Formulation of the boundary-value problem for geoid determination with a higher-degree reference field

In this paper we formulate the boundary-value problem for the determination of the gravimetric geoid considering a satellite gravitational model as a reference. We show that the long-wavelength part of the gravitational field generated by topographical masses must be added to the satellite model in order to prescribe a reference gravitational potential for a partly internal and partly external problem for geoid determination. We choose a reference potential that does not depend on the way topographical masses are compensated or condensed, but only on the satellite reference model and on the difference of gravitational potentials induced by topographical masses in the spaces outside the Earth and below the geoid. The latter contribution to the reference potential is expressed in the form of an ellipsoidal harmonic series, and the expansion coefficients are tabulated numerically up to degree 20.