  We present a numerical study of the spatial correlations of a
quasi-two-dimensional granular fluid kept in a non-static steady state via
vertical shaking. The simulations explore a wide range of packing fractions,
vertical accelerations and restitution coefficients, always staying below the
crystallization limit. From the simulations we obtain the relevant Pair
Distribution Functions (PDFs), and effective potentials for the interparticle
interaction are extracted from these PDFs via the Ornstein-Zernike equation
with the Percus-Yevick closure. The correlations in the granular structures
originating from these effective potentials are checked against the originating
PDF using standard Monte Carlo simulations, and we find in general an excellent
agreement. The resulting effective potentials show an increase of the spatial
correlation at contact with the decreasing values of the restitution
coefficient, and a general tendency of the potentials to display deeper wells
for more dissipative dynamics. An exception to this general trend appears for
certain combinations of density and forcing, where resonant bouncing increases
correlations.
