Reconstruction of rough surfaces from a single receiver at grazing angle

This article develops a method for recovering a one-dimensional rough surface profile from scattered wave field, using a single receiver and repeated measurements when the surface is moving with respect to source and receiver. This extends a previously introduced marching method utilizing low grazing angles, and addresses the key issue of the requirement for many simultaneous receivers. The algorithm recovers the surface height below the receiver point step-by-step as the surface is moved, using the parabolic wave integral equations. Numerical examples of reconstructed surfaces demonstrate that the method is robust in both Dirichlet and Neumann boundary conditions, and with respect to different roughness characteristics and measurement noise.