Impedance and Ellipticity of Fluid/Porous-Medium Interface Waves: Medium Characterization and Simultaneous Displacement–Pressure Measurements

Abstract

The framework introduced in Chap. 6 is extended to the fluid/ porous-medium interface waves, both in view of the parameter estimation from full-waveform attributes, and of the two-component detection and extraction of impedances. We find that the impedance and ellipticity of each of the pseudo-Rayleigh ($pR$) and pseudo-Stoneley ($pSt$) waves can be combined in a cost function to uniquely estimate Young’s modulus and Poisson’s ratio of the porous frame. The $pSt$-wave gives the most stable estimates. Further, unique and stable estimates of permeability and porosity are obtained from the combination of the $pSt$-wave impedance and attenuation when frequencies around Biot’s rollover frequency are incorporated. For much lower frequencies, the best results are obtained using the $pSt$-wave attenuation only, which has the strongest sensitivity to permeability and porosity as it is governed by the radiation of the slow compressional mode. The impedances of the ultrasonic $pR$- and $pSt$-waves at the water/water-saturated QF20 (artificial porous material) interface cannot be successfully extracted using the experimental set-up introduced in Chap. 6: the $pSt$-wave interferes with the fluid compressional wave and the $pR$-wave behaves as a guided wavemode due to sample size limitations. Using a computational model (Chaps. 4 and  5) it can be shown, however, that the $pR$-wave impedance can be extracted once these limitations are overcome.