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.

A high-resolution, very shallow seismic reflection and refraction experiment was conducted to investigate the seismic response of groundwater level changes in beach sand in situ. A fixed 10-m-long receiver array was used for repeated seismic profiling. Direct measurements of water level in a monitoring well and moisture content in the sand were taken as well. The water table in the well changed by about 1 m in slightly delayed response to the nearby ocean tides. In contrast, inversion of the seismic data yielded a totally different picture. The reflection from the water table at high tide appeared at a later time than the reflection at low tide. This unexpected discrepancy can be reconciled using Gassmann's equation: a low-velocity layer must exist between the nearsurface dry sand and the deeper and much faster fully saturated sand. This low-velocity layer coincides with the newly saturated zone and is caused by a combination

By treating contact stiffness as a variable, one can extend the effective medium approximation used to obtain elastic stiffness of a random pack of spherical grains. More specifically, we suggest calibrating effective media approximation based on contact mechanics by incorporating nonuniform contact models. The simple extension of the theory provides a better fit for many laboratory and field experiments and can provide insight into the micromechanical bonds associated with unconsolidated sediments. This approach is motivated by repeated observations of shear-wave measurements in unconsolidated sands where observed shear-wave velocities are lower than predicted by the Hertz-Mindlin contact theory. We present the calibration process for well-log data from a North Sea well penetrating a shallow-gas discovery and a deepwater well in the Gulf of Mexico. Finally, we demonstrate the benefit of using this model for amplitude variation with angle ͑AVA͒ analysis of shallow sand targets in exploration and reservoir studies.

We conducted a shallow high-resolution seismic reflection and refraction experiment on a sandy beach. The depth of investigation was about 2 m . We interpret the data using the Hertz-Mindlin contact theory combined with Gassmann's equation. These were used to obtain the vertical velocity profile. Then the profile was computed from seismic data using the turning-rays approximation. The normal moveout (NMO) velocity at the depth of 2 m matches the velocity profile. As a result, we developed a method to invert measured velocity from first arrivals, i.e., velocity versus distance into velocity versus depth using only one adjustable parameter. This parameter contains all the information about the internal structure and elasticity of the sand. The lowest velocity observed was about 40 m/s. It is noteworthy that the theoretical lower bound for velocity in dry sand with air is as low as 13 m/s. We find that modeling sand as a quartz sphere pack does not quantitatively agree with the measured data. However, the theoretical functional form proves to be useful for the inversion.

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