Inversion of acoustical parameters of layered media

The inversion of acoustical parameters of layered media composed of three and four layers is considered. The three layered samples used are metal-clad specimens. The four-layered samples contain a thin layer of Mylar. The individual thicknesses range from 0.2 to 18 mm. The raw measurements consist of a reference signal across the immersion liquid and a received signal transmitted across or reflected from the layered media using normal-incidence wave propagation. The inversion procedure is carried out as follows. First, the virgin wave, the leading portion of the received signal that contains no internal reverberations, is reconstructed from the reference signal factored by a transmission coefficient T and shifted by a time {dollar}tau.{dollar} Then the difference in the least squares sense between the virgin wave and the reconstructed virgin wave is minimized to obtain estimates for T and {dollar}tau.{dollar} A sensitivity analysis revealed that {dollar}tau{dollar} is obtained with better precision than T.; Second, the measured transfer function is obtained from the ratio of the Fourier transforms of the received and reference time-domain signals. The magnitude of the transfer function shows sharp resonance peaks for the metal-clad specimens. The resonant frequencies where the peaks occur are measured in the range from 1 to 21 MHz. The model for the resonant frequencies for normal-incidence wave propagation across an N-layered medium depends on 2N parameters out of a total of 3N parameters (for example density, thickness, and wavespeed for each layer). By using the virgin wave parameter {dollar}tau,{dollar} one parameter out of the 2N parameters is written in terms of the remaining unknown {dollar}2N{lcub}-{rcub}1{dollar} parameters and the known parameter {dollar}tau.{dollar} Next, by minimizing in the least squares sense the difference between the measured and calculated resonant frequencies up to {dollar}2N{lcub}-{rcub}1{dollar} parameters are estimated. Assuming the densities are known, the inverted thicknesses and impedances are within {dollar}{lcub}pm{rcub}14 mu{dollar}m and {dollar}pm{dollar}5%, respectively, of the expected values. The sensitivities of the resonant frequencies to the acoustical parameters are studied. The confidence intervals for the estimated parameters are obtained. The deviations of the inverted parameters from expected values are consistent in magnitude with the predicted confidence bounds.