This paper introduces methods for the detection of anisotropies which are caused by compression of regular 3D point patterns. Isotropy tests based on directional summary statistics and estimators for the compression factor are developed. Using simulated data, the dependence of the power of these methods on the intensity, the degree of regularity, and the compression strength is studied. Finally, our methods are applied to the point patterns of centers of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet and an increase of their strength with increasing depth are shown. © 2009 Springer-Verlag.