Accurate determination of the parameters of the Earth’s free core nutation (FCN) provides insights into the core-mantle coupling mechanism and helps refine modeling of celestial pole offsets. Recent studies suggest that the FCN period exhibits time-varying characteristics, potentially related to core-mantle interactions, but precise detection remains challenging. Traditionally, FCN periods estimated from superconducting gravimeter (SG) observations, based on resonance phenomena in diurnal tidal waves, rely mostly on the \({\Psi }_{1}\) wave. However, the low signal-to-noise ratio (SNR) of the \({\Psi }_{1}\) wave leads to significant uncertainties in the precise detection of temporal variations in the FCN period. In this study, we propose a method that relies solely on \({K}_{1}\) wave with a higher SNR, based on the sensitivity of the \({K}_{1}\) wave to the time-varying FCN parameter. The simulation results show that the new method can overcome the limitations of using the \({\Psi }_{1}\) wave and can effectively capture the variations in the FCN period within a few days under current SG observational precision. The method is applied to observations from nine SG stations in the International Geodynamic and Earth Tide Service (IGETS) network. The results indicate that the proposed method can significantly improve the detection of temporal variation of the FCN period and can obtain results close to those of the very long baseline interferometry (VLBI) technique. This method can enhance the effective utilization of SG observations in detecting weak signals related to the dynamics of the Earth’s core.
