Precise geoid computation using Stokes-Helmert's scheme and strict integrals of topographic effects

Abstract

The high-precision local geoid model was computed based on the improved Stokes-Helmert′s boundary value problem and strict integrals of topographic effects. This proposed method involves three steps. First, the mathematical form of Stokes-Helmert′s boundary value problem was derived, and strict computational formulas regarding topographic effects were provided to overcome the disadvantage of planar approximations. Second, a gravimetric geoid model was constructed using the proposed Stokes-Helmert′s scheme with a heterogeneous data set. Third, a least squares adjustment method combined with a multi-surface function model was employed to remove the bias between the gravimetric geoid model and the GNSS/leveling data and to refine the final local geoid model. The accuracy of the final geoid model was evaluated using independent GNSS/leveling data. Numerical results show that an external precision of 1.45 cm is achievable. Keywords: Geoid computation, Stokes-Helmert's method, Surface integration, Heterogeneous heights