On evaluation of Newton integrals in geodetic coordinates: Exact formulation and spherical approximation

Author(s)
Peter Vajda, Petr Vanicek, Pavel Novak, Bruno Meurers
Abstract

Newton integrals for the potential and the vertical component of the attraction vecto (gravitational effect), serve for evaluating various topographical effects (negative topographical corrections) as well as for evaluating the potential and the gravitational effect of various bodies and/or models of mass density distribution (real, constant or anomalous). Here we review global evaluation of the Newton integrals in geodetic coordinates (in Gauss ellipsoidal coordinates) formulated exactly and in spherical approximation. Various topographical corrections are addressed by investigating their definitions in terms of the upper and lower topographical boundary and the used density. Numerical aspects of the evaluation of the Newton integrals, such as the weak singularity treatment, split-up into spherical shell and terrain terms, and a requirement to integrate over the entire globe are also addressed. Implications associated with regional and local evaluation of the Newton integrals are indicated. Special attention is paid to the so-called "ellipsoidal topography of constant density" ("ETC") and to NETC topo-corrections to potential and gravity. The abbreviation "NETC" stands for "No ETC" and represents the removal of the effect of "ETC" on potential or gravity.

Organisation(s)
Department of Meteorology and Geophysics
External organisation(s)
Slovenian Academy of Sciences and Arts, University of New Brunswick (UNB), Research Institute of Geodesy, Topography and Cartography, Geodetic Observatory Pecný
Journal
Contributions to geophysics & geodesy: a journal of geophysics, geodesy, meteorology and climatology
Volume
34
Pages
289-314
No. of pages
26
ISSN
1335-2806
Publication date
2004
Peer reviewed
Yes
Austrian Fields of Science 2012
105102 General geophysics
Portal url
https://ucrisportal.univie.ac.at/en/publications/13c23493-0dc2-40f0-9f12-3d0b64bfe766