Integral Representation and Green’s Function Method in Gravity Field Studies

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F19%3AN0000044" target="_blank" >RIV/00025615:_____/19:N0000044 - isvavai.cz</a>

Result on the web

<a href="https://www.czech-in.org/cmPortalV15/CM_W3_Searchable/iugg19/normal#!abstractdetails/0000782360" target="_blank" >https://www.czech-in.org/cmPortalV15/CM_W3_Searchable/iugg19/normal#!abstractdetails/0000782360</a>

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Integral Representation and Green’s Function Method in Gravity Field Studies

Original language description

In the integral representation the use of Green’s function basically rests on the convolution of the data with this specific integral kernel. When studying the gravity field the important and densely distributed date are usually available on the boundary of the solution domain. Boundary value problems have an important position in this field. Regarding the construction of the integral kernel, Green’s function, there exist elegant and powerful methods for simple solution domains as, e.g., the sphere, the outer space of the sphere, the spherical layer. A more complicated, but still manageable, is the construction, e.g., for the exterior of an ellipsoid of revolution. In order to preserve the benefit of the Green’s function method also for more complicated boundaries an iteration procedure is discussed. A transformation of spatial coordinates is used that offers a possibility for an alternative between the boundary complexity and the complexity of the coefficients of Laplace’s partial differential equation governing the solution. The structure of the Laplacian was deduced by means of tensor calculus and in a sense it reflects the geometrical nature of the solution domain, particularly the geometrical nature of the Earth’s surface. In combination with successive approximations the concept above enables to approach the solution of Laplace’s partial differential equation expressed in the system of new coordinates. It is applied for the solution of geodetic boundary value problems as well as for the combination of terrestrial and satellite data. The iteration steps are analysed by numerical as well as functional analytic tools.

Czech name

—

Czech description

—

Type

O - Miscellaneous

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

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)

Publication year

2019

Confidentiality

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