Divergence of Gradient and the Solution Domain in Gravity Field Studies

Kód výsledku v 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>

Výsledek na webu

<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

—

Jazyk výsledku

angličtina

Název v původním jazyce

Divergence of Gradient and the Solution Domain in Gravity Field Studies

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Divergence of Gradient and the Solution Domain in Gravity Field Studies

Popis výsledku anglicky

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.

Druh

A - Audiovizuální tvorba

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LO1506" target="_blank" >LO1506: Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

—

Místo vydání

—

Název nakladatele resp. objednatele

—

Verze

—

Identifikační číslo nosiče

—