This paper is concerned with the inverse scattering of acoustic waves by
an unbounded periodic elastic medium in the three-dimensional case. A
novel uniqueness theorem is proved for the inverse problem of recovering
a bi-periodic interface between acoustic and elastic waves using the
near-field data measured only from the acoustic side of the interface,
corresponding to a countably infinite number of quasi-periodic incident
acoustic waves. The proposed method depends only on a fundamental a
priori estimate established for the acoustic and elastic wave fields and
a new mixed-reciprocity relation established in this paper for the
solutions of the fluid-solid interaction scattering problem.