Gia-related rotational variations for the earth with low-viscosity D" layer

We examine the rotational variations due to the glacial isostatic adjustment (GIA) process for the Earth with a low-viscosity D" layer of 300 km thickness. The rate of change of degree-two harmonics of the Earth's geopotential, J̇₂, proportional to rate of change of the rotation, is not so sensitive to the D" layer with viscosities smaller than 10²⁰ Pa s, but the polar wander rate is significantly sensitive to its low viscosity. The difference is attributed to the physics of Liouville equation describing the rotational variations in the postglacial phase. The J̇₂ only depends on viscous relaxation of inertia elements for the surface mass redistribution in the glacial and deglacial phases (convolution for load Love number), referred to as 'load term' here. On the other hand, the polar wander rate depends on the load term and also rotational potential perturbations for changing polar motion (convolution for tidal Love number), referred to as 'tidal term' here. It is crucially important to note that the tidal term is excited even in the postglacial phase until the relaxation completes. These two terms respond to the GIA process by different sensitivities to the lower-mantle viscosity above the D" layer (η_lm) and the viscosity of the D" layer (ηD"). In fact, the ηlm-sensitivity of the polar wander rate is significantly different in the load and tidal terms, and that for the load term is identical to that for the J̇₂ as expected. Although the η_lm-sensitivity of the tidal term is essentially independent of the low viscosity of D" layer, there is a significant difference in degree of η_lm-sensitivity in adopted viscosity models with no low-viscosity D" layer and with low-viscosity D" layer of (1-10) × 10¹⁸ Pa s. The difference is attributed to the ηD" -sensitivities of two fundamental relaxation modes due to the density jumps at the surface and the core-mantle boundary.