Estimation of sand dune thickness using a vertical velocity profile

Previous field and mathematical studies have shown that sand dunes may have vertical velocity profiles (i.e., continuous increase of velocity with depth). Therefore, computing the dune's thickness using conventional seismic refraction methods that assume a vertically homogeneous layer will likely produce some errors. The purpose of this study is to quantify the effect of the vertical velocity profile in a sand dune on the process of thickness estimation using seismic refraction data. First, the time-distance (T-X) data of the direct wave in the dune is calculated using a vertical velocity profile, V(z), derived from Hertz-Mindlin contact theory. Then, the thickness is estimated from the calculated T-X data, intercept time, and velocity of the refractor at the dune's base assuming a constant velocity in the dune. The error in the estimated thickness due to the constant-velocity assumption increases with increasing thickness and decreasing porosity of the dune. For sand dunes with porosities greater than 0.2 and thicknesses less than 200 m, the error is less than 15%.