Geoid determination through ellipsoidal Stokes boundary-value problem

Martinec and Grafarend (1997) have shown how the construction of Green's fu nction in the Stokes boundary-value problem with gravity data distributed o n an ellipsoid of revolution is approached in the O(e(0)(2))-approximation. They have also expressed the ellipsoidalStokes function describing the eff ect of ellipticity of the boundary as a finite sum of elementary functions. We present an effective method of avoiding the singularity of spherical an d the ellipsoidal Stokes functions, and also an analytical expression for t he ellipsoidal Stokes integral around the computational point suitable for numerical solution. We give the numerical results of solving the ellipsoida l Stokes boundary-value problem and their difference with respect to the sp herical Stoke boundary-value problem.