It is known that in the North Sea basin the depths to major reflectors as determined from surface seismic data are often larger than the well-log depths. From a study of data sets which tie 21 wells, I found a strong correlation between the occurrence of the depth error and the presence of shales in the subsurface. Assuming that the error is caused by elliptical velocity anisotropy in shales, I measured the anisotropy from a comparison of the well-log sonic data and the interval velocity profile obtained from the surface seismic data and also from a comparison of the seismic depth and the well-log depth. It was found that the two methods of measurements agree with each other and also agree qualitatively with the previous laboratory measurements of anisotropy in shale samples. The results strongly suggest that the depth anomaly in the North Sea basin is caused by the velocity anisotropy of shales. A simple method to correct the seismic depth is given.