Truncation Errors in the Stokes and Vening Meinesz Formulae for Different Order Spherical Harmonic Gravity Terms

Summary A detailed analysis of truncation errors in the Stokes formula integration, using Molodenskii's method, shows the mode of dependence of the errors on the spherical harmonic components of Δg of different order. The results indicate that significant reduction in the truncation errors can be achieved by adopting a reference model for normal gravity of higher order than that based on the International Ellipsoid. Particularly, the use of a seventh order reference model combined with truncation at the first zero crossing of the Stokes kernel function appears very promising. The treatment of truncation errors for deflection of the vertical as given by Molodenskii et al. and Hirvonen & Moritz yields results for deflections as derivatives of geoidal heights explicitly obtained from Stokes formula. These errors can be reduced by the same techniques as suggested for the Stokes integration. The truncation error behaviour of the Vening Meinesz formulae is shown to be different. An adaptation of Molodenskii's approach using an expansion of the truncated deflection of the vertical kernel function in terms of associated Legendre polynomials of first order provides a means for spherical harmonic analysis of the truncation errors in the Vening Meinesz formulae.