Detection of fast and slow waves propagating through porous media

Abstract

Porous media can support two longitudinal waves, which often overlap in time and frequency domains. Each wave has its own attenuation coefficient and phase velocity. These properties are related to volume fraction of solid phase, tortuosity, viscous characteristic length, and elasticity. Therefore, knowledge of individual wave properties is useful for characterizing porous media. Accordingly, methods for recovering separate reconstructions of fast and slow waves are of interest. The transfer function of a porous sample may be expressed as a weighted sum of two complex exponentials. The Modified Least Squares Prony’s (MLSP) method may be used to recover the two individual components for non-dispersive media. Porous media are dispersive, however. The MLSP method may be augmented with curve-fitting (MSLP + CF) to account for dispersion. An alternative approach, based on Bayesian probability theory, is also powerful for recovering fast and slow waves. These approaches have been tested in through-transmission experiments on cancellous bone samples. Bayesian and MLSP + CF approaches successfully separated fast and slow waves and provided good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains.