Adaptation of the iterative Marchenko scheme for imperfectly sampled data

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 colocated 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 2-D numerical data example. The results show clear improvement of the proposed scheme over the standard iterative scheme. By removing the requirement for perfect geometries, the Marchenko method can be more widely applied to field data.