Predominant Period and Magnitude

Abstract

A relation between predominant period and magnitude is investigated both experimentally and theoretically. If we disregard the difference in the predominant periods of P and S waves, the results for earthquakes with magnitude less than about 5 are consistent with those derived from the velocity spectra of two theoretical source models given by HASKELL and AKI. For earthquakes with magnitude larger than about 6, the periods theoretically derived deviate largely from the observed ones. This is caused by the definition of magnitude which is based on the amplitudes of surface waves with period of 20 seconds.
Assuming a linear relation between magnitude and logarithm of seismic energy, we find logT=-A-B log σ+CM, where σ is the stress drop and A, B and C are constant. Corresponding to various relations between the stress drop and magnitude, the curves relating log T with M can be drawn in various forms. Only when the stress drop is constant through all the magnitudes, log T is a linear function of magnitude.
The above-mentioned tneoretical models give the same source spectra for P and S waves. Therefore the difference in the predominant periods for P and S waves must be explained by other factors, for example, by the difference in the attenuation of seismic waves. When the attenuation factor Q for S waves is appreciably smaller than that for P waves, the difference in the predominant periods may be explained for microearthquakes, but for large earthquakes, because of their long periods, the difference in the values of Q is not effective.