Distributed source method for retrieval of the cross-sectional contour of an impenetrable cylindrical obstacle immersed in a shallow water waveguide
Résumé
The nonlinear retrieval of the cross-sectional contour of a sound-soft or sound-hard, closed cylindrical obstacle which is fully immersed in the water column of a shallow water waveguide is investigated. Time-harmonic pressure field data are acquired on two nearby vertical arrays when the obstacle is illuminated by a line source operated at one or at best two discrete frequencies. These data are inverted by a distributed source method. This involves the minimization of a two-term cost functional which is characteristic of the fit between data and wavefield associated to a test obstacle, and of the satisfaction of the boundary condition on the contour of this test obstacle. The method relies on the modeling of the acoustic wavefields as a superposition of elementary waves (the Green's functions of the waveguide) and uses the smoothness of the sought contour as a main constraint. Numerical experimentation shows that it yields good shape reconstructions for soft, and at a lesser extent hard, obstacles above a sedimentary fluid-like sea bottom of low as well as of high contrast using a fairly limited dataset (with some substantial improvement using the two frequencies), whereas it has the potential for generalization to elastic bottom layers as well as to obstacles fully buried in the bottom.