The Earth's Global Density Distribution and Gravitational Potential Energy

The Earth's global density model given by the restricted solution of the 3D Cartesian moments problem inside the ellipsoid of revolution was adopted to preserve in this way the external gravitational potential up to second degree/order, the dynamical ellipticity, the geometrical flattening, and six basic radial jumps of density as sampled for the PREM model. Comparison of lateral density anomalies with estimated accuracy of density leads to the same order values in uncertainties and density heterogeneities. Hence, four radial density models were chosen for the computation of the Earth's gravitational potential energy E: Legendre-Laplace, Roche, Bullard, and Gauss models. The estimation of E according to these continuous density models leads to the inequality with two limits. The upper limit EH agrees with the homogeneous distribution. The minimum amount E(Gauss) corresponds to the Gauss' radial density. All E-estimates give a perfect agreement between E(Gauss), the value E derived from the piecewise Roche's density with 7 basic shells, and the values E based on the four simplest models separated additionally into core and mantle only.