Abstract
The aim of the paper is to implement the Green’s function method for the solution of the Linear Gravimetric Boundary Value Problem. The approach is iterative by nature. A transformation of spatial (ellipsoidal) 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 solution domain is carried onto the exterior of an oblate ellipsoid of revolution. Obviously, the structure of Laplace’s operator is more complex after the transformation. It was deduced by means of tensor calculus and in a sense it reflects the geometrical nature of the Earth’s surface. Nevertheless, the construction of the respective Green’s function is simpler for the solution domain transformed. It gives Neumann’s function (Green’s function of the second kind) for the exterior of an oblate ellipsoid of revolution. In combination with successive approximations it enables to meet also Laplace’s partial differential equation expressed in the system of new (i.e. transformed) coordinates.
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Acknowledgements
The work on this paper was supported by the Ministry of Education, Youth and Sports of the Czech Republic through Project No. LO1506. This support is gratefully acknowledged.
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Holota, P., Nesvadba, O. (2019). Green’s Function Method Extended by Successive Approximations and Applied to Earth’s Gravity Field Recovery. In: Novák, P., Crespi, M., Sneeuw, N., Sansò, F. (eds) IX Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 151. Springer, Cham. https://doi.org/10.1007/1345_2019_67
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