The knowledge that a gravity anomaly is due to an edge effect is sufficient to resolve the inherent ambiguity of the inverse potential problem. Thus given the gravity field across the contact between two laterally uniform structures, the density difference between the adjacent sections can be calculated by means of integral transforms operating on the data. The Backus-Gilbert inversion technique allows a rational trade-off between accuracy and resolution. The kernels associated with the physics of the problem indicate a resolution comparable to that of surface waves.