Developing and testing the ellipsoidal gravity model manipulator ELGRAM

The commonly used representation of potential as a truncated series of spherical harmonics leads to global models that consist of set of coefficients c nm , s nm (OSU91, EGM96), that can be successively used by a spherical harmonics manipulator to compute values of the potential and its functionals (geoid undulation, gravity anomaly, deflection of the vertical) at any point of given coordinates (φ, λ, h). The approximations involved both in the computations of the coefficients, from satellite and terrestrial measurements, and in their use in the synthesis of potential functionals make desirable the development of different computational techniques. In view of the actual requirements of more and more precise potential representation it is useful to develop a manipulator working with series of ellipsoidal harmonic functions. To this aim, appropriate equations relating geoid undulation, gravity anomaly, deflections of the vertical to anomalous potential T expanded in ellipsoidal series have been deduced, and a source code for their computation have been written and tested, comparing results with 'classical' spherical synthesis. In the paper the main steps of analytical computations are shown, the structure and use of the new software is illustrated and some results of the comparisons are reported.