A Meissl-modified Vanicek and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations

Abstract

A deterministic modification of Stokes's integration kernel is presented which reduces the truncation error when regional gravity data are used in conjunction with a global geopotential model to compute a gravimetric geoid. The modification makes use of a combination of two existing modifications from Vanicek and Kleusberg and Meissl. The former modification applies a root mean square minimisation to the upper bound of the truncation error, whilst the latter causes the Fourier series expansion of the truncation error to coverage to zero more rapidly by setting the kernel to zero at the truncation radius. Green's second identity is used to demonstrate that the truncation error converges to zero faster when a Meissl-type modification is made to the Vanicek and Kleusberg kernel. A special case of this modification is proposed by choosing the degree of modification and integration cap-size such that the Vanicek and Kleusberg kernel passes through zero at the truncation radius.