We present a calculation of the elastic displacements due to periodic lines of force at a surface or buried under the surface. This applies, for example, to steps on vicinal surfaces or to self-organized one-dimensional systems. The choice of a calculation in the reciprocal space allows a detailed description of the topography of the displacement field. Far from the surface, the elastic crystal behaves like a low-$q$ filter and the displacement topography does not depend on the details of the force distribution but mainly on the surface orientation. Near the surface, vortices always appear; their characteristics depend mainly on the force orientation rather than the surface orientation. For step-step interactions, the vortices are responsible for the important role of the lever arm orientation of the dipoles associated with steps.

• Received 17 October 2005

DOI:https://doi.org/10.1103/PhysRevB.73.045434