Earth's rotation, density discontinuity and mantle viscosity

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Perturbations of the Earth's rotation caused by the Quaternary glacial cycles will provide an important constraint on the viscosity of the deep mantle because they are 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 (η_<lm>), the density jump at 670 km depth, and the lithospheric thickness and viscosity. Particularly, in earth models with η_<lm> <5x10^<21> Pa s and an elastic lithosphere, the present-day PWS is very sensitive to the Ml mode (buoyancy mode) related to the density jump at 670 km depth. The contribution of the M1 mode is, however, less significant for earth models with a viscoelastic lithosphere. This is due to the fact that its contribution to the PWS depends on the relative strength of the M1 mode, Δk_2^T(M1)/k_f^T, where Δk_2^T(M1) is the magnitude of tidal Love number (k_2^T) of the M1 mode and k_f^T is the value of k_2^T in the fluid limit (fluid Love number).The magnitude of k _f^T for earth models with a viscoelastic lithosphere is significantly larger than that for an elastic lithosphere, and that for a thicker elastic lithosphere is smaller than that for a thinner one. Then, for earth models with a viscoelastic lithosphere, the PSW is mainly sensitive to the lower mantle viscosity only regardless of the behavior of the response of the 670 km density discontinuity. This relation also explains why the predicted PWS increases with increasing thickness of an elastic lithosphere. That is, the value of Δk_2^T(M1)/k_f^T with a thicker elastic lithosphere is larger than that with a thinner elastic lithosphere, indicating a relatively higher contribution of the Ml mode for a thicker elastic lithosphere.