Residual deformation of real earth models with application to the Chandler Wobble

Abstract

By using Volterra's relation, it is shown that a tangential dislocation in a gravitating radially inhomogeneous sphere can be characterized by discontinuities in the stress and displacement fields across the source surface r=r₀. This representation of the source facilitates the numerical evaluation of the displacement field. It is found that at the free surface of the Earth the six simultaneous linear differential equations governing the spheroidal field associated with the Legendre polynomial of the first degree (l=1) degenerate into five. The two equations corresponding to the toroidal field for l=1 degenerate into one. Therefore, when dealing with the case l=1, one must in-corporate additional conditions, namely, that the angular momentum of the sphere about its centre is zero and that the centre of mass of the sphere is not displaced. The changes in the inertia tensor due to an earthquake of arbitrary depth and orientation are calculated with the assumption that the Adams-Williamson condition holds at the core. No difference in the numerical results are obtained if the Adams-Williamson conditions does not hold. Comparison with homogeneous, non-gravitating Earth model shows that, in general, real Earth models render a smaller value for the changes in the inertia tensor. It appears from our results that earthquakes are insufficient to maintain the Chandler wobble.