Green's function solution to spherical gradiometric boundary-value problems |
| |
Authors: | Z. Martinec |
| |
Affiliation: | (1) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic e-mail: zdenek@hervam.troja.mff.cuni.cz; Tel.: +420-2-2191-2539; Fax: +420-2-2192-2555, CZ |
| |
Abstract: | Three independent gradiometric boundary-value problems (BVPs) with three types of gradiometric data, {Γ rr }, {Γ r θ,Γ r λ} and {Γθθ−Γλλ,Γθλ}, prescribed on a sphere are solved to determine the gravitational potential on and outside the sphere. The existence and uniqueness conditions on the solutions are formulated showing that the zero- and the first-degree spherical harmonics are to be removed from {Γ r θ,Γ r λ} and {Γθθ−Γλλ,Γθλ}, respectively. The solutions to the gradiometric BVPs are presented in terms of Green's functions, which are expressed in both spectral and closed spatial forms. The logarithmic singularity of the Green's function at the point ψ=0 is investigated for the component Γ rr . The other two Green's functions are finite at this point. Comparisons to the paper by van Gelderen and Rummel [Journal of Geodesy (2001) 75: 1–11] show that the presented solution refines the former solution. Received: 3 October 2001 / Accepted: 4 October 2002 |
| |
Keywords: | : Geodetic boundary-value problem – Gravitation tensor – Green's function – Addition theorem – Tensor spherical harmonics |
本文献已被 SpringerLink 等数据库收录! |
|