Alternative validation method of satellite gradiom

Authors: Michal Šprlák Eliška Hamáčková Pavel Novák

Publish Date: 2015/04/24

Volume: 89, Issue: 8, Pages: 757-773

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Abstract

Integral transforms of the disturbing gravitational potential derived from satellite altimetry onto satellite gradiometric data are formulated investigated and applied in this article First corresponding differential operators that relate the disturbing gravitational potential to the six components of the disturbing gradiometric tensor in the spherical local northoriented frame are applied to the spherical AbelPoisson integral equation This yields six new integral equations for which respective kernel functions are given in both spectral and spatial forms Second truncation error formulas for each of the integral transforms are provided in the spectral form Also expressions for the corresponding truncation error coefficients are derived Third practical estimators for evaluation of the disturbing gravitational gradients are formulated and their correctness and expected accuracy are investigated Finally the practical estimators are applied for validation of a sample of the gradiometric data provided by the GOCE satellite mission Obtained results demonstrate applicability of the new apparatus as an alternative validation method of the satellite gravitational gradientsMichal Šprlák and Pavel Novák were supported by the project no GA1508045S of the Czech Science Foundation Eliška Hamáčková was supported by the project SGS2013024 The authors thank P L Woodworth for providing the mean dynamic topography models Thoughtful and constructive comments of three anonymous reviewers are gratefully acknowledged Thanks are also extended to the EditorinChief R Klees and the responsible editor C Jekeli for handling our manuscriptProposition 8 follows from Eqs 40–42 and from the spectral form of the modified isotropic kernel Kbullet given by Eq 37 Note that Eq 52 defines the socalled Paul coefficients which can be evaluated by recurrence formulas see eg Paul 1973To prove Proposition 9 we start with the modified truncation error coefficient Q nbullet First the spatial form of the modified isotropic kernel Kbullet see Eq 37 is inserted into Eq 40 Second we make use of the analytical solution for the resulting integral given by Pavlis 1991 Eq A 29a–b and Eq 53 immediately follow The modified truncation error coefficients Q nbullet t and Q nbullet tt are the first and second derivatives of Q nbullet with respect to the variable t see Eqs 41 42 Performing the differentiations of Eq 53 we get the recurrence formulas of Eqs 54 and 55

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