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The M_L scale in central California

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

where A_ij = A (mm) for earthquake i on seismograph component j, _ik = Kronecker delta, R = hypocentral distance, and n, K, S_l, and C_k are variables determined by regression analysis. The C_k are a magnitude measure, and the S_l 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 M_L = 3 earthquake as one for which A = 1 mm at = 100 km and S₁ = 0, we express the local magnitude M_L as M_L = 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 M_L scale as commonly used underestimates the sizes of small shocks that are predominantly recorded at 30 km.

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