- Title
- Vertical and horizontal spheroidal boundary-value problems
- Creator
- Šprlák, Michal; Tangdamrongsub, Natthachet
- Relation
- Journal of Geodesy Vol. 92, Issue 7, p. 811-826
- Publisher Link
- http://dx.doi.org/10.1007/s00190-017-1096-9
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2018
- Description
- Vertical and horizontal spheroidal boundary-value problems (BVPs), i.e., determination of the external gravitational potential from the components of the gravitational gradient on the spheroid, are discussed in this article. The gravitational gradient is decomposed into the series of the vertical and horizontal vector spheroidal harmonics, before being orthogonalized in a weighted sense by two different approaches. The vertical and horizontal spheroidal BVPs are then formulated and solved in the spectral and spatial domains. Both orthogonalization methods provide the same analytical solutions for the vertical spheroidal BVP, and give distinct, but equivalent, analytical solutions for the horizontal spheroidal BVP. A closed-loop simulation is performed to test the correctness of the analytical solutions, and we investigate analytical properties of the sub-integral kernels. The systematic treatment of the spheroidal BVPs and the resulting mathematical equations extend the theoretical apparatus of geodesy and of the potential theory.
- Subject
- differential operator; gravitational gradient; vector spheroidal harmonics; spheroidal harmonic analysis
- Identifier
- http://hdl.handle.net/1959.13/1444322
- Identifier
- uon:42268
- Identifier
- ISSN:0949-7714
- Language
- eng
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