On the convergence of spherical harmonic expansion of topographic and atmospheric biases in gradiometry - ESHAGH, Mehdi (Contributions to Geophysics and Geodesy, 2009)
The gravity gradiometric data are aﬀected by the topographic and atmospheric masses. In order to fulﬁll Laplace-Poisson’s equation and to simplify the downward continuation process, these eﬀects should be removed from the data. However, if the analytical downward continuation is considered, the gravity gradients can be continued downward disregarding such eﬀects but the result will be biased. The topographic and atmospheric biases can be expressed in terms of spherical harmonics and studying these biases gives some ideas about analytical downward continuation of these quantities to sea level. In formulation of harmonic coeﬃcients of the topographic and atmospheric biases, a truncated binomial expansion of topographic height is used. In this paper, we show that the harmonics are convergent to the third term of this binomial expansion. The harmonics of the biases on Vzz are convergent to the ﬁrst term and they are convergent in Vxy for all the terms. The harmonics of the other components of the gravity gradient tensor are convergent to the second terms, while the third terms are only asymptotically convergent. This means that in terrestrial and airborne gradiometry the biases should be computed just to the second order term, while in satellite gravity gradiometry, e.g. GOCE, the third term can also be considered.