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. It is shown that 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, and the material parameters enter into these terms in explicit manner. Moreover, the zeroth-order term contains only two of the unknown material constants (i.e., the real and imaginary parts of complex compressibility of the cylinder $κ_{1}$) whereas the $\pm 1$ order terms contain the other material constant (i.e., the density of the cylinder $ρ_{1}$). A method, relying on the knowledge of the totality of the far-zone scattered field and resulting in explicit expressions for $ρ_{1}$ and $κ_{1}$, is devised and shown to give highly-accurate estimates of these quantities even for frequencies such that $k_{0}a$ is as large as 0.1.