Seismograms have been generated by cross-correlating noise traces for a variety of Earth models with moderate lateral variations in velocity. Sources of the ambient energy were modeled to be both at infinity, leading to plane waves at the Earth's surface, and within the zone of interest, leading to diverging wavefronts at the surface. In all cases the kinematic of the reflections agree with either the results of a conventional seismic reflection experiment (or with simple ray theory) to within the resolution of the finite-difference modeling. This suggests that the kinematics of the cross-correlation method are robust to moderate lateral velocity variations, and the location of the sources of the ambient noise.
However, both lateral variations in velocity and source locations at finite distance mean the wavefronts arriving at the surface are not planar. Although this does not affect the kinematics of the reflections, it does affect the kinematics of the first arrival, the event that resembles the direct wave.
In cases where most of the incoming energy has one angle of incidence it is recognized that it may be beneficial to apply a filter which whitens the slowness spectra of the incoming energy. In this paper we have applied a weighting function in the slant-stacked shot domain. This approach works best for a plane-layered Earth