An Ellipsoidal Analogue to Hotine’s Kernel: Accuracy and Applicability
In this paper a mathematical apparatus is discussed that involves effects of the flattening of the Earth in the determination of the gravity potential. It rests on the use of Green’s function of the second kind (Neumann’s function) constructed for Neumann’s boundary value problem in the exterior of an oblate ellipsoid of revolution. The apparatus has a natural tie to the reproducing kernel of Hilbert’s space of functions harmonic in the solution domain considered. For at least one of the points (arguments of the kernel) inside the solution domain an expression of the reproducing kernel is developed. However, for both the points (arguments) on the ellipsoidal boundary a practical use of the kernel represented by means of series of ellipsoidal harmonic is not possible. Therefore the application of an approximate closed formula as the integral kernel is discussed and tested. A quality enhancement, if compared with the use of the spherical apparatus, is demonstrated by means of closed loop simulations. The paper contributes to methods related to the geoid (quasigeoid) computations.
KeywordsGravimetric boundary value problem Neumann’s function Oblate spheroid Reproducing kernel
The work on this paper was partly supported by the European Regional Development Fund (ERDF), project “NTIS – New Technologies for Information Society”, European Centre of Excellence, CZ.1.05/1.1.00/02.0090 and also by the Czech Science Foundation through Project No. 14-34595S. All this support is gratefully acknowledged.
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