We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three-component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively.
The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz-Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz-Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086.
The second disparity is between the observed Poisson's ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson's ratio increases.