A line integral approach for the computation of the potential harmonic coefficients of a constant density polyhedron
Résumé
A novel approach for the computation of the spherical harmonic coefficients of the gravity field of a constant density polyhedron is presented. Based on the expression of the solid harmonics involved in the integrals in term of a gradient of the same function of higher degree, and on the ho-mogeneity and harmonicity of theses functions, the approach leads, after subsequent application of the divergence theorem in 3D and the Stokes theorem on the plane, to explicit line integrals defined along each polyhe-dral face, which are then summed for all faces of the polyhedral source. In contrast to previous approaches that involved recurrent relations for the integrals of the same functions, the proposed algorithm concludes to a numerical computation of line integrals linked directly to the coefficients. The performed numerical implementation revealed the stability of the proposed algorithm up to degree 360 for a prismatic test source.
Domaines
Géophysique [physics.geo-ph]
Origine : Fichiers produits par l'(les) auteur(s)
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