Polar wander of the earth associated with the quaternary glacial cycle on a convecting mantle

Observed true polar wander (TPW) at the present-day, with the speed of ∼1° Myr^-1 towards Hudson Bay, has been generally examined based on the glacial isostatic adjustment (GIA) for the Quaternary glacial cycle. The observation is, however, affected by the present-day melting events of polar ice sheets and mountain glaciers and convective processes in the mantle. In this study, I examine TPW due to GIA and convective processes by developing the Liouville equation including these two processes, referred to as generalized Liouville equation here. The generalized Liouville equation makes it possible to evaluate the effects of convective related non-forcing inertia elements (I₁₁, I₂₂, I₃₃ and I₁₂) and forcing elements (I₁₃ and I₂₃) on the polar wander for the Quaternary ice age phase, and clearly indicates that the excess flattening of the Earth, inferred from the non-hydrostatic geoid, stabilizes the polar motion as discussed by Mitrovica et al. (2005). Also, numerical experiments for examining the effects of time-dependent convective processes on TPW indicate that reasonable convection scenarios with a time dependence in the inertia tensor of ∼10³¹ kg m² Myr^-1 (Ricard et al. 1993) insignificantly contribute to the observed present-day TPW; moreover, the predicted TPW with magnitude of convective related forcing rates, dI₁₃/dt and dI₂₃/dt, larger than ∼5 × 10³¹ kg m² Myr^-1 is significantly different from the observation. These results may provide a framework for separating the contributions of GIA and convection to the observed present-day polar wander.