SPHERICAL CAP HARMONIC EXPANSION FOR LOCAL GRAVITY-FIELD REPRESENTATION

This paper proposes an approach to local gravity field representation by spherical cap harmonic expansion that is a generalized spherical harmonic series with nonintegral degree and integral order. This approach is mathematically rigorous, and overcomes the shortcomings of planar approximation solution of Laplace's equation in planar Cartesian coordinates expressed by a Fourier series. The simple mathematical background of spherical cap harmonic analysis and its application in solving the geodetic boundary value problem for local gravity field determination are described in detail. As a numerical example, the spherical cap harmonic coefficient model of gravity potential has been computed using the surface free-air gravity anomaly data over the region of China, and geoidal undulations derived by this model and Stokes formula are compared with results from GPS leveling in some areas of China.