Secular rotational motions and the mechanical structure of a dynamical viscoelastic Earth

We give a survey of the analytical methods for computing the linear responses of the rotational axis of a layered viscoelastic Earth to surface loading. The two classes of eigenspectra involving isostatic relaxation of the mantle and readjustment of the spin axis are emphasized as being essential for a uniformly valid description of polar wander. The rotational responses due to the application of an equilibrium phase or a chemically layered boundary condition at the 670 km discontinuity are studied. The displacement fields associated with rotational deformation are affected to a much greater extent by the amount of chemical enrichment than are the eigenfunctions associated with isostatic relaxation. The present polar motion data from International Latitude Service (I.L.S.) can be fit equally well by a pure chemical or an equilibrium phase boundary with a 9% change in density across the interface. On the other hand, responses from models with a smaller amount of chemical stratification, <7%, are not compatible with the data. The secular variation of the Earth's gravitational harmonic J₂ is insensitive to the chemical nature of the 670 km discontinuity. From the rotational data it is not possible to rule out the existence of a high viscosity region with values of O(10²³)P at the bottom 500 km of the mantle, although a solution with a relatively uniform viscosity profile, O(10²²P), still can be found. Inferences of the globally averaged thickness of the elastic lithosphere from rotational data are not affected too much by the particular density stratification used for the lithosphere and upper mantle. They lie in the range between 120 and 170 km.