The VLBI nutation series from GSFC and the USNO, now both in excess of 23 years in length, allow the exploration of the temporal behaviour of the retrograde (RFCN) and prograde (PFCN) free core nutations. Our analysis implements Singular Value Decomposition to solve the least squares problem of fitting the Discrete Fourier Transform to the non-equispaced VLBI nutation observations. A novel feature of our procedure is to use the Parseval relation to determine the number of singular values of the coefficient matrix to be eliminated. We report the observation for the first time of the prograde mode predicted by Jiang (1993). We find periods of -417 ± 5 and -413 ± 4 days for the retrograde mode and 388 ± 2 and 387 ± 5 days for the prograde mode. Spectral analyses at 500 day intervals down the two records show the RFCN in both the GSFC and USNO data to be in free ring down. The PFCN in the GFSC series appears to be in a similar free ring down. The PFCN in the USNO series does not show similar behaviour, possibly because it is at the noise level. Free decay of the nutation modes allow the direct measurement of the viscosity at the top of the core. We find a value of 795 Pa · s in contrast to the commonly cited value of 0.008 Pa · s found by Gans (1972) by the extrapolation of laboratory measurements.
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