Abstract The second geodetic boundary value problem plays an important role in physical geodesy, as complex mountainous terrain significantly affects its solution, making accurate computation of topographic effects essential for generating a high-precision geoid. The traditional prism model formulation suffers from singularities at computation points and does not account for the Earth’s curvature. These limitations become more pronounced when high-resolution data are employed and in regions with complex terrain, thereby degrading the accuracy of the computed results. This study adopts the reference ellipsoid as the boundary surface and applies Helmert’s second condensation method to divide the pre-condensation topography into prisms, which are then transformed into rectangular thin plates after condensation. By transforming the computation points to eliminate the influence of Earth’s curvature, an analytical formulation for evaluating the topographic effects, based on a prism-thin plate model that explicitly accounts for the Earth’s curvature is proposed. A typical mountainous region in western China is selected as the study area. Comparisons between the proposed formulation and those of the prism-thin plate model without curvature consideration, the conventional prism model, and the curvature-corrected prism model show numerical consistency. All four models reveal that the direct topographic effects on gravity are predominantly governed by near-field contributions, while the indirect effects on height anomalies and geoid undulations are characterized by cumulative influences. The proposed formulation eliminates singularities while rigorously accounting for Earth’s curvature, establishing unified and numerically stable expressions for the direct and indirect effects under Helmert’s second condensation, thereby providing a robust theoretical and computational framework for high-precision gravity field modeling and quasigeoid refinement.
Duan et al. (Thu,) studied this question.