Addressing the ill-posedness of multi-layer porous media characterization in impedance tubes through the addition of air gaps behind the sample: Numerical validation

This paper is concerned with plane wave propagation in multi-layer assemblies of rigid isotropic porous media inside impedance tubes. The focus is placed on the inverse problem, i.e., the retrieval of the intrinsic properties defining the pore micro-structure of each layer: the porosity, the pore mean size and the pore size standard deviation. Each layer is considered isotropic. Such an inverse problem can be ill-posed due to the non-uniqueness of the solution. The technique explored in this work is the consideration of additional acoustic observations, where air gaps are placed behind the multi-layer assembly. The aptitude of this strategy to overcome the ill-posedness of the inverse problem is evaluated on numerical synthetic data, on assemblies made of three layers. For a given fixed amount of input data, inverse problems including different observations with air gaps can yield more accurate results, removing the ill-posedness.