Abstract
Marchenko focusing and imaging are novel methods for correctly handling multiple scattered energy while processing seismic data. However, strict requirements in the acquisition geometry, specifically the colocation of sources and receivers as well as dense and regular sampling, currently constrain their practical applicability. We have reformulated the Marchenko equations to handle the case in which there are gaps in the source geometry while the receiver sampling remains regular (or the opposite, by means of reciprocity). Using synthetic data based on a velocity model that produces strong interbed multiples, we test different solvers for the newly formulated inversion problem, and we compare these results to results obtained by applying standard Marchenko inversion to a previously reconstructed data set. When using the unreconstructed data set, the ability of the Marchenko equations to retrace multiple reflected energy deteriorates. Sparsity-promoting Marchenko inversion, while improving the appearance of focusing functions, barely decreases multiple leakage in gathers and does not visibly improve the final image when compared to standard least-squares inversion. On the other hand, reconstructing the wavefield in advance restores the proper functioning of the Marchenko methods. Further, we test a joint inversion technique designed for time-lapse data with nonrepeated geometries and originally intended to be solved using sparsity promoting inversion. Motivated by our previous results, we compare images produced by this method to images produced by solving the same joint inversion problem without sparsity constraint. We find that the joint inversion alone hardly improves the resulting images but, when combined with the sparsity constraint, it leads to better noise and multiple suppression and produces a clean time-lapse image. Overall, none of the results from sparsity-promoting inversion techniques match the results obtained when reconstructing the wavefield in advance. We show that this can be explained by the comparatively slow convergence rate of the sparsity-promoting Marchenko inversion.