Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields

Abstract

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. To second order in k 0 a ( k 0 the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, −1 and +1) in the partial wave representation of the scattered field are non-vanishing. This enables the scattered field to be expressed algebraically in terms of the unknown material constants, i.e., the density ρ 1, and the real and imaginary parts of complex compressibility κ 1 of the cylinder. It is shown that these relations can be inverted to yield explicit, decoupled expressions for ρ 1 and κ 1 in terms of the totality of the far-zone scattered field. These expressions furnish accurate estimations of the material parameters provided the probe frequency is low and the radius of the cylinder is known very precisely. To cite this article: T. Scotti, A. Wirgin, C. R. Mecanique 332 (2004).