Ultrasonic characterization of porous absorbing materials: Inverse problem

This paper concerns the ultrasonic characterization of air-saturated porous materials by solving the inverse problem using experimental data. It is generally easy to solve the inverse problem via transmitted waves, obtaining optimized values of tortuosity, viscous and thermal characteristic lengths, but this is not the case for the porosity because of its weak sensitivity in the transmitted mode. The reflection mode is an alternative to the transmission mode, in that it gives a good estimation of porosity and tortuosity by processing the data relative to measurements of the wave reflected by the first interface. The viscous and thermal characteristic lengths cannot be determined via the first interface reflection. The wave reflected by the second interface can be experimentally detected only for the weakly resistive porous materials. In this case, the characteristic lengths can be estimated. But for common air-saturated porous materials, the second reflection is very damped and its experimental detection is difficult. We propose in this paper to solve the inverse problem numerically by the least-squares method, using both reflected and transmitted experimental data. We determine simultaneously all the physical parameters intervening in the propagation. The minimization between experiment and theory is made in the time domain. The inverse problem is well posed, and its solution is unique. As with the classic ultrasonic approach for characterizing porous material saturated with one gas, the characteristic lengths are estimated by assuming a given ratio between them. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.