Abstract
In a harmonic mode of scattering of planar acoustic waves we study the problem of determining the shape of a prolate acoustically rigid solid of revolution. From experimental measurements we assume that the complex amplitude of inverse scattering is known on a discrete set of test wave numbers in directions that are nearly perpendicular to the axis of revolution of the scatterer.
Similar content being viewed by others
Literature Cited
A. B. Bakushinskii and A. V. Goncharskii,Ill-posed Problems. Numerical Methods and Applications [in Russian], Moscow University Press (1989).
L. G. Velichko, Yu. K. Sirenko, and Z. P. Shestopalov, “Inverse problems of diffraction theory for compact and periodic ideally reflecting objects: A survey of methods and results”, Preprint, No. 93-2 of the Ukrainian Academy of Sciences Institute of Radiophysics and Electronics, Khar'kov (1993).
I. I. Vorovich and M. A. Sumbatyan, “Recovery of the image of a defect from the scattered wave field in acoustic approximation,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 6, 79–84 (1990).
V. F. Emets, “On the inverse scattering problem of acoustic waves for thin acoustically rigid bodies”,Prikl. Mat. Mekh.,48, No. 1, 133–136 (1984).
V. F. Emets, “The inverse scattering problem of acoustic waves by a nondeformable closed obstacle,”Akust. Zh.,37, No. 3, 469–476 (1991).
Yu. A. Eremin and A. G. Sveshnikov,The Discrete Source Method in Problems of Electromagnetic Diffraction [in Russian], Moscow University Press (1992).
V. V. Muzychenko and S. A. Rybak, “Low-frequency resonance scattering of sound by bounded cylindrical shells: A survey,”Akust. Zh.,34, No. 4, 561–577 (1988).
H. Henle, A. Maue, and K. Westphal,Theory of Diffraction [Russian translation], Mir, Moscow (1964).
D. Colton and B. Sleeman, “A uniqueness theorem for the inverse problem of acoustic scattering,”IMA J. Appl. Math.,31, No. 3, 253–259 (1983).
V. Isakov, “Uniqueness and stability in multidimensional inverse problems,”Inv. Probl.,9, No. 6, 579–621 (1993).
P. A. Martin and G. Dassios, “Karp's theorem in elastodynamic inverse scattering,”Inv. Probl.,9, No. 1, 97–111 (1993).
V. K. Varadan, V. V. Varadan, L. R. Dragonette, and L. Flax, “Computation of rigid body scattering by prolate spheroids using theT-matrix approach,”J. Acoust. Soc. Amer.,71, No. 1, 22–25 (1982).
Additional information
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 124–130.
Rights and permissions
About this article
Cite this article
Emets', V.F., Porokhovs'kii, V.V. The inverse scattering problem for a prolate acoustically rigid solid of revolution. J Math Sci 86, 2627–2632 (1997). https://doi.org/10.1007/BF02356110
Issue Date:
DOI: https://doi.org/10.1007/BF02356110