The geomagnetic field over sedimentary basins is very sensitive to variations in basement depth. Therefore, magnetic surveys are widely used to map basement topography in petroleum and groundwater exploration. We propose variogram analysis as a more accurate alternative to power spectral methods. Data variograms are computed from aeromagnetic flight-line data. To estimate depth, the data variograms are compared with model variograms for a range of source depths. We use the exact space domain counterparts of a fractal power spectral model as model variograms. To demonstrate the utility of this method for groundwater exploration, we map the basement topography of the Omaruru Alluvial Plains in Namibia. A comparison with electromagnetic (EM) resistivities and drilling information confirms the high accuracy - but also the limitations - of variogram analysis depth. Variogram analysis makes maximum use of short-wavelength contributions to the magnetic signal, which is the key to the resolution of shallow basement topography. Moreover, by using a realistic source model and avoiding extensive data preconditioning and the transform to wavenumber domain, variogram analysis is likely to provide improved magnetic depth estimates even for deep basins.