A spectral search for the inner core wobble in Earth’s polar motion

The inner core wobble (ICW) is a normal mode of rotation of the inner core (IC) relative to the mantle predicted theoretically. While many papers have been devoted to its theoretical formulation, no attempt of its detection has been published in the literature. In this work, we first give a preliminary formulation for the variations of gravity and geopotential coefficients associated with the ICW that complements the formulation for the polar motion by Mathews et al. [1991a]. The results show that the ICW is most likely detectable using polar motion data. Then we attempt to detect the ICW by comparing the spectrum of an Earth orientation parameter (EOP) time series with that of the sum of an oceanic angular momentum (OAM) time series and an atmospheric angular momentum (AAM) time series. We found no firm evidence of the ICW using our approach to a resolvability of a few mili-arc-second (mas). At such a low amplitude in polar motion, the ICW is far below the current detectability of the variations of gravity measured by absolute and superconducting gravimeters, and of the variations of the geopotential coefficients obtained from the Gravity Recovery and Climate Experiment (GRACE).