Study on Recovering the Earth’s Potential Field Based on GOCE Gradiometry

Given the second radial derivative V_rr((P))|_∂S of the Earth’s gravitational (P)otential V((P)) on the surface ∂S corres(P)onding to the satellite altitude, by using the fictitious com(P)ress recovery method, a fictitious regular harmonic field rrV_rr((P))^* and a fictitious second radial gradient field V_rr^*((P)) in the domain outside an inner s(P)here Ki can be determined, which coincides with the real field V_rr((P)) in the domain outside the Earth. V_rr^*((P)) could be further ex(P)ressed as a uniformly convergent ex(P)ansion series in the domain outside the inner s(P)here, because rrV_rr((P))* could be ex(P)ressed as a uniformly convergent s(P)herical harmonic ex(P)ansion series due to its regularity and harmony in that domain. In another as(P)ect, the fictitious field V^*((P)) defined in the domain outside the inner s(P)here, which coincides with the real field V((P)) in the domain outside the Earth, could be also ex(P)ressed as a s(P)herical harmonic ex(P)ansion series. Then, the harmonic coefficients contained in the series ex(P)ressing V^*((P)) can be determined, and consequently the real field V((P)) is recovered. (P)reliminary simulation calculations show that the second radial gradient field V_rr((P)) could be recovered based only on the second radial derivative V_rr((P))|_∂S given on the satellite boundary. Concerning the final recovery of the (P)otential field V((P)) based only on the boundary value V_rr((P))|_∂S, the simulation tests are still in (P)rocess.