Generalized geoidal estimators for deterministic modifications of spherical Stokes’ function

Abstract

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.