Quantification of corrections for the main lunisolar nutation components and analysis of the free core nutation from VLBI-observed nutation residuals

Abstract

The attempt to quantify the corrections of lunisolar nutation components was made after analysis of six sets of Earth’s orientation parameters (EOP). The deviations of the long-term nutation components about IAU2006/IAU2000A precession–nutation model are consistent with the uncertainties suggested by Mathews et al. (J Geophys Res Solid Earth, 2002. https://doi.org/10.1029/2001JB000390), but they exceed the errors determined in this work. The corrections are validated using the IERS 14C04 and IVS 19q4e combined solutions. After applying the corrections found in this work to the 14C04 nutation residuals, we analyzed the remaining signals, which contain the signature of the free core nutation (FCN). The eigenperiod of the FCN is fixed to the value derived from the resonance of the non-hydrostatic earth model in a priori. The amplitude of FCN is computed by fitting observations to the empirical model using a sliding window, the length of window is determined by taking into account the interference between those close nutation components and the FCN. In addition, we also fitted the nutation residuals by a viscous damping function; both methods produce the same results in the amplitudes of FCN. The magnitude of the free core nutation bears a “V-shape” distribution, and furthermore, the oscillation of the FCN shows a decay and a steady reinforcement before and after 1999. In order to examine the origin of the modulation in FCN’s magnitude, we briefly analyzed the possible damping or beating mechanism behind it. We diagnosed the magnitude and running phase changes of FCN by comparing it with the occurrence of the transient geomagnetic jerks. The weighted root mean square errors of nutation residuals are minimally reduced about $36\%$ when the corrections to the 21 nutation components and the FCN signature are considered together.

A Appendix

The 11 sets of EOP solutions are used to estimate the uncertainties of the 21 nutation component are showed in Fig. 9.

We computed the power spectral density with the complex number ($\mathrm{d}X+i\mathrm{d}Y$) built from the IERS and IVS corrected residuals (Fig. 10), which partly explains the diversity of the eigen-period of the FCN found by different studies. One possible interpretation about the wider $\delta T$ is that the eigen-period and phase of FCN may be changed due to the rotation of the Earth as indicated by Krásná et al. (2013), which hints a splitting of the mode; however, this need be investigated further.

We tested different window lengths starting from 2 to 8 years (Fig. 11) and compared the results with 4 years time window (Fig. 12). The amplitude of the short-term oscillations were decreasing with the increasing of the length of the window. The time reference is the mid point of each window. We used a one day sliding step to track the time variation of the mode.