Some Problems With Using Magnitude Scales For Eastern North American Earthquakes

Abstract

Body wave magnitude scales are of the form m b = B + C log 10 D + log 10 ( A / T ) , where B and C are constants, D is the epicentral distance, and A is some measure of maximum ground motion amplitude at the period T. By accepted definition, m b applies to waves with periods of 1 second. However, the Lg wave amplitude data in eastern United states, typically within the period range of 0.6 to 1.5 seconds, are currently being used in determining m b magnitudes of eastern earthquakes. Implicit in the use of periods other than 1 second is the assumption that the ground velocity (A/T), is constant over that period range. This paper points out the errors introduced into the mb estimate of an earthquake when T is not restricted to lie relatively close to 1 second. These errors arise because of the shape of the seismic source spectrum and the relative scaling of 1 second period amplitudes with respect to other periods. As an example, it will be shown that the use of amplitudes with a period of 0.3 seconds can lead to error in the estimated mb magnitude by as much as 0.5 magnitude units. However, by using the known source spectrum scaling in a region, it will be shown how to obtain an equivalent mb magnitude from waves with periods other than 1 second.