On the Characterization of Objects in Shallow Water Using Rigorous Inversion Methods
We are concerned herein with inverse obstacle scattering problems in underwater acoustics, where the goal is to characterize an unknown object from measurements of the pressure field which results from its interaction with a known probing (incident) wave. Two configurations are considered, i.e., an impenetrable, sound-soft or sound-hard object immersed in a shallow-water open waveguide, the source and the receivers also being located in it, and a penetrable object embedded in a semi-infinite sediment, illuminated and observed from a semi-infinite water column. The inverse problem consists in retrieving the contour of the impenetrable object or a contrast function representative of the constitutive physical parameters of the penetrable one. This is done by means of deterministic nonlinearized iterative solution methods, one devoted to each configuration, i.e., the distributed source method and the binary modified gradient method. Both of them attempt to build up a solution by minimizing, in an appropriate L 2 setting, a two-term cost functional which expresses the discrepancies between the fields computed by means of the retrieved solution and the data, the latter being either the field measured on the receivers or the known incident field on the boundary of the object (impenetrable case) or inside it (penetrable case). In both configurations the well-known ill-posedness of the inverse scattering problem is enhanced either by range filtering or by the limited aspect of the data, a strong regularization being then needed. This is done by introducing, in the inversion algorithms, some a priori information on the object to be retrieved, which consists in the smoothness of its contour or in its homogeneity.
KeywordsInverse Problem Boundary Integral Equation Scattered Field Unknown Object Underwater Acoustics
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- [AKRL96]T.S. Angelí, R.E. Kleinman, C. Rozier, and D. Lesselier. Uniqueness and complete families for an acoustic waveguide problem. Technical Report 96–4, Center for the Mathematics of Waves, University of Delaware, Newark, 1996.Google Scholar
- [Buc92]M.J. Buckingham. Ocean-acoustics propagation models. J. of Acoust., 5:223–287,1992.Google Scholar
- [KvdB97]R.E. Kleinman and P.M. van den Berg. Gradient methods in inverse acoustic and electromagnetic scattering. In L.T. Biegler, T.F. Coleman, A.R. Conn, and F.N. Santosa, (eds.), Large-Scale Optimization with Applications, pp. 173–194. Springer-Verlag, Berlin, 1997.Google Scholar
- [LD91]D. Lesselier and B. Duchêne. Buried two-dimensional penetrable objects illuminated by line sources: FFT-based iterative computations of the anomalous field. In T.K. Sarkar (ed.), Application of Conjugate Gradient Methods to Electromagnetics and Signal Analysis, pp. 400–438. Elsevier, New York, 1991.Google Scholar
- [LD96]D. Lesselier and B. Duchêne. Wavefield inversion of objects in stratified environments. From backpropagation schemes to full solutions. In W.R. Stone, (ed.), Review of Radio Science1993–1996, pp. 235–268. Oxford University Press, Oxford, 1996.Google Scholar
- [LL99]M. Lambert and D. Lesselier. Distributed source method for retrieval of the cross-sectional contour of an impenetrable cylindrical obstacle immersed in a shallow water waveguide. To appear in ACUSTICA—Acta Acustica, 86 (4): 45–24. 2000.Google Scholar
- [MLD+99]V. Monebhurrun, D. Lesselier, B. Duchêne, A. Ruosi, M. Valentino, G. Pepe, and G. Peluso. Eddy current nondestructive evaluation using SQUIDs. In D. Lesselier and A. Razek (eds.), Electromagnetic Non-Destructive Evaluation (III), pp. 171–181. IOS Press, Amsterdam, 1999.Google Scholar
- [SabOO]P.C. Sabatier. Past and future of inverse problems. J. Math. Phys., 2000, to appear.Google Scholar