Detecting Free Oscillations Using a Multiple Taper Method

The free oscillations of the earth appear as decaying sinusoids in low frequency seismic records. We present a method for detecting decaying sinusoids in a time series based on a statistical test that measures the confidence one can assign to a sinusoid's existence at any given frequency. The data are multiplied by LK tapers derived by a variational principle, creating K independent time series. A decaying sinusoid model is fit to the K time series in the frequency domain. A statistical test of the fit gives a measure of the chance that a decaying sinusoid is in the data. We compare the method to conventional direct spectral estimates and find it superior. We present a number of examples of the method's use on single and multiple records. This method may help in increasing the number of free oscillation observations for constraining earth structure.