We present analytic expressions for the static deformations produced by point forces and point force couples embedded in two elastic Poissonian half-spaces that are welded on a horizontal interface. We show that the deformations from point forces and from vertically dipping strike-slip point double couples vary continuously (except at the strike-slip source) as the source is moved across the welded interface. We show that the pattern of deformations from vertically dipping (or horizontally dipping) dip-slip point double couples also vary continuously as the source is moved across the welded interface, but the amplitude of the deformations jumps by the ratio of the rigidities. Finally, we show that the pattern of deformation from a point explosion source or from a point double-couple source dipping at angles other than 0° or 90° jumps as the source is moved across the boundary. We demonstrate that integration of point double-couple sources on a plane of finite extent mimics the deformation of slip on a fault plane where the total moment of the double-couples is μAD. We also demonstrate that deformations from a distribution of double couples on a horizontally dipping finite plane just above the interface are indistinguishable from the deformations produced by a similar distribution of double couples located just below the interface but with a total moment that is different by the ratio of the rigidities. This demonstrates that the moment of a dislocation that occurs between two materials is ambiguously defined. We discuss reasons why seismic moment is not a very satisfying way to parameterize the size of an earthquake. We show that potency, defined to be the integral of the slip over the rupture surface, is a more natural size scaling parameter than seismic moment.