System identification of lossless layered media from input-output data

Abstract

Abstract In this paper we model the interior of the earth as a lossless layered medium, and we are concerned with the reconstruction of the parameters of such a medium from the input and the output (input-output data). In the first part of the paper we assume that the input-output data is noise free, and we derive a so-called layer stripping algorithm for the reconstruction of the parameters of the medium. The algorithm is just one of the many versions of layer stripping algorithms that are available in the literature. In the second and major part of the paper we assume that both the input and the output are corrupted by noise, and we derive two new methods for the estimation of the parameters of the medium using the noisy input-output data. The methods are based on the estimation of the parameters of an ARX-representation of a lossless layered medium. The distinction between the two methods is that in one method the ARX parameters are free, while in the other method the ARX parameters have to correspond to parameters of a lossless layered medium that are physically realistic. We illustrate the methods by means of a numerical experiments.