Mountain building and Earth rotation

Whereas the present-day true polar wander and the secular non-tidal acceleration of the Earth have usually been attributed to postglacial rebound, it has recently been suggested that non-glacially induced vertical tectonic movements taking place under non-isostatic conditions can also be effective in changing the Earth's rotation. We present a case study in which we analyse the effects of some simple uplift histories of the Himalayas and the Tibetan Plateau on the rotational axis and on the second-degree zonal harmonic of the geoid, for time-scales of up to a few million years. We first assume a permanent amount of overcompensation, which is consistent with observed geoid anomalies over the Himalayas, and then we model by means of the normal-mode techniques, the viscous relaxation in the mantle, with the elastic lithosphere supporting elastically 2 per cent of isostatic disequilibrium. In our normal-mode analysis, the Earth is divided into five layers: an effectively elastic lithosphere, a viscoelastic shallow upper mantle, transition zone and lower mantle characterized by the Maxwell rheology and an inviscid core. The readjustment of the equatorial bulge due to viscous flow in the mantle is taken into account in our studies by solving the linearized Liouville equations for the conservation of angular momentum, via the Love numbers formalism. Polar wander is sensitive to the rate of relaxation of the modes M1 and M2 due to the discontinuities between the three mantle layers, positioned at 420 and 670 kilometres depth. The rate of readjustment is sensitive to the viscosity of the transition zone whenever the lower mantle/shallow upper mantle viscosity ratio is small. The highest present-day velocity of polar wander due to Himalayan and Tibetan Plateau uplift is estimated to be 1° Myr−1 for an isoviscous mantle that has the same magnitude of the observed value, reduced to 0.1° Myr−1 for a factor 50 viscosity increase in the lower mantle. These numbers are about the same as those found from postglacial rebound that occurs on the short time-scale of a thousand years instead of the million years of our analysis, but represent upper bounds for mountain building, obtained only in the case in which a permanent deviation from isostasy of at least 2 per cent is assumed. In general, the proposed mechanism is less efficient in driving long-term rotation instabilities than deep-seated processes characterized by the same time-scale of a million years such as subduction; polar-wander velocity is extremely sensitive to the depth of the uncompensated anomalous root of the topography for the models in which full mantle relaxation is allowed.