Multiple taper spectral analysis of terrestrial free oscillations: Part I.

We present a new method for determining the frequencies of the earth's free oscillations. This method is an extension of the techniques of Thomson(1982) for finding harmonic lines in the spectrum of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best N tapers creates N samples of the time series. A decaying sinusoid model is fit to the N samples by a least squares procedure. A statistical F-test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillations in the data. The F-test is performed at a number of chosen frequencies, giving a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a Hanning tapered time series.