Estimation of the gravitational potential energy of the earth based on different density models

Abstract

The estimation of the Earth’s gravitational potential energy E was obtained for different density distributions and rests on the expression E = − (Wmin + ΔW) derived from the conventional relationship for E. The first component Wmin expresses minimum amount of the work W and the second component ΔW represents a deviation from Wmin interpreted in terms of Dirichlet’s integral applied on the internal potential. Relationships between the internal potential and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error propagation rule) accuracy σE of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement between E = EGauss derived from Gaussian distribution and other E, in particular for E = EPREM based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information about density jumps is absent or incomplete.