A comparison of broadband models for sand sediments

Chotiros and Isakson [J. Acoust. Soc. Am. 116(4), 2011-2022 (2004)] recently proposed an extension of the Biot-Stoll model for poroelastic sediments that makes predictions for compressional wave speed and attenuation, which are in much better accord with the experimental measurements of these quantities extant in the literature than either those of the conventional Biot-Stoll model or the rival model of Buckingham [J. Acoust. Soc. Am. 108(6), 2796-2815 (2000)]. Using a local minimizer, the Nelder-Mead simplex method, it is shown that there are generally at least two choices of the Chotiros-Isakson parameters which produce good agreement with experimental measurements. Since one postulate of the Chotiros-Isakson model is that, due to the presence of air bubbles in the pore space, the pore fluid compressibility is greater than that of water, an alternative model based on a conjecture by Biot [J. Acoust. Soc. Am. 34(5), 1254-1264 (1962)], air bubble resonance, is considered. While this model does as well or better than the Chotiros-Isakson model in predicting measured values of wave speed and attenuation, the Rayleigh-Plesset theory of bubble oscillation casts doubt on its plausibility as a general explanation of large dispersion of velocity with respect to frequency.