THE ROLE OF NONLINEARITY IN INVERSE PROBLEMS

In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. I t follows from a simple variable count that this cannot be done in a u nique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of mo dels that is consistent with the data; this is called the appraisal pr oblem. Nonlinearity makes the appraisal problem particularly difficult . The first reason for this is that nonlinear error propagation is a d ifficult problem. The second reason is that for some nonlinear problem s the model parameters affect the way in which the model is being inte rrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, thr ee attempts are shown to carry out the model appraisal for nonlinear i nverse problems that are based on an analytical approach, a numerical approach and a common sense approach.