A simple procedure is presented for analyzing magnitudes and seismicity rates reported in earthquake catalogs in order to discriminate between inadvertently introduced changes in magnitude and real seismicity changes. We assume that the rate and the frequency-magnitude relation of the independent background seismicity do not change with time. Observed differences in the frequency-magnitude relation (a and b values) between data from two periods are modeled as due to a transformation of the magnitude scale. The transformation equation is found by a least-squares-fitting process based on the seismicity data for earthquakes large enough to be reported completely and by comparing the linear relation of one period to the other. For smaller events, an additional factor accounting for increased (decreased) detection is allowed. This fitting technique is tested on a data set from Parkfield for which two types of magnitudes, amplitude and duration, were computed for each earthquake. We found that the b-value fitting technique yielded virtually the same result as a linear regression assuming the same errors in the two magnitudes. The technique is also applied to interpret the nature of reporting rate changes in a local (Guerrero, Mexico) and a regional (Italy) earthquake catalog. In Guerrero, a magnitude change in 1991.37 can be modeled about equally well by Mnew = Mold + 0.5 or by Mnew = 1.02 Mold + 0.38, but residuals with the latter transformation are smaller. In Italy, a magnitude change in 1980.21 cannot be modeled satisfactorily by a simple magnitude shift but is well described by a compression of the magnitude scale given by Mnew = 0.67 Mold + 1.03.
The proposed b-slope fitting method provides a means to interpret quantitatively, and in some cases correct for, artificial reporting rate changes in earthquake catalogs.