## 1 Introduction  
Frequently, sound propagation inside the pores of porous absorbers is described by its effective density, without thermal effects, and an effective bulk modulus, without viscous effects [1]. As waves can propagate through the material pores, it is reasonable to consider that some energy is transmitted to the frame. In that case, no rigid frame is considered. Instead, an elastic frame should be used. [PERSON] et al. [2, 3], conceive a model in which this behavior is presented as a set of tensors for strains and displacements. Years later, an empirical method was developed by [PERSON] and [PERSON] [4], in which the absorption process is taken into account by means of the material characteristic impedance and its wavenumber, both being complex numbers. A large number of impedance tube measurements were performed, and afterwards, absorption coefficients were fitted into a power law relation. As a result, a set of equations are given and, from them, it is possible to calculate porous absorption in a wide frequency range. Considering that the solid skeleton can often be set as immobile, and non-deformable, the acoustic movements are those of the saturating fluid, normally air, affected by viscous friction and thermal exchanges at the pore walls [5]. In harmonic regime, the material can be described, at macroscopic level, as an equivalent fluid, by following local equations [6]. In local theory, where a surface point is described by itself, without neighboring point's dependence, the material is characterized by the effective density and the effective compressibility, which are, respectively, \(\rho_{\rm f}\alpha(\omega)\) and \(\beta(\omega)/\mathrm{K}_{\rm a}\)[5; 7],  
\[\rho_{f}\alpha(\omega)\frac{\partial\mathbf{u}_{\mathbf{m}}}{\partial t}=-\
abla p_{m} \tag{1}\]  
\[\frac{\beta(\omega)}{k_{f}}\frac{\partial p_{m}}{\partial t}=-\
abla\mathbf{u}_{ \mathbf{m}} \tag{2}\]  
where \(\rho_{\rm f}\) is the static fluid density, \(\mathbf{u}_{\mathbf{m}}\) the material particle velocity, \(\mathrm{p}_{\mathbf{m}}\) the material pressure and \(k_{f}\) the static fluid compressibility. Subscript m denotes \"material\" in order to differentiate from fluid values. Those terms are governed by the dynamic tortuosity, \(\alpha(\omega)\), and the dynamic compressibility, \(\beta(\omega)\), of the air immersed in the material pores, and are frequency dependent. Their theoretical expressions were given initially by [PERSON] [8], and later modified by Lafarge in the so-called JCAL (Johnson-Champoux-Allard-Lafarge) model [7], being the most used phenomenological model to calculate sound absorption in porous materials. The JCAL model uses six parameters to fully represent the porous absorber performance, being the open porosity, the static air-flow resistivity, the dynamic tortuosity, the viscous and thermal lengths and, finally, the thermal permeability. [PERSON] et al. [9], clearly attempt to a direct evaluation of the six parameters through a simple impedance tube measurement. Regardless of how they extracted the data to obtain a representative value for the parameters, they showed some limitations to this method, such us leakages around the sample or the internal vibrations in the material skeleton. These drawbacks could have a high impact in the final characterization of the material. In a similar manner, [PERSON] et al. [10], relied on the porous material characterization by also using a set of impedance tube measurements. An equivalent density and bulk modulus was considered by fitting the measured and modeled values to outline the JCAL parameters. Resembling the mentioned methods is the use of the six parameters given by the JCAL model to represent the acoustical performance of porous materials. The recurrence taken in the JCAL model makes necessary to relate the absorption mechanisms, which are given by the dynamic tortuosity and the dynamic permeability in Equations (1) and (2), due to the viscous and thermal exchanges between the air and the material structure [11].