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U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MAIL STOP 977, MENLO PARK, CALIFORNIA 94025
Abstract
Nine hundred fifty-seven maximum zero-to-peak Wood-Anderson amplitudes A (synthesized or recorded) from 40 horizontal-component seismographs (20 sites) with 0 
400 km for 106 earthquakes with 18 
log M0 22.3 in central California have been fit in a least-squares sense using the parametric form
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ik = Kronecker delta, R = hypocentral distance, and n, K, Sl, and Ck are variables determined by regression analysis. The Ck are a magnitude measure, and the Sl are station corrections constrained to have zero average. We find n = 1.018 ± 0.107 and K = 0.00291 ± 0.00070 km–1. Setting n = 1, appropriate for body-wave propagation in homogeneous media, yields K = 0.00301 ± 0.00036 km–1. Following Richter's definition of an ML = 3 earthquake as one for which A = 1 mm at = 100 km and S1 = 0, we express the local magnitude ML as ML = log A – log A0, where -log A0 = n log (R/100) + K (R – 100) + 3. For 30 475 km, the -log A0 values using n = 1 and K = 0.00301 km–1 are within 0.15 of Richter's values for southern California. For 30 km, Richter's values are significantly smaller than those obtained here, a result consistent with recent studies of –log A0 for southern California. Our results suggest that the ML scale as commonly used underestimates the sizes of small shocks that are predominantly recorded at 30 km. This article has been cited by other articles:
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