Determination of the global and regional gravitational fields from satellite and balloon gradiometry missions

Abstract

Future satellite gradiometry missions (e. g. GOCE, STEP) and projects for low altitude freefalling probes, with gravity gradiometers on board, will be the most promising experiments for refining the Earth's gravitational field. An optimal approach is developed for solving the spatial gradiometry problems. The full magnitude Δ Γ of the disturbance of the gravity gradient vector, with respect to its normal value, is chosen as the observable. Correspondingly, a unique spatial boundary value relation (A) is derived, Δ Γ = ΔΓ N , where ΔΓ N is the truncated to the degree N spherical harmonic series with the unknown global potential coefficients C n,m . Based on (A), from satellite gradiometry missions the potential coefficients can be evaluated by the least squares technique. Besides, an explicit integral formula is derived for C n,m . Low altitude balloon missions with free falling gradiometers will allow to evaluate the regional surface gravity anomaly Δg. For solving this problem from (A) another basic relation (B) is derived by means of downward continuation of Δ γ from a spatial observation domain to its projection onto a terrain region of interest. Formula (B) represents Δg in form of a sum of a Stokes integral, depending on Δ Γ , and correction terms due to downward continuation and the Earth's nonsphericity. In addition to (B) corresponding to a point-wise approach, a mean-value relation is derived by averaging Δ Γ over observation altitudes of a free falling gradiometer.