Reconstruction of an impenetrable obstacle immersed in a shallow water acoustic waveguide

Abstract

We investigate the reconstruction of the shape of a sound-soft cylindrical obstacle of smooth cross-section in a planar acoustic waveguide. This obstacle is located in the farfield of a single time-harmonic line source operating at one given frequency. Scattered pressure fields are observed on two arrays of hydrophones, one on each side of the obstacle. Using a complete family approach, the scattered field is represented as a finite sum of Green’s functions whose source locations evolve with the retrieved contour. The inversion is cast as a penalized optimization problem where the unknown contour is retrieved by iterative minimization of a two-term functional. The first term measures the discrepancy between the data and the field scattered by a given obstacle, the second term measures the error in satisfying the boundary condition on its contour. After a short description of the mathematical formulation and of the needed numerical machinery, illustrative results are shown for convex and concave obstacles, low and high frequencies (few and many modes are propagated), vertical and horizontal arrays, exact and noisy data observed in the nearfield or in the farfield.