Finite-difference modeling is used to investigate the conjecture that, by cross-correlating noise traces recorded at the surface, we can construct what would be recorded at one of locations if there was a source at the other. Synthetic experiments are conducted on a variety of Earth models with lateral variations in velocity. For each model, conventional seismograms are compared with seismograms constructed by cross-correlating noise traces. Sources of the ambient noise are first taken to be at infinity (planar wavefronts), and then within the zone of interest (curved wavefronts). The kinematics of the reflection events in all the cross-correlation seismograms are consistent with the conventional seismograms, suggesting the conjecture is robust to moderate lateral velocity variations and the location of the source of the background noise. In cases where most of the incoming energy has one angle of incidence, it is shown that by applying a weighting function in the slant-stack domain, the coherency of hyperbolic reflection events is increased.