The use of duration as a measure of seismic moment and magnitude

The observed relationship between magnitude and duration is shown to be a result of the particular shape of the signal coda as a function of time. If the envelope of the coda follows a t−q relationship with increasing time, then the magnitude, mτ, based on a duration τ is consequently of the form m τ = q log ⁡ 10 τ + r . A study of the duration-magnitude and duration-moment relationships for a set of central United States earthquakes indicates that the linear relationship between mτ and log10τ is valid only over a limited range. The departure from the simple linear dependence is explained in terms of instrumental response and the shift of the source-spectrum corner frequency with increasing event size.