The dynamical equations of polar wander and the global characteristics of the lithosphere as extracted from rotational data

The initial value problem describing the linear responses of the spin axis of a layered viscoelastic planet from surface loading is studied by means of Laplace transform techniques. A complete solution of polar motion requires the usage of two classes of eigenspectra: one arising from viscoelastic relaxation of the mantle due to surface forcing, the other involving the gradual readjustment of the spin axis as a consequence of mantle viscoelasticity. Our analytical 4-layer model comprising an elastic lithosphere, a two-layer, adiabatically stratified, viscoelastic mantle and an inviscid core has been incorporated into this formalism in which rotational deformation and isostatic relaxation are taken into account for all times. From employing both sets of rotational data, polar variations from the 70 years of data from the International Latitude Service (I.L.S.) and the non-tidal deceleration of the length of the day (l.o.d.) an estimate of the globally averaged lithosphere of between 130 and 200 km is obtained from the long wavelength flexural mode due to the degree-two harmonic. This range of values may have strong implications on the mode of continental evolution.