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Truncation error formulas for the geoidal height and the deflection of the vertical

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Bulletin Géodésique (1946-1975)

Abstract

A general formula giving Molodenskii coefficientsQ n of the truncation errors for the geoidal height is introduced in this paper. A relation betweenQ n andq n, Cook’s truncation function, is also obtained. Cook (1951) has treated the truncation errors for the deflection of the vertical in the Vening Meinesz integration. Molodenskii et al. (1962) have also derived the truncation error formulas for the deflection of the vertical. It is proved in this paper that these two formulas are equivalent.

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References

  1. A.H. COOK: A Note on the Errors involved in the Calculation of Elevations of the Geoid. Proc. R. Soc. A 208, 133, 1951.

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  2. L. de WITTE: Truncation Errors in the Stokes and Vening Meinesz Formulae for Differnet Order Spherical Harmonic Gravity Terms. Geophys. J.R. astr. Soc. 12, 449, 1967.

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  3. W.A. HEISKANEN & H. MORITZ: Physical Geodesy. Freeman, 1967.

  4. R. A. HIRVONEN & H. MORITZ: Practical Computation of Gravity at High Altitudes. Inst. Geod. Phot. Cart., Ohio States Univ., Rep. 27. 1963.

  5. R.S. MATHER: The Australian Geodetic Datum in Earth Space. Unisurv. Rep. 19, 1970.

  6. M. S. MOLODENSKII, V. F. EREMEEV & M.I. YURKINA: Methods for Study of the External Gravitational Field and Figure of the Earth. Translated from the Russian by the Israel Progr. for Sc. Transl. Jurusalem 1962.

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Hagiwara, Y. Truncation error formulas for the geoidal height and the deflection of the vertical. Bull. Geodesique 106, 453–466 (1972). https://doi.org/10.1007/BF02522052

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  • DOI: https://doi.org/10.1007/BF02522052

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