On the identification of the flatness of a sound-hard acoustic crack

Inverse problemsIn this paper, we present results concerning the far field pattern generated by flat and almost flat cracks in 3D and the possibility of identifying these geometrical features from direct inspection of the far field pattern. We address the direct problem using a variational formulation of the boundary integral equation to avoid the hipersingularity in the double layer potential representation. Concerning the inverse problem, some estimates presenting a direct dependence on the far field behavior and the flatness of the crack are derived. From the knowledge of the plane that defines the main directions of the crack it is possible to get a first approximation that may be used as an initial guess for the Newton method. Numerical simulations validate the direct relation between a far field plane having almost null amplitude and the main directions of a plane that defines an almost flat crack