  The Marchenko method retrieves the responses to virtual sources in the
subsurface, accounting for all orders of multiples. The method is based on two
integral representations for focusing and Green's functions. In discretized
form these integrals are represented by finite summations over the acquisition
geometry. Consequently, the method requires ideal geometries of regularly
sampled and co-located sources and receivers. However, a recent study showed
that this restriction can, in theory, be relaxed by deconvolving the
irregularly-sampled results with certain point spread functions (PSFs).The
results are then reconstructed as if they were acquired using a perfect
geometry. Here, the iterative Marchenko scheme is adapted in order to include
these PSFs; thus, showing how imperfect sampling can be accounted for in
practical situations. Next, the new methodology is tested on a 2D numerical
example. The results show clear improvement between the proposed scheme and the
standard iterative scheme. By removing the requirement for perfect geometries
the Marchenko method can be more widely applied to field data.
