Ellipsoidal spectral properties of the Earth’s gravitational potential and its first and second derivatives

The spectral analysis of the Earth’s gravitational potential, its first and second derivatives is performed in spherical/ellipsoidal harmonics relative to the International Reference Sphere/International Reference Ellipsoid. The highlights of the diagrammatic approach are: (1) Up- and downward continuation of incremental gravity gradients, (2) Downward continuation of incremental gravity gradients (four tensor-valued harmonic functions) to the incremental gravity potential on the International Reference Figure, (3) Direct conversion of external incremental gravity gradients to geoidal undulation by means of the spherical/ellipsoidal Bruns Formula. The International Reference Ellipsoid was chosen as an equipotential surface in the Somigliana-Pizzetti reference potential field.