Earth's rotation, density discontinuity and mantle viscosity

第四纪冰川旋回引起的地球自转扰动将对深部地幔的粘性产生重要的制约作用，因为它们是地球对地表负荷重分布的长波响应。然而，预测的现今极地漂移速度对下地幔粘度(η&lt；lm&gt；)、670公里深度的密度跳跃以及岩石圈的厚度和粘度都很敏感。特别是，在具有η_&lt；lm&gt；&lt；5x10；&lt；21&gt；PaS和弹性岩石圈的地球模型中，现今的PWS对与670公里深度的密度跃变相关的ML模(浮力模)非常敏感。然而，对于具有粘弹性岩石圈的地球模型，M1模式的贡献就不那么显著了。这是因为它对PwS的贡献取决于M1模的相对强度Δk_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是流体极限中k_2^T的值(流体勒夫数)。粘弹性岩石圈地球模型的k_f^T值明显大于弹性岩石圈模型的k_f^T值，而较厚的弹性岩石圈模型的kf^T值明显小于较薄的弹性岩石圈模型。然后，对于具有粘弹性岩石圈的地球模型，PSW主要对下地幔粘性敏感，而与670公里密度不连续的响应行为无关。这个关系也解释了为什么预测的PWS随着弹性岩石圈厚度的增加而增加。也就是说，弹性岩石圈较厚的Δk_2^T(M1)/k_f^T的值大于弹性岩石圈较薄的岩石圈，表明弹性岩石圈较厚的岩石圈对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.