Abstract
In the evaluation of the geoid done according to the Stokes-Helmert method, the following topographical effects have to be computed: the direct topographical effect, the primary indirect topographical effect and the secondary indirect topographical effect. These effects have to be computed through integration over the surface of the earth. The integration is usually split into integration over an area immediately adjacent to the point of interest, called the near zone, and the integration over the rest of the world, called the far zone. It has been shown in the papers by Martinec and Vaníček (1994), and by Novák et al. (1999) that the far-zone contributions to the topographical effects are, even for quite extensive near zones, not negligible.
Various numerical approaches can be applied to compute the far-zone contributions to topographical effects. A spectral form of solution was employed in the paper by Novák et al. (2001). In the paper by Smith (2002), the one-dimensional Fast Fourier Transform was introduced to solve the problem in the spatial domain. In this paper we use two-dimensional numerical integration. The expressions for the far-zone contributions to topographical effects on potential and on gravitational attraction are described, and numerical values encountered over the territory of Canada are shown in this paper.
Similar content being viewed by others
References
Bruns H., 1878. Die Figur der Erde. Publ. Preuss. Geod. Inst., Berlin, Germany.
Gradshteyn I.S. and Ryzhik I.M., 1980. Table of Integrals, Series and Products. Corrected and Enlarged Edition. Academic Press, New York, USA.
Heiskanen W.H. and Moritz H., 1967. Physical Geodesy. W.H. Freeman and Co., San Francisco, USA.
Helmert F.R., 1884. Die mathematische und physikalische Theorien der höheren. Geodäsie, 2, B.G. Teubner, Leipzig, Germany.
Lambert W.D., 1930. Reduction of the observed values of gravity to the sea level. Bulletin Géodésique, 26, 107-181.
Novák P., Vaní?ek P., Martinec Z. and Véronneau M., 2001. Effect of the spherical terrain on the gravity and the geoid. J. Geodesy, 75, 491-504.
Martinec Z., 1993. Effect of lateral density variations of topographical masses in view of improving geoid model accuracy over Canada. Final Report of contract DSS No. 23244-2-4356, Geodetic Survey of Canada, Ottawa.
Martinec Z. and Vaní?ek P., 1994. Indirect effect of topography in the Stokes-Helmert technique for a spherical approximation of the geoid. Manuscripta Geodaetica, 19, 213-219.
Smith D.A., 2002. Computing components of the gravity field induced by distant topographic masses and condensed masses over the entire Earth using the 1-D FFT approach. J. Geodesy, 76, 150-168.
Somigliana C., 1929. Teoria Generale del Campo Gravitazionale dell.Ellisoide di Rotazione. Memoire della Societa Astronomica Italiana, IV.
Vaní?ek P. and Martinec Z., 1994. The Stokes-Helmert scheme for the evaluation of a precise geoid. Manuscripta Geodaetica, 19, 119-128.
Vaní?ek P., Huang J., Novák P., Pagiatakis S.D., Véronneau M., Martinec Z. and Featherstone W.E., 1999. Determination of the boundary values for the Stokes-Helmert problem. J. Geodesy, 73, 180-192.
Wichiencharoen C., 1982. The Indirect Effects on the Computation of Geoid Undulations. Sci. Report No.336, Deptartment of Geodesy, Ohio State University, Columbus, USA.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tenzer, R., Vaníček, P. & Novák, P. Far-Zone Contributions to Topographical Effects in the Stokes-Helmert Method of the Geoid Determination. Studia Geophysica et Geodaetica 47, 467–480 (2003). https://doi.org/10.1023/A:1024799131709
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1024799131709