Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition |
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Authors: | Z. Martinec |
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Affiliation: | (1) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, CZ-180 00 Prague 8, Czech Republic Tel.: +420 2 2191 2539; Fax: +420 2 2191 2555; e-mail: zdenek@hervam.troja.mff.cuni.cz, XX |
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Abstract: | Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e 2 0)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant. Received: 5 June 1997 / Accepted: 20 February 1998 |
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Keywords: | . Spherical Stokes's function Ellipsoidal corrections Surface spherical harmonics Addition theorem |
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