  The paper 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 to some degree of
measurement noise.
