Abstract
Generalized geoidal estimators for deterministic modifications of spherical Stokes' function
Stokes' integral, representing a surface integral from the product of terrestrial gravity data and spherical Stokes' function, is the theoretical basis for the modelling of the local geoid. For the practical determination of the local geoid, due to restricted knowledge and availability of terrestrial gravity data, this has to be combined with the global gravity model. In addition, the maximum degree and order of spherical harmonic coefficients in the global gravity model is finite. Therefore, modifications of spherical Stokes' function are used to obtain faster convergence of the spherical harmonic expansion. Decomposition of Stokes' integral and modifications of Stokes' function have been studied by many geodesists. In this paper, the proposed deterministic modifications of spherical Stokes' function are generalized. Moreover, generalized geoidal estimators, when the Stokes' integral is decomposed in to spectral and frequency domains, are introduced. Higher derivatives of spherical Stokes' function and their numerical stability are discussed. Filtering and convergence properties for deterministic modifications of the spherical Stokes' function in the form of a remainder of the Taylor polynomial are studied as well.