  The Marchenko method retrieves the responses to virtual sources in the
Earth's subsurface from reflection data at the surface, accounting for all
orders of multiple reflections. 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. Recently new representations were derived,
which handle imperfectly sampled data. These new representations use
point-spread functions (PSFs) that reconstruct results as if they were acquired
using a perfect geometry. Here, the iterative Marchenko scheme is adapted,
using these new representations, to account for imperfect sampling. This 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.
