Earth's rotation, density discontinuity and mantle viscosity

第四纪冰期旋回引起的地球自转扰动是地球对地表负荷再分配的长波长响应，对深部地幔的粘度具有重要的制约作用。然而，预测的现今极移速度（PWS）对下地幔粘度（η_<lm>）、670 km深度的密度跃变以及岩石圈厚度和粘度都很敏感。特别是在η &lt;<lm>5 × 10 ~ 4 <21>Pa·s的弹性岩石圈地球模型中，现今PWS对与670 km深度密度跃变有关的Ml模（浮力模）非常敏感。然而，M1模式的贡献是不太重要的地球模型与粘弹性岩石圈。这是因为它对PWS的贡献取决于M1模的相对强度Δ k_2 ^T（M1）/k_f^T，其中Δk_2^T（M1）是M1模的潮汐勒夫数（k_2^T）的大小，k_f^T是k_2^T在流体极限的值粘弹性岩石圈地球模型的k _f^T值明显大于弹性岩石圈地球模型的k _f^T值，弹性岩石圈厚度越大，弹性岩石圈的弹性模量越小。对于具有粘弹性岩石圈的地球模型，无论670 km密度不连续的响应行为如何，PSW主要对下地幔粘度敏感。这种关系也解释了为什么预测的PWS随弹性岩石圈厚度的增加而增加。也就是说，弹性岩石圈较厚时的Δ k_2 ^T（M1）/k_f^T值大于弹性岩石圈较薄时的Δ k_2 ^T（M1）/k_f^T值，表明弹性岩石圈较厚时M1模的贡献相对较大。

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.