Abstract
A second-order hydrostatic theory is developed on the assumption that the trace of the earth's inertia tensor and its mass and mean radius are invariant under any process causing deviations from the hydrostatic state. Values are obtained for the hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field. These values are compared with those from the internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981). The agreement is seen as indicating that PREM is suitable as a reference model since it represents the spheroidal density perturbation distribution in a state of zero nonhydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities. The small discrepancy between the hydrostatic flattening and the value deduced from PREM is interpreted as suggesting that the density is underestimated at large depths and/or is slightly overestimated in shallow regions of the earth. The discrepancies between the hydrostatic and observed quantities are found to persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal formation and the present mass anomalies associated with the Late-Pleistocene deglaciation.