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Seismic magnitude from Fourier analysis

DEPARTMENT OF GEOPHYSICS FACULTY OF SCIENCE UNIVERSITY OF WESTERN ONTARIO, LONDON, ONTARIO, Canada

Abstract

The inherent frequency dependence of the maximum peak-to-peak amplitude of seismograms suggests the use of Fourier analysis to calculate magnitudes. Since most magnitude scales use logarithms of amplitudes and amplitude/period ratios, the stability of the equivalent frequency-domain quantities was examined in a study of the spectra of Rayleigh waves from five earthquakes, a total of 73 records. The use of spectral amplitudes in formulas which were empirically developed for use with time-domain measurements resulted in smaller values of magnitude. Nevertheless, the two quantities were found to be linearly related. It was found that the use of the maximum Fourier amplitude resulted in the most stable spectral magnitudes with respect to epicentral distance and the time-domain magnitudes. This indicates that the maximum peak-to-peak amplitude of the time-series is not directly related to the Fourier amplitude at the same period, but rather to the maximum Fourier amplitude. Based on these 73 records for events with M_S = 5.9 to M_S = 6.7, we conclude that magnitudes may be determined from spectral measurements, with a marginal reduction in standard deviation over the time-domain formulas.

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