Ultrasonic characterization of air-saturated double-layered porous media in time domain

Abstract

This paper concerns the ultrasonic characterization of air-saturated double-layered porous materials by solving the inverse problem using experimental reflected signals at normal incidence. The double-layered porous media consist of two slabs of homogeneous isotropic porous materials with a rigid frame. The ultrasonic propagation in double-layered porous material is modeled using a temporal model in which the inertial effects are described by the tortuosity. The viscous and thermal losses of the medium are described by two susceptibility kernels which depend on the viscous and thermal characteristic lengths. The sensitivity of porosity, tortuosity, and viscous characteristic length of each layer is studied showing their effect on the reflected interface waveforms. The inverse problem is solved numerically by the least-squares method. Five parameters are inverted: porosity and tortuosity of the two layers and the viscous characteristic length of the first layer. The minimization of the discrepancy between experimental and theoretical data is made in the time domain. The inverse problem is shown to be well posed and its solution to be unique. Experimental results for waves reflected by the interfaces of the double-layered porous material are given and compared with theoretical predictions.