Abstract
The inverse gravimetric problem, namely the determination of the internal density distribution of a body from the exterior gravity field, is known to have a very large indeterminacy while it is well identified and described in functional terms. However, when density models are strongly reduced to simple classes, or functional subspaces, the uniqueness property of the inversion is retrieved. Uniqueness theorems are proved for three simple cases in Cartesian approximation: ∙ The recovery of the interface between two layers of known density ∙ The recovery of a laterally varying density distribution, in a two layers model, given the geometry of the problem (topography and depth of compensation) ∙ The recovery of the distribution of the vertical gradient of density, in a two layers model, given the geometry of the problem (topography and depth of compensation) and the density distribution at sea level.
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Sampietro, D., Sansò, F. (2012). Uniqueness Theorems for Inverse Gravimetric Problems. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_17
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DOI: https://doi.org/10.1007/978-3-642-22078-4_17
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