Instability of Earth's rotation at the decadal time resolution

Due to the gravitational pull from the distant planets, the Earth's axis of rotation is wandering around its figure axis. The trace of the motion will bear a circular or elliptical shape if the external tuque is unique and the body itself is entirely rigid. In reality, it is not the case, the Earth has a satellite moon, and itself is revolving around the Sun together with other members of the solar system, all those bodies exert forces on the Earth, among them the strongest pull is coming from its own satellite Moon and the Sun. Considering the distances to those bodies and their masses are well determined, their effects on the orientation and rotation of a simplified non-rigid Earth could be precisely modeled at the sub-centimeter level. However, after removing the forced nutation terms, a tiny displacement signature in the residuals of the nutation remains, which is mainly caused by the free core nutations. The mechanism to excite the mode has been attributed to the atmosphere, which has enough power to generate 0.01" (0.31m) displacement according to Sasso and Wahr 1981. From the cumulated VLBI observations, the reported amplitude of FCN is about 0.0002" (0.2mas), which is two orders of magnitude lower than the upper limit suggested by previous study. Besides, the FCN exhibit a nonlinear behavior at the decadal time scale, we separated those signatures from the FCN time series. The nonlinear decal signature will be furthermore compared with the rotation speed variations manifest in length of day (LOD). We will discuss the possibility to probe the core by combing that information.