Seismic wave attenuation and magnitude relations for eastern North America

Observational data on the attenuation of short-period Rayleigh waves in North America east of the Rocky Mountains yield the following average values for the coefficient of anelastic attenuation: γ = 0.07 deg−1 for 1-sec-period waves and γ = 0.10 deg−1 for waves with a maximum particle velocity in the period range 3–12 sec. By way of comparison, the amplitude data that form the basis of Richter's empirical local magnitude scale for southern California give γ = 0.60 deg−1. Differences in γ values are sufficient to explain the observation that earthquakes in the eastern United States have a radius of perceptibility as much as 10 times larger than that of earthquakes of the same magnitude in the western United States. Theoretical curves of log A/T versus log Δ are not linear. Thus magnitude formulas of the type M = B + C (log Δ) + log A/T are valid only over a limited range of distance, for which the curve can be approximated by a straight line. Formulas of this kind, which give mb and Ms from short-period Rayleigh waves, are proposed for eastern North America.