Elliptical harmonic series and the original Stokes problem with the boundary of the reference ellipsoid

Since the earth is closer to a revolving ellipsoid than a sphere, it is very important to study directly the original model of the Stokes BVP [GRAPHICS] on the reference ellipsoid, where Sigma denotes the reference ellipsoid, gamma is the Somigliana normal gravity, and h is the outer normal direction of Sigma. This paper deals with: 1) simplification of the above BVP under preserving accuracy ro O(E(2)/b(2)) derivation or computational, formula of the elliptical harmonic series, 3) solving the BVP by the elliptical harmonic series, and 4) providing a principle for finding the elliptical harmonic model of the earth's gravity field from the spherical harmonic coefficients of Delta g. All results given in the paper have the same accuracy as the original BVP, that is, the accuracy of the BVP is theoretically preserved in each derivation step.