On estimating period and quality factor of Chandler wobble

While numerous studies have been dedicated to the determination of Chandler wobble parameters, namely its period T_CW and quality factor Q_CW, most of their results lack self-consistency. We proposed a rigorous approach to achieve self-consistent estimates of T_CW and Q_CW using only geodetic excitations (χ^obs) derived from observed polar motion (PM) data in 2023 (denoted as CCRLL). However, a study published in 2025 (denoted as YF) criticized CCRLL's approach and argued that either T_CW or Q_CW cannot be optimized without access to geophysical excitations (χ^geo), relying on their misleading numerical simulations using real-valued PM transfer functions. Our present study has established theoretical relations between (T_CW, Q_CW), degree-2 Love numbers and complex-valued transfer functions while proving that traditional Earth's rotation theories, employing real-valued transfer functions, are incapable of providing self-consistent estimates of T_CW and Q_CW. This study also demonstrates that either χ^obs or χ^geo can be used to invert for T_CW and Q_CW, but χ^geo must be recalculated using the complex transfer functions derived by this study and χ^obs-based estimates are more reliable. Thus, CCRLL's approach and results are validated while YF's arguments are refuted. Further, some updates and corrections to CCRLL's Love numbers and transfer functions are also presented.