Abstract
The aim of this paper is to discuss the solution of the simple gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. The solution domain is carried onto the exterior of a sphere and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their internal structure is analyzed and modified by using integration by parts. As a result of the transformation a spherical mathematical apparatus may be applied at each iteration step, including the spherical form of Green’s function of the second kind, i.e. Neumann’s function, in the integral representation of the successive approximations.
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This work was supported by Czech Science Foundation through Project No. 14-34595S. This support is gratefully acknowledged.
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Holota, P. (2016). Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem. In: Freymueller, J.T., Sánchez, L. (eds) International Symposium on Earth and Environmental Sciences for Future Generations. International Association of Geodesy Symposia, vol 147. Springer, Cham. https://doi.org/10.1007/1345_2016_236
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DOI: https://doi.org/10.1007/1345_2016_236
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69169-5
Online ISBN: 978-3-319-69170-1
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