Wave momentum and scattering of elastic waves by two-dimensional thin objects

The elastic wave momentum equation is applied to scattering of dilatational and shear waves by two-dimensional thin objects. It is shown that the sources of wave momentum are located at the edges of these objects. For a stress-zero crack or for a rigid inclusion there are two sources at each edge, for a fluid-filled crack there is just one. The scattered wave is expressed in terms of these sources. This reduces the number of independent variables by a factor two. An application to inverse scattering problems is also given.