In this work we present several regularization techniques for the solution of geophysical ill-posed inverse problems, in the case of discrete data and discrete model parameters. In particular, the Twomey (1963) algorithm Is applied to Invert synthetic tomographic data, In both noise-free data and data corrupted by noise. This algorithm Is based on a smoothness criterion where the second differences of the model parameters are minimum. The selection of the regularization parameter Is also considered, and a practical trial and error procedure Is suggested for the selection of an optimal parameter, based on the behaviour of the RMS misfit curves for data and model parameters, the entropy of the solution, and the qualitative/quantitative analysis of the estimated model parameters.