Compressional-wave velocities in attenuating media: A laboratory physical model study

Elastic-wave velocities are often determined by picking the time of a certa in feature of a propagating pulse, such as the first amplitude maximum. How ever, attenuation and dispersion conspire to change the shape of a propagat ing wave, making determination of a physically meaningful velocity problema tic. As a consequence, the velocities so determined are not necessarily rep resentative of the material's intrinsic wave phase and group velocities. Th ese phase and group velocities are found experimentally in a highly attenua ting medium consisting of glycerol-saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from similar to 200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepa ncy but are in poor agreement with the corresponding phase velocity. Wave v elocities determined from the time at which the pulse is first detected (si gnal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high- frequency limit of the phase velocity in a material where wave velocity inc reases with frequency. Each method of time picking, however, is self-consis tent, as indicated by the high quality of linear regressions of observed ar rival times versus propagation distance.