SHAPE RETRIEVAL OF AN OBSTACLE IMMERSED IN SHALLOW-WATER FROM SINGLE-FREQUENCY FARFIELDS USING A COMPLETE FAMILY METHOD

The cross sectional contour of a sound-soft closed cylindrical obstacl e placed in an acoustic planar waveguide modelling a shallow water con figuration is retrieved from a limited knowledge of scattered farfield patterns in the water layer at a single frequency. A complete Dirichl et family of fundamental solutions of the corresponding boundary value problem is introduced (Green's functions of the waveguide). Iterative construction of the contour is carried out by minimizing a two-term c ost functional. The first term measures how well the data are fitted, the second term how well the boundary condition is satisfied. In pract ice, a star-shaped contour is sought while the scattered field is take n as a finite weighted sum of Green's functions whose source locations evolve with the retrieved contour. Reconstructions from independently generated synthetic data for both convex and non-convex shapes at a l ow and a high frequency are shown. Influence of numerical parameters ( initial shape, number of Green's functions and sampling nodes of the c ontour, relative weight of each term in the cost functional) and physi cal ones (location of sources, location and positioning accuracy of th e receivers, measurement noise) is investigated. The good efficiency o f this complete family method is confirmed in a demanding situation wh ere, in addition to filtering out of high-spatial-frequency wavefields with range, only finitely many modes are propagated; and where lack o f information due to aspect-limited data is not alleviated by frequenc y diversity.