Three-dimensional acoustic scattering by complex obstacles: The accuracy issue

In this paper, we are concerned with the identification of complex obstacles from the scattering data for the 3D acoustic problem. We focus mainly on the question of the accuracy of the reconstruction. Our approach is based on the asymptotic expansion of the indicator functions generated by multipolar sources. We found out that the second term in the expansion is given by the mean curvature of the surface of the obstacle instead of its Gaussian curvature. This shows how the 3D inverse scattering is more complicated and richer than the 2D one where the curvature, which appears also in the second-order term of the corresponding expansion, characterizes completely the (strict convexity of the) shape in contrast to the mean curvature in the 3D case. We discuss in more detail the effects of the geometry and the surface impedance on the reconstruction accuracy and we present extensive numerical examples to support this discussion.