Free decay and excitation of the chandler wobble: self-consistent estimates of the period and quality factor

The period TCW and quality factor QCW of the Chandler wobble (CW) as well as polar motion (PM) transfer functions are all determined by the Earth’s layered structure, mass distribution, elasticity, rheology and energy dissipation, via the Earth’s dynamic figure parameters and complex degree-2 Love numbers. However, most previous studies used geophysical excitations derived from real-valued PM transfer functions to invert for TCW and QCW, thus leading to results that are not self-consistent. By separating the observed PM into the freely decaying CW and the excited PM, a traverse-based method is proposed to search values of TCW and QCW that can fit both sides simultaneously, yielding the self-consistent estimates of TCW = 430.4 mean solar days and QCW = 130. This implies the degree-2 tidal Love number k = 0.35011 − 0.00226i and load Love number k' =  − 0.36090 + 0.00233i, and the PM transfer functions TNL = 1.80001 − 0.00692i (non-loading) and TL = 1.15040 − 0.00023i (loading) valid at the Chandler period.