Estimation of free core nutation parameters and availability of computing options

The Earth's Free Core Nutation (FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects. High-precision superconducting gravimeter (SG) and very long baseline interferometry (VLBI) provide good observation techniques for detecting the FCN parameters. However, some choices in data processing and solution procedures increase the uncertainty of the FCN parameters. In this study, we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data, SG data from thirty-one stations, and the 10 celestial pole offset (CPO) series. The results show that significant discrepancies are caused by different computing options for a single SG station. The stacking method, which results in a variation of 0.24–5 sidereal days (SDs) in the FCN period (T) and 10³-10⁴ in the quality factor (Q) due to the selection of the weighting function and the ocean tide model (OTM), can effectively suppress this influence. The statistical analysis results of synthetic data shows that although different weight choices, while adjusting the proportion of diurnal tidal waves involved, do not significantly improve the accuracy of fitted FCN parameters from gravity observations. The study evaluated a series of OTMs using the loading correction efficiency. The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results. Through the estimation of the FCN parameters based on the forced nutation, it was found that the weight function P₁ is more suitable than others, and different CPO series (after 2009) resulted in a difference of 0.4 SDs in the T and of 10³ in the Q. We estimated the FCN parameters for SG (T = 430.4 ± 1.5 SDs and Q = 1.52 × 10⁴ ± 2.5 × 10³) and for VLBI (T = 429.8 ± 0.7 SDs, Q = 1.88 × 10⁴ ± 2.1 × 10³).