Multifrequency mismatch functions for nonlinear parametric identifications

Overview & Synopsis

This investigation is concerned with the ill-posed nature of (non-linear) inverse problems, in the frequency domain, for which the unknown parameters are determined, in iterative manner, by seeking the minima of a mismatch function quantifying the discrepancy between given data and the output of a numerical model. One might think that the identification can be done solely by the search of the minima of the mismatch function, but this problem is mathematically ill-posed and it is illusory to try to identify a satisfactory solution until the problems of stability (noisy data) and non-uniqueness (local minima) are resolved. This paper shows that a mismatch function resulting from summing up mono frequency mismatch functions corresponding to several different frequencies turns the inverse problem into a global optimization problem and overcomes the problem of the sensitivity of solutions to noisy data, without requiring a priori information on the probed medium.