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 MS, leading to the false assumption that mean MS of PDE are inherently 0.19 larger than Gutenberg and Richter (1954) magnitudes, MGR. Recomputation of MS using Gutenberg's methods and Gutenberg-Richter (G-R) notepad data shows that MS values in the G-R notepads are ∼0.1 unit of MS too large on average, while MGR values are 0.05 larger still. Total inflation of MGR over recomputed MS values is 0.16 on average. MS for the same events recomputed with the Prague formula are thus only 0.03 unit of MS higher on average than MGR. Thus, PDE values of MS are on average directly comparable to MGR. This relationship probably is a consequence of the Prague formula having been calibrated to Gutenberg's revised magnitudes and MGR 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-MS for two large independent samples. Thus, anomalous single-station MS values can be excluded from averaging, using probabilistic criteria rather than the ad hoc criteria used currently, and standard deviations of MS from the mean are valid estimates of error.

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