On the Use of Analog Filters in Evaluating Amplitude Spectra of Seismic Waves

Abstract

To investigate the frequency characteristic of a particular part of a seismic-wave train, such as P, S and other prominent waves, it may be best to observe the filtered waves using filters of various frequency-bands. This paper presents a method to obtain a smoothed amplitude spectrum by means of analog-filters. The procedure is quite simple and it is easy to treat a number of data by this method. We take a series of band-pass filters, their transfer functions B_n(ω) n=1, 2, …and the peak frequencies ω_0, n n=1, 2, …being defined as follow : B_n(ω)=B_1(ω/n), ω_0, n=n・ω_0, 1 Then the spectral density at ω_0, n is approximately given by |F(ω_0, n)|≒a_n/n・a, where a_n and a are the maximum trace-amplitudes of the wave filtered by the n-th filter and of the impulse response of the 1-st filter, respectively. Comparison of the measured spectrum with the theoretical one for a rectangular wave shows good agreement. This method is applied to several examples of seismic waves from microearthquakes and found to be effective for distinguishing between various parts of the wave train in the frequency characteristic.