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The problem of global geoid determination is usually solved using satellite altimetry data on the oceans, together with an
oceanographic model of sea surface topography, and gravity anomaly data on the continents. Such data, however, enable to obtain
only potential differences with respect to a reference surface whose absolute potential is unknown. This situation suggests
to modify the classical mixed boundary-value problem of physical geodesy by inserting into the boundary conditions an unknown
additive constant, that must be determined by imposing a suitable additional constraint. Yet, such formulation of the boundary-value
problem, from the point of view of its mathematical properties, is not unconditionally well-posed, and, furthermore, does
not reflect faithfully the available physical model, as the present knowledge of ocean circulation does not allow to connect
along coastlines the reference surfaces defined on the oceans and on the continents. The introduction of two different unknown
additive constants, one for the oceans and one for the earth, to be determined by imposing two additional constraints, gives
rise to a more faithful picture of the present physical knowledge, and, at the same time, to a new well-posed formulation
of the boundary-value problem.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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