Divergence of Gradient and the Solution Domain in Gravity Field Studies
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F19%3AN0000042" target="_blank" >RIV/00025615:_____/19:N0000042 - isvavai.cz</a>
Result on the web
<a href="https://leibnizsozietaet.de/wp-content/uploads/2017/04/Potsdam-LS2017-Holota.pdf" target="_blank" >https://leibnizsozietaet.de/wp-content/uploads/2017/04/Potsdam-LS2017-Holota.pdf</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Divergence of Gradient and the Solution Domain in Gravity Field Studies
Original language description
This paper focuses on the solution of the linear gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. In the introductory part of the paper the relation is interpreted in general terms by means of the apparatus of tensor calculus. The solution domain is carried onto the exterior of an oblate ellipsoid of revolution and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their structure is analyzed and modified by using integration by parts. As a result of the transformation an ellipsoidal mathematical apparatus may be applied at each iteration step. In particular Green’s function of the second kind, i.e. Neumann’s function, constructed for the exterior of an oblate ellipsoid of revolution, may be used in the integral representation of the successive approximations.
Czech name
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Czech description
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Classification
Type
A - Audiovisual production
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
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