  This paper is concerned with the inverse scattering problem of time-harmonic
elastic waves by an unbounded rigid rough surface. A direct imaging method is
developed to reconstruct the unbounded rough surface from the elastic scattered
near-field Cauchy data generated by point sources. A Helmholtz-Kirchhoff-type
identity is derived and then used to provide a theoretical analysis of the
direct imaging algorithm. Numerical experiments are presented to show that the
direct imaging algorithm is fast, accurate and robust with respect to noise in
the data.
