Detection of multilayered media in the acoustic waveguide

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:415

Article

Al-Musallam, Fadhel^1,2  Boumenir, Amin³  Sini, Mourad¹ 

[1] Austrian Acad Sci, RICAM, A-4040 Linz, Austria

[2] Kuwait Univ, Dept Math, Safat 13060, Kuwait

[3] Univ West Georgia, Dept Math, Carrollton, GA 30118 USA

关键词: Inverse scattering problems;    Waveguide;    Inverse spectral problems;   

DOI  :  10.1016/j.jmaa.2014.02.002

来源: Elsevier

【 摘 要 】

This work is concerned with the inverse problem for ocean acoustics modeled by a multilayered waveguide with a finite depth. We provide explicit formulae to locate the layers, including the seabed, and reconstruct the speed of sound and the densities in each layer from measurements collected on the surface of the waveguide. We proceed in two steps. First, we use Gaussian type excitations on the upper surface of the waveguide and then from the corresponding scattered fields, collected on the same surface, we recover the boundary spectral data of the related 1D spectral problem. Second, from these spectral data, we reconstruct the values of the normal derivatives of the singular solutions, of the original waveguide problem, on that upper surface. Finally, we derive formulae to reconstruct the layers from these values based on the asymptotic expansion of these singular solutions in terms of the source points. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free