The response of a realistic earth to ocean tide loading

Abstract

A novel ocean tide loading model is developed which allows the earth to be self-gravitating, compressible, layered, anisotropic viscoelastic and rotating, with a solid inner core and fluid outer core. The equations of deformation of the earth are developed, following Lagrangean mechanics. The standard-linear-solid-type rheology, as well as the grain-boundary relaxation model for the dissipation mechanism within the earth are adopted in this study. The thermodynamic state of the earth is accounted for, through its absolute temperature, Gibbs free activation energy, viscosity and Q profiles. Complex load numbers h'n, k'n and l'n, are calculated up to degree 10 000. It is shown that the rotation of the earth, as well as the anisotropy in the upper mantle affect the load numbers by a few per cent. There is a weak latitude dependence of the load numbers for n ≤ 4. At fortnightly periods, viscoelastic load numbers are 1–2 per cent larger than their corresponding elastic values. Complex Green's functions are evaluated for displacements, gravity and tilt. Tests of the present model against accurately determined M2 gravity tide residuals show that the present model is very promising indeed.