My talk deals with the same subject as that of the previous speaker, Dr. Szabo, except I am not going to assert that it involves residual stresses necessarily. I consider some kind of a perturbation of the elastic properties and/or density due to some kind of surface treatment. As in all problems of this kind I assume, at least for the time being, some kind of an ansatz about mutual proportionality between the various kinds of perturbed physical properties as they vary with depth.

There are, perhaps, four ways of classifying approaches to this kind of problem. One is a parametric approach where one assumes that the candidate profile is defined by a finite set of parameters which are adjusted to give the best fit to the experimental data. Another is a nonparametric approach in which one does not have a finite set of parameters but an essentially infinite set of parameters. Another dimension of classification is whether one is using a probabilistic or a nonprobabilistic approach. In the nonparametric case one is forced to use a probabilistic approach. Here one treats every conceivable profile as being present in a statistical ensemble but with probability weightings reflecting one's a priori knowledge of what is more or less reasonable.