  We investigate the use of Tikhonov regularization with the minimum support
stabilizer for underdetermined 2-D inversion of gravity data. This stabilizer
produces models with non-smooth properties which is useful for identifying
geologic structures with sharp boundaries. A very important aspect of using
Tikhonov regularization is the choice of the regularization parameter that
controls the trade off between the data fidelity and the stabilizing
functional. The L-curve and generalized cross validation techniques, which only
require the relative sizes of the uncertainties in the observations are
considered. Both criteria are applied in an iterative process for which at each
iteration a value for regularization parameter is estimated. Suitable values
for the regularization parameter are successfully determined in both cases for
synthetic but practically relevant examples. Whenever the geologic situation
permits, it is easier and more efficient to model the subsurface with a 2-D
algorithm, rather than to apply a full 3-D approach. Then, because the problem
is not large it is appropriate to use the generalized singular value
decomposition for solving the problem efficiently. The method is applied on a
profile of gravity data acquired over the Safo mining camp in Maku-Iran, which
is well known for manganese ores. The presented results demonstrate success in
reconstructing the geometry and density distribution of the subsurface source.
