The period and Q of the Chandler wobble

TLDR

The authors use Rayleigh’s principle to constrain mantle anelasticity’s frequency dependence by combining the theoretical–observed Chandler wobble period discrepancy with the observed Q. They extend the Chandler wobble period calculation to include the non‑hydrostatic equatorial bulge and fluid‑core effects on pole‑tide‑induced period lengthening. The elastic Earth model yields a 426.7‑day period, 8.5 days shorter than the 435.2‑day observed value, and the study limits mantle anelasticity’s frequency exponent α to roughly 0.04–0.19, with the bounds robust to pole‑tide variations.

Abstract

We have extended our calculation of the theoretical period of the Chandler wobble to account for the non-hydrostatic portion of the Earth's equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide. We find the theoretical period of a realistic perfectly elastic Earth with an equilibrium pole tide to be 426.7 sidereal days, which is 8.5 day shorter than the observed period of 435.2 day. Using Rayleigh's principle for a rotating Earth, we exploit this discrepancy together with the observed Chandler Q to place constraints on the frequency dependence of mantle anelasticity. If Qμ in the mantle varies with frequency σ as σα between 30 s and 14 months and if Qμ in the lower mantle is of order 225 at 30 s, we find that 0.04 ρ α ≤ 0.11; if instead Qμ in the lower mantle is of order 350 near 200 s, we find that 0.11 ≤ α ≤ 0.19. In all cases these limits arise from exceeding the 68 per cent confidence limits of ± 2.6 day in the observed period. Since slight departures from an equilibrium pole tide affect the Q much more strongly than the period we believe these limits to be robust.