Updated estimation of the free core and inner-core nutation resonance parameters using 2023 VLBI solutions

The elliptical fluid core and solid inner core undergo rotational wobbles within the rotating Earth. Under
tidal forcing, the presence of these rotational modes induces resonances in the Earth’s nutations as observed
by VLBI. The strengths and frequencies of these Free Core Nutation (FCN) and Free Inner Core Nutation (FICN)
resonances depend on a few fundamental geophysical parameters of the deep Earth’s interior. Since the first estimates
of the FCN and FICN resonance parameters in 2000, nutation measurements by VLBI have accumulated
with a better accuracy due to a number of improvements in the modeling of the delay, including a more reliable
celestial reference frame with a highest number of reference points of high precision. We propose an updated
determination of the FCN and FICN resonance parameters using a Bayesian inversion of the most recent VLBI
solutions. Various nutation series are analyzed to retrieve a combined solution with consistent uncertainties. We
obtain estimates of the FCN resonant period and quality factor that are in agreement with previous estimates. The
FICN resonant parameters are also deduced from the coupling constant at the inner core boundary. The later is
however much less constrained resulting in a large variability in the value of the FICN frequency.