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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 3 October 2001 / Accepted: 4 October 2002
Rights and permissions
About this article
Cite this article
Martinec, Z. Green's function solution to spherical gradiometric boundary-value problems. Journal of Geodesy 77, 41–49 (2003). https://doi.org/10.1007/s00190-002-0288-z
Issue Date:
DOI: https://doi.org/10.1007/s00190-002-0288-z