So far we have treated the model parameters as continuous functions in three-dimensional space, e.g. ρ(r) for the density at location r. Sooner or later, however, we must represent the model by a finite set of numbers in order to perform the direct and inverse calculations. One could, of course, simply discretize the model by sampling it at a sufficiently dense set of pixels (sometimes called ‘voxels’ in 3D). This has the advantage that one does not restrict the smoothness of the model, but the price to be paid is a significant loss of computational efficiency, and this is something we can ill afford. The proper approach is to parametrize the model – taking care, however, that the imposed smoothness does not rule out viable classes of models. In addition, the model parametrization should allow for the data to be fit to the error level attributed to them. Note that these two conditions are not identical! In practice, one does well to overparametrize and allow for more parameters than can be resolved. This reduces the risk that the limitations of the parameter space appreciably influence the inversion. Overparametrization poses some problems to the inverse problem, but these can be overcome. We shall deal with that in Chapter 14. If one is forced to underparametrize, effects of bias can be suppressed by using an ‘anti-leakage’ operator such as proposed by Trampert and Snieder.