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

Thierry Scotti (1) , Armand Wirgin (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

The inverse medium problem for a circular cylindrical domain isstudied using low-frequency acoustic waves as the probe radiation.It is shown that to second order in $k_{0}a$ ($k_{0}$ thewavenumber in the host medium, $a$ the radius of the cylinder),only the first three terms (i.e., of orders 0, -1 and +1) in thepartial wave representation of the scattered field arenon-vanishing, and the material parameters enter into these termsin explicit manner. Moreover, the zeroth-order term contains onlytwo of the unknown material constants (i.e., the real andimaginary parts of complex compressibility of the cylinder$\kappa_{1}$) whereas the $\pm 1$ order terms contain the othermaterial constant (i.e., the density of the cylinder $\rho_{1}$).A method, relying on the knowledge of the totality of the far-zonescattered field and resulting in explicit expressions for$\rho_{1}$ and $\kappa_{1}$, is devised and shown to givehighly-accurate estimates of these quantities even for frequenciessuch that $k_{0}a$ is as large as 0.1.

Mots clés: inverse medium problem; acoustics

Domaines: Acoustique [physics.class-ph]

Thierry Scotti, Armand Wirgin. Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields. 2003. ⟨hal-00000843⟩