  We study an inverse problem that consists in estimating the first
(zero-order) moment of some R2-valued distribution m supported within a closed
interval S $\subset$ R, from partial knowledge of the solution to the
Poisson-Laplace partial differential equation with source term equal to the
divergence of m on another interval parallel to and located at some distance
from S. Such a question coincides with a 2D version of an inverse magnetic
"net" moment recovery question that arises in paleomagnetism, for thin rock
samples. We formulate and constructively solve a best approximation problem
under constraint in L2 and in Sobolev spaces involving the restriction of the
Poisson extension of the divergence of m. Numerical results obtained from the
described algorithms for the net moment approximation are also furnished.
