Recently developed mathematical models of subsidence in extensional
basins provide a good basis for forward modeling. However, the large
number of parameters to be specified by the user makes it difficult not
only to do the modeling itself, but also to judge the meaning of the
results. We present a new method for automatic searching of the
best-fitting parameter set of a 2D basin formation model. Weighted goal
functions are used in the minimization process by the inverse problem
solver algorithm. The nominal parameter set in the present case includes
profiles of the crustal and subcrustal thinning factors, and the level
of lithosphere necking. The method was tested on synthetic data with
parameters that were perturbed beforehand. With some restrictions, the
algorithms are capable of resolving such perturbations. The inversion
technique has been applied to two profiles crossing the Dnieper-Donets
Basin (Ukraine). The crustal thinning factors obtained argue for a
scissors-like style of basin opening. High subcrustal thinning values
are necessary in order to explain the abnormally thick Carboniferous
section in the basin. These values should be treated as cumulative ones
due to the currently unresolvable influence of other rifting-related
processes, particularly phase transitions.