Numerical solutions of rotational normal modes of a triaxial two-layered anelastic Earth

The Earth's rotational normal modes depend on Earth model used, including the layer structures, principal inertia moments of different layers and the compliances. This study focuses on providing numerical solution of the rotational normal modes of a triaxial two-layered anelastic Earth model without external forces but with considering the complex forms of compliances and the electromagnetic coupling between the core and mantle. Based on the present knowledge of the Chandler wobble (CW) and Free Core Nutation (FCN), we provide a set of complete compliances which could be used for reference in further investigations. There are eight rotational normal mode solutions, four of which might exist in nature. However, in reality only two of these four solutions correspond to the present motion status of the prograde CW and the retrograde FCN. On one hand, our numerical calculations show that the periods and quality factors (Qs) of CW and FCN are respectively 434.90 and 429.86 mean solar days (d) and 76.56 and 23988.47 under frequency-dependent assumption, and the triaxiality prolongs CW about 0.01 d and has hardly effect on FCN. On the other hand, we analyze the sensibility of compliances and electromagnetic coupling parameter on the periods and Qs of CW and FCN and find the sensitive parameters with respect to them. Keywords: Earth rotation, Triaxial two-layered anelastic Earth model, Compliances, Rotational normal modes, Numerical solutio