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Non-singular expressions for vector and gradient tensor of gravitation in a geocentric spherical frame
University West, Department of Engineering Science, Division of Computer, Electrical and Surveying Engineering.ORCID iD: 0000-0003-0067-8631
2008 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 34, no 12, p. 1762-1768Article in journal (Refereed) Published
Abstract [en]

The traditional expressions of the gravitational vector (GV) and the gravitational gradient tensor (GGT) have complicated forms depending on the first- and the second-order derivatives of associated Legendre functions (ALF), and also singular terms when approaching the poles. This article presents alternative expressions for the GV and GGT, which are independent of the derivatives, and are also non-singular. By using such expressions, it suffices to compute the ALF to two additional degrees and orders, instead of computing the first and the second derivatives of all the ALF. Therefore, the formulas are suitable for computer programming. Matlab software as well as an output of a numerical computation around the North Pole is also presented based on the derived formulas.

Place, publisher, year, edition, pages
2008. Vol. 34, no 12, p. 1762-1768
Keywords [en]
Non-singularity, associated Legendre functions, normalization
National Category
Geophysics
Research subject
ENGINEERING; ENGINEERING, Geodesy
Identifiers
URN: urn:nbn:se:hv:diva-7902DOI: 10.1016/j.cageo.2008.02.022OAI: oai:DiVA.org:hv-7902DiVA, id: diva2:845884
Available from: 2015-08-13 Created: 2015-08-13 Last updated: 2019-11-21Bibliographically approved

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Eshagh, Mehdi

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