Using sparsity to improve the accuracy of Marchenko imaging given imperfect acquisition geometries

Marchenko focusing and imaging are novel methods for processing seismic data while correctly handling multiply scattered energy. Strict requirements in the acquisition geometry, specifically co-location of sources and receivers as well as dense and regular sampling, currently constrain their practical applicability. We reformulate the Marchenko equations to handle the case where there are gaps in the source geometry while receiver sampling remains regular. Comparing different solvers for the newly formulated inversion problem, we find that sparse Marchenko inversion enhances the recovery of focusing functions, filling the gaps caused by the missing sources. This does, however, not translate into a significant improvement in the subsequently produced images, as both least-squares and sparse inversion struggle to eliminate overburden effects in the presence of gaps. Further, we develop a method for co-processing two time-lapse datasets with different source geometries using sparse Marchenko inversion to image 4D effects. Sparse joint Marchenko inversion of multiple datasets results in clear time-lapse images, despite non-repeated source geometries and large fractions of missing sources.