Current Estimation of the Earth’s Mechanical and Geometrical Parameters

Abstract

The Earth's mechanical and geometrical parameters were estimated from the simultaneous adjustment of the 2nd-degree harmonic coefficients of six gravity field models and seven values of the dynamical ellipticity H D all reduced to the common MHB2000 precession constant at epoch J2000. The transformation of 2nd-degree harmonic coefficients in the case of a finite commutative rotation was developed to avoid uncertainty in the deviatoric part of inertia tensor. This transformation and the exact solution of eigenvalueeigenvector problem are applied to determine (a) the static components and accuracy of the Earth's tensor of inertia at epoch 2000 and (b) the time-dependent constituents of the inertia tensor. Special attention was given to the computation of temporally varying components of the Earth's inertia tensor, which are based on the time series of 2nd-degree coefficients through GRACE observations. A remarkable stability in time of the position of the axis A of inertia as the parameter of the Earth's triaxiality is discussed.

The Earth’s Global Density Distribution and Gravitational Potential Energy

“…Thus, the global density distribution and accuracy at different depths were based on the value δ m = (5.5145±0.0026) g/cm 3 , the flattening f, and the principal moments of inertia A, B, and C from Table 1. The principal moments of inertia (given here in the zero frequency tide system) are results from the adjustment (Marchenko, 2007) of the 2nd-degree harmonic coefficients of 6 gravity field models and 7 values H D of the dynamical ellipticity all transformed to the common value of precession constant at epoch J2000. The reference radial density profile δ(ρ) R in Eq.…”

“…The Earth's mass and principal moments of inertia represent initial information for the unique solution of the restricted Cartesian moments problem providing in this way the density δ(ρ, ϑ, λ) and the potential energy E. The principal moments of inertia given in Marchenko (2007) were used for the computation of the 3D global density δ(ρ, ϑ, λ). It should be pointed out, that accuracy of the global density and potential energy was derived especially to restrict the possible solution domain in such a way that a reasonable solution may be selected either from 3D-spatial or radial density inside the ellipsoidal or spherical planet.…”

Geodynamics

“…and H D ([24], [22]) and used for the computation of the density δ. It has to be pointed out, that accuracy of this global density should be derived especially from error propagation to restrict the possible solution domain in such a way that a reasonable solution may be selected either from spatial or radial density.…”

“…the corresponding Cartesian moments , , (22) This radial density is also treated within the ellipsoid of revolution if we use according to Moritz [27] , ,…”

“…Thus, the global density distribution and accuracy at different depths were based on the flattening f, the principal moments of inertia A, B, Геодинаміка 1(7)/2008 and C from Table 1, and the value m δ = (5.51483±0.0026) g/cm 3 . The principal moments of inertia (given here in the zero frequency tide system) are results from the adjustment [22] of the 2nd-degree harmonic coefficients of 6 gravity field models (EGM96, GGM01S, GGM02C, EIGEN-CHAMP03S, EIGEN-GRACE02S, EIGEN-GL04S1) and 7 values H D of the dynamical ellipticity all transformed to the common value of precession constant at epoch J2000. Table 1.…”