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Integral Representation and Green’s Function Method in Gravity Field Studies
Holota, Petr ; Nesvadba, Otakar

Publication type: anotace
Extent1 strana

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.

Citation: HOLOTA, Petr a Otakar NESVADBA. Integral Representation and Green’s Function Method in Gravity Field Studies [online]. [cit. 2020-12-7]. Dostupné z:!abstractdetails/0000782360

The record appears in these collections:
Focus on VÚGTK > VÚGTK Departments > Geodesy and Geodynamics
Focus on VÚGTK > Staff VÚGTK > Otakar Nesvadba
Focus on VÚGTK > Staff VÚGTK > Petr Holota
Documents of VÚGTK > Articles VÚGTK
Focus on VÚGTK > RIV

 Record created 2020-08-20, last modified 2020-12-07

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