000196321 001__ 196321
000196321 003__ CZ-ZdVUG
000196321 005__ 20210823112533.0
000196321 041__ $$aeng
000196321 040__ $$aABC039$$bcze
000196321 1001_ $$aHolota, Petr
000196321 1112_ $$aEGU General Assembly 2020$$bVienna$$d4–8 May 2020
000196321 24510 $$aLaplacian structure, solution domain geometry and successive approximations in gravity field studies
000196321 300__ $$a1 strana
000196321 5203_ $$aWhen 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.
000196321 655_4 $$aanotace
000196321 7001_ $$aNesvadba, Otakar
000196321 7730_ $$92020
000196321 8564_ $$uhttps://doi.org/10.5194/egusphere-egu2020-12839
000196321 85642 $$ahttps://www.isvavai.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F20%3AN0000061%21RIV21-MSM-00025615
000196321 910__ $$aABC039
000196321 980__ $$aclanky_vugtk
000196321 985__ $$aholota
000196321 985__ $$ariv
000196321 985__ $$autvar24