High‐resolution shallow‐seismic experiments in sand, Part II: Velocities in shallow unconsolidated sand

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Abstract
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.