Multiple-taper spectral analysis of terrestrial free oscillations: part I

We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components 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 K tapers creates K time series. A decaying sinusoid model is fit to the K time series 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, producing 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 cosine-tapered time-series. The multiple-taper method is found to be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.