Abstract
The topographic masses (TM) load the interfaces within the earth; namely TMs are compensated by an isostatic adjustment which might depend on time. Here we focus on the loading gravitational potential to which we refer as the topographic potential. We aim at a rigorous integral representation for the topographic potential of gravity which results in corollary one and two.
In addition, a rigorous computation of the gravitational potential of a massive non-spherical shell is achieved which is limited by shape functions which represent the earth's topography (‘heights’) and the “negative topography” (‘depths’) which substitutes the internal surface of isostatic compensation. Finally by the third corollary the “single layer” potential is given of those masses which are condensed onto a reference sphere, the basis for the standard loading potential. The hypothesis of mass condensation is confronted with the exact representation, namely in the external distant zone, the near zone and the internal distant zone.
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Grafarend, E.W., Engels, J. The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation. Surv Geophys 14, 495–524 (1993). https://doi.org/10.1007/BF00690574
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DOI: https://doi.org/10.1007/BF00690574