  This paper is concerned with the inverse time-harmonic elastic scattering
problem of recovering unbounded rough surfaces in two dimensions. We assume
that elastic plane waves with different directions are incident onto a rigid
rough surface in a half plane. The elastic scattered field is measured on a
horizontal straight line segment within a finite distance above the rough
surface. A direct imaging algorithm is proposed to recover the unbounded rough
surface from the scattered near-field data, which involves only inner products
between the data. Numerical experiments are presented to show that the
inversion scheme is not only efficient but also accurate and robust with
respect to noise.
