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

الأصل · EN

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 k₀a (k₀ 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 κ₁) whereas the ± 1 order terms contain the other material constant (i.e., the density of the cylinder ρ₁). A method, relying on the knowledge of the totality of the far-zone scattered field and resulting in explicit expressions for ρ₁ and κ₁, is devised and shown to give highly-accurate estimates of these quantities even for frequencies such that k₀a is as large as 0.1.