The effect of data windows on the estimation of free oscillation parameters

Summary In seeking to estimate the frequencies, decay rates, amplitudes and phases of the free oscillations of the Earth using observed seismic spectra, data windows are required to reduce the effects of mode—mode interference. Formal expressions for the variances and covariances of these estimated parameters are derived here, for the case of a single isolated mode and an arbitrary data window. Explicit results are given for a Hann and Blackman—Harris minimum four-term window as well as for a boxcar. The optimum or minimum variance record length for measuring frequencies and decay rates using a Hann window is 1.1 Q -cycles, and that for determining amplitudes and phases is 0.5 Q -cycles.