Hydrostatic theory of the Earth and its mechanical implications

Abstract

A second-order hydrostatic theory is developed on the assumption that the trace of the Earth's inertia tensor, its mass and mean radius are invariant under any process causing deviations from the hydrostatic state. The hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field are obtained as ϵ −1 = 299.638, J 2 = 1072.618 × 10 −6 and J 4 = −2.992 × 10 −6, respectively. The internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981) yields ϵ −1 = 299.627, J 2 = 1072.701 × 10 −6 and J 4 = −2.992 × 10 −6. The agreement between these and the hydrostatic values indicate that PREM is suitable as a reference model as it represents the spheroidal density distribution in a state of zero non-hydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities. The small discrepancy between the hydrostatic flattening and the value deduced from PREM suggests that the density is underestimated at large depths and/or it is slightly overestimated in shallow regions of the Earth. The discrepancies between the hydrostatic and observed quantities persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal deformation and the present mass anomalies associated with the Late-Pleistocene deglaciation. These ‘corrected’ discrepancies point to a triaxial non-hydrostatic figure which cannot be explained by the delayed response of the Earth to tidal deceleration.