Inverse methods in the reconstruction of acoustical impedance profiles

Three methods for the reconstruction of inhomogeneities in a one‐dimensional lossless medium from incident and reflected wave signals are presented in this paper: the method of characteristics, the Gel’fand–Levitan method, and the newly developed method of iterative local regulization. Reconstructed results from numerical experiments are compared with emphasis on inversion in the presence of noise, and on general excitations. An error analysis and a study of computation requirements are also presented.