The inverse problem for the one-dimensional propagation of waves through a medium with an unknown impedance profile is considered. From the reflected pulses caused by an excitation of short duration, this profile is reconstructed by applying the method of characteristics with finite difference approximations. This leads to a simple and fast algorithm, which is demonstrated by the numerical examples in the paper.
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one he had constructed. H. Schwetlick gratefully acknowledges the Deutscher Akademischer Ausstausch Dienst for supporting him with a fellowship during the 1980-1981 academic year.
We would like to express our gratitude to Professor Y.H. Pao for his continual support and advice. This work was sponsored by the National Science Foundation under Grant ENG-79-10311. We would also like to thank Professor W.W. Symes for his helpful participation in the discussions on inverse problems. On the basis of our brief conversation, it appears that our method may be very similar to the
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