Comparison of Spectral Combination of Solutions to Vertical and Horizontal Spherical and Spheroidal Boundary-Value Problems: A Theoretical Study
摘要
This study investigates the spectral weighting and combination of solutions to vertical and horizontal spherical and spheroidal boundary-value problems (BVPs) for downward continuation of satellite gravitational field observations. We derive the integral kernels required for transforming vertical and horizontal components of the disturbing gravitational vector into the radial derivative of disturbing gravitational potential in the spheroidal approximation. The methods are tested in a closed-loop numerical experiment over Greenland using synthetic data generated from EGM2008 and contaminated with the Gaussian noise. The results show that the vertical component of the disturbing gravitational vector provides the most accurate input for downward continuation in both geometries. The spherical vertical-only estimator yields the best fit for the disturbing potential and its radial derivative. However, normalized standard deviation (NSTD) analysis reveals that the spheroidal approximation results in consistently smaller relative errors for the radial derivative, indicating a modest but systematic benefit when modelling quantities with strong dependence on Earth’s ellipticity.