Generalized geoidal estimators for deterministic modifications of spherical Stokes’ function - ŠPRLÁK, Michal (Contributions to Geophysics and Geodesy, 2010)
Stokes’ integral, representing a surface integral from the product of terrestrialgravity data and spherical Stokes’ function, is the theoretical basis for the modelling of thelocal geoid. For the practical determination of the local geoid, due to restricted knowledgeand availability of terrestrial gravity data, this has to be combined with the global gravitymodel. In addition, the maximum degree and order of spherical harmonic coefficients inthe global gravity model is finite. Therefore, modifications of spherical Stokes’ functionare used to obtain faster convergence of the spherical harmonic expansion. Decompositionof Stokes’ integral and modifications of Stokes’ function have been studied by many geodesists.In this paper, the proposed deterministic modifications of spherical Stokes’ functionare generalized. Moreover, generalized geoidal estimators, when the Stokes’ integral isdecomposed in to spectral and frequency domains, are introduced. Higher derivativesof spherical Stokes’ function and their numerical stability are discussed. Filtering andconvergence properties for deterministic modifications of the spherical Stokes’ function inthe form of a remainder of the Taylor polynomial are studied as well.