In this paper, we have illustrated how to introduce in the inverse problem, constraints consistent with the least squares formalism (through covariance matrices) on both the data and the model space. The incorporation of all our a priori knowledge of the parameters and all statistical studies on data, allows not only the algorithmic stabilization of the inversion process, but also the reduction of the solution set for an underdetermined problem. The purpose being not necessarily to converge quickly towards a good model (in term of residuals), but to prospect regions of the model space populated by models that are sensible, a priori, and also yielding the lowest possible misfit.