Angular momentum perturbation, polar excitation and axialnear-symmetry

Abstract

The mechanism of the excitation of the Earth’s rotation instability in the absence of external torques is explored in more detail. The conventional perturbation scheme used to simplify the Liouville equation has oversimplified the excitation physics. The scheme is improved in the following ways. (1) A reference frame is chosen which is unique and physically located in the Earth, and which is also consistent with observations. (2) First-order perturbation is introduced only into rotation, whilst change in the moment of inertia is physically linked to motion through relative angular momentum, rather than being treated as a mathematical perturbation. (3) The Earth’s axial near-symmetry and slightly triaxial nature are included. Polar excitation is due to mass redistribution within part of the Earth and appears as a relative angular momentum that involves both motion and rotation, whilst the rest of the Earth is only in rotation. A relative angular momentum consists of two terms, that due to motion and that due to the products of inertia induced by the motion under the gyroscopic effect from the rotation. Wobble of the rotation axis can be excited by motion alone, but secular polar shift is always accompanied by a wobble and can only be excited by the products of inertia. The residual products of inertia induced by motion and the products of inertia arising from axial near-symmetry constitute continued polar excitation. During polar excitation, the instantaneous figure axis around which the rotation axis revolves is no longer the principal axis, and the principal axis is no longer symmetrical and its new location is to be determined. This new scheme facilitates a simpler and physically more justified determination of the angular momenta of different parts of the Earth such as the atmosphere, oceans, earthquakes, tectonic movements in the lithosphere and asthenosphere, the outer core, and even meteorite impact that involve motion. The Earth’s total angular momentum can then be determined by summing up these relative angular momenta together with that of the rest of the Earth that is only in rotation. Recent observations such as true polar wandering in geological history, the excitation of the present secular polar shift by the viscoplastic response to Pleistocene deglaciation, the excitation of the Chandler wobble by earthquakes, and meteorite impact are reviewed under this improved perturbation scheme.