A method is presented for determining the local magnitude, ML, from records from seismoscopes and similar instruments. The technique extrapolates the maximum response of the standard Wood-Anderson seismograph, which determines ML, from the maximum response of the seismoscope. The standard deviation of the steady-state response of an oscillator subjected to white noise excitation is used to derive a relation correcting for the different periods, dampings, and gains of the two instruments. The accuracy of the method is verified by application to data from the San Fernando and Parkfield earthquakes wherein both accelerograph and seismoscope records are available from the same sites. The accelerograms are used to synthesize Wood-Anderson responses whose maxima are compared to those extrapolated from the seismoscope data. In both earthquakes, the average magnitudes and standard deviations determined by the two approaches are very nearly equal.
The method is then applied to the strong-motion data from the Managua, Nicaragua earthquake of December 23, 1972 (MS = 6.2, mb = 5.6). A value of ML = 6.2 is indicated from the seismoscope and accelerograph data. The next application is to the Guatemala earthquake of February 4, 1976 (MS = 7.5, mb = 5.8). The only seismic instrumentation available for determining ML is a seismoscope record from Guatemala City, which indicates ML = 6.9 when a representative distance of about 35 km is used. As a final example, the records obtained during the 1906 San Francisco earthquake from the Ewing duplex pendulum seismograph at Carson City, Nevada and the simple pendulum at Yountville, California are analyzed. After restoring the Carson City instrument, its period and damping were determined experimentally as were the period and damping of a similar instrument in the London Science Museum. On the basis of the strong-motion records from Carson City and Yountville, it is estimated that the local magnitude of the 1906 earthquake lies in the range to 7.
The use of seismoscope data further extends the instrumental base from which ML can be determined and allows the rapid determination of ML in earthquakes where seismoscope data are available. The applications in this study provide further instrumental evidence for the saturation of ML in the 7 to range, with the value of 7.2 for the Kern County earthquake of 1952, the largest so far determined.