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Document: Monographie

Determination of the geoid using heterogeneous data / Gérard Lachapelle (1975)

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Titre :	Determination of the geoid using heterogeneous data
Type de document :	Monographie
Auteurs :	Gérard Lachapelle, Auteur
Editeur :	Graz : Technische Universität Graz
Année de publication :	1975
Collection :	Mitteilungen der geodätischen Institute num. 19
Importance :	122 p.
Format :	21 x 30 cm
Note générale :	Bibliographie
Langues :	Anglais (eng)
Descripteur :	[Vedettes matières IGN] Géodésie physique [Termes IGN] anomalie de pesanteur [Termes IGN] coefficient de géopotentiel [Termes IGN] collocation par moindres carrés [Termes IGN] covariance [Termes IGN] déviation de la verticale [Termes IGN] geoïde astro-géodésique [Termes IGN] géoïde gravimétrique [Termes IGN] harmonique sphérique
Index. décimale :	30.41 Géoïde
Résumé :	(Auteur) The object of this work was to develop a method for determining the geoid over large territories using the following types of geodetic data: astrogeodetic deviations of the vertical, gravity anomalies, dynamic data in the form of geo-potential coefficients and topographic-isostatic deviations of the vertical. In Part One, the application of least squares collocation to Molodenskii's, astrogravimetric levelling is considered. Instead of solving the fundamental equation of astrogravimetric levelling by classical methods, which involves much work for extensive applications, it was solved by least squares collocation. The least squares collocation solution offers important advantages in both practical and theoretical aspects. Practically, the solution presented here requires much less data preparation than previously because the observed deviations of the vertical and gravity anomalies can be used as such, regardless of their distribution; the interpolation is made automatically as it is contained implicitly in the fundamental equation of astrogravimetric levelling in least squares collocation. Theoretically, the contribution of the deviations of the vertical together with the gravity anomalies can be studied according to their distribution and accuracy; this is because least squares collocation can be directly applied to heterogeneous data. In this respect, important results are presented in Chapter IV. The use of geopotential coefficients is considered in Chapter III and the accuracy of the current geopotential coefficients solutions is studied. The improvement of accuracy attainable when removing low geopotential coefficients is also studied. The covariances, which play a basic role in the application of least squares collocation, are dealt with in Chapter II; several covariance functions for use in areas of flat and rugged topography are presented. Comparisons are made between the accuracy estimates obtained when using these covariance functions and those obtained when using Bomford's empirical formulae for astrogeodetic levelling; results are in good agreement; two Canadian astrogeodetic profiles were used for this purpose. In Part Two, a method for estimating deviations of the vertical from a combination of topographic-isostatic deviations of the vertical with geopotential coefficients is presented. This method is especially well suited for large areas, either continental or oceanic, where no other geodetic measurements are available. It is ideally applicable in mountainous areas and along coastlines where the deviations depend much on the topography. Numerical results using topographic-isostatic deviations calculated in Canada, Switzerland and West-Germany are presented. The results of a geoid determination in Eastern Canada using these predicted deviations with the results obtained when using the corresponding observed deviations are also presented. Further possible improvements are proposed. A spherical harmonics expansion of the isostatic reduction potential, which is needed in connection with the method mentioned above, is presented; this method is rigorous within the usual spherical approximations made in physical geodesy.
Numéro de notice :	44319
Affiliation des auteurs :	non IGN
Thématique :	POSITIONNEMENT
Nature :	Monographie
Permalink :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=58196

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