Bibliografie VÚGTK
Small Modifications of Curvilinear Coordinates and Successive Approximations Applied in Geopotential Determination
Holota, Petr ; Nesvadba, Otakar

Source: online

Publication type: anotace

RIV: RIV/00025615:_____/16:N0000045


The mathematical apparatus currently applied for geopotential determination is undoubtedly quite developed. This concerns numerical methods as well as methods based on classical analysis, equally as classical and weak solution concepts. Nevertheless, the nature of the real surface of the Earth has its specific features and is still rather complex. The aim of this paper is to consider these limits and to seek a balance between the performance of an apparatus developed for the surface of the Earth smoothed (or simplified) up to a certain degree and an iteration procedure used to bridge the difference between the real and smoothed topography. The approach is applied for the solution of the linear gravimetric boundary value problem in geopotential determination. 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. As examples the use of modified ellipsoidal coordinates for the transformation of the solution domain is discussed. However, the complexity of the boundary is then reflected in the structure of Laplace’s operator. This effect is taken into account by means of successive approximations. The structure of the respective iteration steps is derived and analyzed. On the level of individual iteration steps the attention is paid to the representation of the solution in terms of Green’s function method. The convergence of the procedure and the efficiency of its use for geopotential determination is discussed.
Keywords: Earth’s gravity field ; boundary value problems ; transformation of coordinates ; Laplace’s operator ; Green’s function method ; successive approximations

Citation: HOLOTA, Petr. Small Modifications of Curvilinear Coordinates and Successive Approximations Applied in Geopotential Determination In: AGU´s Fall Meeting 12.-16.2016, San Francisco. Dostupné z:
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The record appears in these collections:
Focus on VÚGTK > VÚGTK Departments > Geodesy and Geodynamics
Focus on VÚGTK > Staff VÚGTK > Petr Holota
Documents of VÚGTK > Articles VÚGTK

 Record created 2017-06-08, last modified 2019-05-24

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