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Comparison of two surface-wave magnitude scales: M of Gutenberg and Richter (1954) and M_S of "Preliminary determination of epicenters"

OFFICE OF EARTHQUAKES, VOLCANOES, AND ENGINEERING U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025

Abstract

The Prague formula (Vanek et al., 1962), which is used for Preliminary Determination of Epicenters (PDE) magnitudes, exceeds that of Gutenberg (1945) by 0.19 unit of M_S, leading to the false assumption that mean M_S of PDE are inherently 0.19 larger than Gutenberg and Richter (1954) magnitudes, M_GR. Recomputation of M_S using Gutenberg's methods and Gutenberg-Richter (G-R) notepad data shows that M_S values in the G-R notepads are 0.1 unit of M_S too large on average, while M_GR values are 0.05 larger still. Total inflation of M_GR over recomputed M_S values is 0.16 on average. M_S for the same events recomputed with the Prague formula are thus only 0.03 unit of M_S higher on average than M_GR. Thus, PDE values of M_S are on average directly comparable to M_GR. This relationship probably is a consequence of the Prague formula having been calibrated to Gutenberg's revised magnitudes and M_GR values.

Surface-wave magnitude residuals summed over many events appear to fit a normal Gaussian distribution with a standard deviation of 0.28 unit-of-M_S for two large independent samples. Thus, anomalous single-station M_S values can be excluded from averaging, using probabilistic criteria rather than the ad hoc criteria used currently, and standard deviations of M_S from the mean are valid estimates of error.

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