical processes control the size distribution. Nevertheless, some earthquake populations do exhibit huge differences in the proportions of big and little events, e. g., contrast deep focus earthquakes beneath Tonga, South America, and Spain. Moreover, there is emerging evidence that large differences may occur over distance scales of only a few km. Ongoing research efforts should avoid simply reporting b and beta, and instead should focus on documenting and better understanding the physical reasons for the different proportions of large and small earthquakes.