The rotational stability of a convecting earth: assessing inferences of rapid TPW in the late cretaceous

We outline a linearized rotational stability theory for predicting the time dependence of true polar wander (TPW) on a Maxwell viscoelastic body in response to mantle convective loading. The new theory is based on recent advances in ice age rotation theory. A comparison between predictions based on the new theory and analytic expressions for equilibrium (infinite-time) TPW on planetary models with elastic lithospheres demonstrates that the linearized theory can, in the case of loading at mid-latitudes, predict TPW of over 20 degrees to better than 5 per cent accuracy. We present predictions of TPW for loading with periodic and net ramp-up time histories. Moreover, we compare the time dependence of TPW under assumptions consistent with the canonical equilibrium stability theory adopted in most previous analyses of convection-induced TPW, and a stability theory that includes two effects that have not been considered in previous geophysical analyses: (1) the so-called 'remnant rotational bulge' associated with the imperfect reorientation of the rotational bulge due to the presence of an elastic lithosphere; and (2) a stable (over the timescale of the forcing) excess ellipticity. As a first application of the new theory, we consider recent inferences of rapid (order 1 Myr) TPW motion of amplitude 10 degrees-20 degrees during the Late Cretaceous. We conclude that excursions of this amplitude and timescale are physically implausible.