TheMLscale in central California

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 ≲ Δ ≲ 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 $logAij=−nlogRij−KRij−∑l=140Slδij+∑k=1106Ckδik$ where A_ij = A (mm) for earthquake i on seismograph component j, δ_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 Δ = 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 ≲ Δ ≲ 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 Δ ≲ 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 Δ ≲ 30 km.