Estimation of Moment Magnitude (M) for Small Events (M<4) on Local Networks

We develop a simple model to estimate moment magnitude for events of M <4 at distances out to similar to 300 km, based on readily available ShakeMap parameters and seismological scaling principles. Estimates of moment magnitude for such small events are not available from standard methods but are needed for local-network applications and for traffic light systems for induced-seismicity applications. This issue is currently of particular interest in central and eastern North America. The method takes advantage of the fact that for small events the response spectrum is well-correlated with seismic moment for periods greater than 0.3 s and can be predicted from a simple stochastic point-source model. We develop an equation by which we calculate M from the 1 s pseudoacceleration amplitudes (PSA) (M >= 3) or the 0.3 s PSA (M <3) at each station, using a simple linear equation that corrects for the effects of attenuation. We show that this method produces unbiased estimates of moment magnitudes in both eastern and western North America, for M <= 4 events recorded at distances <300 km.