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Green's function solution to spherical gradiometric boundary-value problems
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DOI：10.1007/s00190-002-0288-z.png)
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摘要
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Three independent gradiometric boundary-value problems (BVPs) with three types of gradiometric data, {Gamma(rr)}, {Gamma(rtheta), Gamma(rlambda)} and {Gamma(theta) - Gamma(lambda), Gamma(thetalambda)} 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 {Gamma(rtheta), Gamma(rlambda)} and {Gamma(theta) - Gamma(lambdalambda), Gamma(thetalambda)}, 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 psi = 0 is investigated for the component Gamma(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.
Keyword:
geodetic boundary-value problem
gravitation tensor
Green's function
addition theorem
tensor spherical harmonics
