# Formulation of a Triaxial Three-Layered Earth Rotation: I. Theory and Rotational Normal Mode Solutions

## TL;DR

This paper develops a comprehensive triaxial three-layer Earth rotation model considering various core-mantle couplings, providing numerical solutions for normal modes and analyzing their periods and dissipations.

## Contribution

It introduces a novel formulation of Earth rotation theory with detailed core-mantle coupling effects and offers four numerical solutions for rotational normal modes.

## Key findings

- Triaxiality increases CW and ICW periods by about 0.01 and 0.35 days.
- Mantle anelasticity and ocean tide dissipation mainly affect CW.
- Viscoelectromagnetic coupling primarily influences FCN, FICN, and ICW.

## Abstract

In this study, we formulated a triaxial three-layered anelastic Earth rotation theory con-sidering various core mantle couplings, including the pressure and gravitational couplings acting on the inner core by the outer core and mantle, the viscoelectromagnetic couplings between the outer core and mantle, and between the outer and inner cores. With this formulation, we provided four numerical solutions for the rotational normal modes, including the Chandler Wobble (CW), Free Core Nutation (FCN), Free Inner Core Nutation (FICN), an the Inner Core Wobble (ICW). The triaxiality led to increased periods for the CW and ICW of about 0.01 and 0.35 mean solar days (d), respectively. The mantle anelasticity and ocean tide induced dissipations were mainly responsible for the CW, but contributed little to the FCN, while the viscoelectromagnetic coupling induced dissipations were mainly responsible for the FCN, FICN, and ICW. By investigating different types of couplings, we found that pressure coupling played the dominant role in prograde FICN, while viscoelectromagnetic or gravitational couplings either alone, or together gave rise to retrograde FICN. On the other hand, the ICW period varied extensively from 130 d to 21 yr under different core mantle coupling conditions.