Wideband acoustic response of fluid-saturated porous rocks: Theory and preliminary results using waveguided samples

Abstract

The complex dilatational (C*12) and shear (C*44) frequency-dependent elastic constants of nonporous and porous solids are measured in a frequency range 5kHz to 1 MHz. The measurements are performed in a continuous wave acoustic transmission bridge using cylindrical samples. Using samples with free external surfaces produces waveguided modes, enabling experiments to be conducted circumventing problems of diffraction and wavefront spreading, which are difficult to correct over broad frequency ranges. The theory of waveguided elastic wave propagation in isotropic media with complex elastic constants [generalization of the Pochammer–Cree solution, Pochammer, J. Math. (Crelle) 81, 324 (1876)] is presented. For solids with frequency-independent complex elastic constants (constant Q), solution of the resulting dispersion relations reveals the appearance of specific dissipation peaks associated with waveguide geometry. The dispersion relations are utilized in the inversion of torsional shear and extensional experimental results from nonporous and porous solids, thus obtaining their complex frequency-dependent effective elastic constants. A great variation in the elastic constants of Plexiglas with frequency is demonstrated. Evidence of the effects of pore scattering and the reduction of matrix moduli due to water adsorption is shown for porous glass. The effects of adsorption on the effective elastic moduli of porous solids are quantified utilizing the concept of surface elastic constants [M. E. Gurtin and I. A. Murdoch, Arch. Rat. Mech. Anal. 57, 291 (1975)]. The resulting equation reveals the importance of the surface to volume ratio in determining the effective elastic constants.