Polar wander caused by the Quaternary glacial cycles and fluid Love number

Perturbations of the Earth’s rotation caused by the Quaternary glacial cycles provide an important constraint on the viscosity of the deep mantle because they represent a long-wavelength response of the Earth to surface load redistribution. The predicted present-day polar wander speed (PWS) is, however, sensitive to both the lower mantle viscosity (ηlm), the density jump at 670 km depth, and the lithospheric thickness and viscosity (e.g., Sabadini and Peltier, Geophys. J. R. Astron. Soc. 66 (1981) 553–578; Yuen et al., J. Geophys. Res. 87 (1982) 10745–10762; Peltier and Wu, Geophys. Res. Lett. 10 (1983) 181–184; Wu and Peltier, Geophys, J. R. Astron. Soc. 76 (1984) 753–791; Peltier, J. Geophys. Res. 89 (1984) 11303–11316; Vermeersen et al., J. Geophys. Res. 102 (1997) 27689–27702; Mitrovica and Milne, J. Geophys. Res. 103 (1998) 985–1005; Johnston and Lambeck, Geophys. J. Int. 136 (1999) 537–558; Nakada, Geophys. J. Int. 143 (2000) 230–238). For earth models with ηlm<5×1021 Pa s and an elastic lithosphere, the present-day PWS is very sensitive to the M1 mode (buoyancy mode) related to the density jump at 670 km depth [Mitrovica and Milne, J. Geophys. Res. 103 (1998) 985–1005]. The contribution of the M1 mode, however, is less significant for earth models with a viscoelastic lithosphere [Nakada, Geophys. J. Int. 143 (2000) 230–238]. This is due to the fact that this contribution depends on the relative strength of the M1 mode, Δk2T(M1)/kfT, where Δk2T(M1) is the magnitude of tidal Love number (k2T) of the M1 mode and kfT is the value of k2T in the fluid limit (fluid Love number). The magnitude of kfT for earth models with a viscoelastic lithosphere is larger than that for an elastic lithosphere, and it is smaller for a thicker elastic lithosphere than for a thinner one. Thus, for earth models with a viscoelastic lithosphere, the PWS is mainly sensitive to the lower mantle viscosity regardless of the behavior of the 670 km density discontinuity. This relation also explains why the predicted PWS increases with increasing thickness of an elastic lithosphere. That is, since the value of Δk2T(M1)/kfT with a thicker elastic lithosphere is larger than that with a thinner elastic lithosphere, the M1 mode will have a higher contribution in the case of a thicker elastic lithosphere.