  Precise measurements of the baryon acoustic oscillation (BAO) scale as a
standard ruler in the clustering pattern of large-scale structure is a central
goal of current and future galaxy surveys. The BAO peak may be sharpened using
the technique of density-field reconstruction, in which the bulk displacements
of galaxies are estimated using a Zel'dovitch approximation. We use numerical
simulations to demonstrate how the accuracy of this approximation depends
strongly on local environment, and how this information may be used to
construct an improved BAO measurement through environmental re-weighting and
using higher-order perturbation theory. We outline further applications of the
displacement field for testing cosmological models.
