The frequency-dependent seismic properties of cracked and fluid-saturated glass-bead media

The expected frequency dependence of seismic wave velocities in cracked and fluid-saturated crustal rocks complicates the use of laboratory velocity measurements, traditionally limited to MHz frequencies, for interpretation of seismic data collected at lower frequencies. For appropriately low frequencies of wave propagation, such dispersion results from the relaxation of spatial gradients in pore-fluid pressure by fluid flow. The solution to this dilemma lies in laboratory measurements of elastic velocities, or corresponding moduli, over an appropriately wide range of frequencies. To this end, conventional measurements with ultrasonic (MHz) wave propagation methods are being complemented by sub-resonant forced-oscillation techniques that provide access to lower frequencies. Ultrasonic measurements of P and S wave velocities, and forced-oscillation measurements in both torsional and flexural modes at low frequencies (MHz-Hz), have been conducted on a series of soda-lime silica glass samples with porosities varying from 0 to 6%. Samples were prepared either from dense glass rod or by sintering glass beads under controlled conditions, and subjected to subsequent thermal cracking. All samples are successively tested dry, and with argon and water as pore fluids. The results show systematic increases in wave velocities or elastic moduli with increasing differential pressure (confining pressure minus pore pressure) – interpreted in terms of crack closure. Fluid saturation, especially with water, results in a substantial increase in the moduli measured at MHz frequencies - evidence that the ultrasonic technique is sampling the saturated isobaric regime. A micromechanical model, based on Eshelby's results and using the differential effective medium scheme, yields crack aspect ratios and crack density as functions of pressure, as well as providing theoretical estimates of the effect of saturation and frequency on elastic moduli. Such dispersion between Hz and MHz frequencies needs to be taken into account in seismological applications of laboratory wave-speed measurements.