Direct Harmonic Analysis for the Ellipsoidal Topographic Potential with Global and Local Validation

Forward gravity field modelling requires high accurate determination of the topographic potential on the surface of the Earth’s ellipsoid. Since the topography is recently known with high resolution, the determination of the harmonic analysis of the topographic ellipsoidal potential should be carried-out to an ultra-high degree. The paper presents a direct technique to determine the harmonic analysis of the ellipsoidal potential to an ultra-high degree. The detailed derivation of the developed expressions is given. The proposed technique can be used to compute the harmonic analysis of the topographic potential of the whole Earth or for a local/regional window. This has a great advantage when using the proposed technique for local/regional geoid determination within the window remove–restore technique (Abd-Elmotaal and Kühtreiber, Phys Chem Earth Part A 24(1):53–59, 1999, J Geod 77(1–2):77–85, 2003). The developed technique has been compared to existing global solutions for the ellipsoidal topographic potential and it shows quite good agreement. Local tests for the developed technique proved that it works very well.