We outline the inverse scattering theory for acoustic waves in a perturbed stratified medium developed by Dr. Yongzhi Xu .
Consider wave scattering by an obstacle in a stratified medium shown in Waves scattered by an obstacle.
The shape determination problem we consider is that given information on incident waves and far-field patterns of scattered waves, determine the shape of the scatterer.
Computer simulation has been performed to reconstruct the shape of a 2-D scatterer using incomplete far-field data for different incident waves.
The scattered far-field data is obtained by solving the direct scattering problem using an approximate boundary integral method.
To reconstruct the shape of the scatterer, we use only the scattered free-wave far-field data corresponding to different incident waves. The inverse problem is solved by a minimization algorithm developped by Xu. Our results are shown in Figure A and Figure B . The solid curve outlines the original scatterer. The reconstruction is shown by the shaded area.
In Figure A , we plot three shape reconstruction results for incident waves chosen from only guided-mode or only downward free-waves.
In Figure B (a), one guided mode is used. In Figure B (b), two guided modes are used. In Figure B (c) one downward free-wave is used. Obviously, the results in Figure A are very poor shape reconstruction results. The results in Figure B are much better reconstructions.
These results, consistent with the theory, show that carefully chosen incident waves can greatly improve the quality of shape reconstruction in a stratified medium.