Dynamical influences on the moment of inertia tensor from lateral viscosity variations inferred from seismic tomographic models

We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements δI_xz and δI_yz in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered ( < 300), δI_xz and δI_yz can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of δI_xz and δI_yz. This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the δI_xz and δI_yz terms are directly responsible for exciting rotational movements.