Bibliografie VÚGTK
Laplacian structure, solution domain geometry and successive approximations in gravity field studies
Holota, Petr ; Nesvadba, Otakar ; EGU General Assembly 2020



Publication type: anotace
Extent1 strana

Link: https://doi.org/10.5194/egusphere-egu2020-12839
Annotation:
When treating geodetic boundary value problems in gravity field studies, the geometry of the physical surface of the Earth may be seen in relation to the structure of the Laplace operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. The Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a sphere or an oblate ellipsoid of revolution, even if these are optimally fitted. The situation may be more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. The structure of the Laplace operator, however, is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of geodetic boundary value problems expressed in terms of new coordinates. The structure of iteration steps is analyzed and if useful, it is modified by means of the integration by parts. Subsequently, the individual iteration steps are discussed and interpreted.

Citation: HOLOTA, Petr a Otakar NESVADBA. Laplacian structure, solution domain geometry and successive approximations in gravity field studies, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12839, https://doi.org/10.5194/egusphere-egu2020-12839, 2020

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

 Record created 2021-08-04, last modified 2021-08-23


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