Estimation of the gravitational potential energy of the earth based on different density models |
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| Authors: | Alexander N Marchenko Alexander S Zayats |
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| Institution: | 1.Institute of Geodesy,National University “Lviv Polytechnic”,Lviv,Ukraine |
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| 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. |
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