Interferometric redatuming with simultaneous and missing sources using sparsity promotion in the curvelet domain

Interferometric redatuming is a velocity-independent method to turn downhole receivers into virtual sources. Accurate redatuming involves solving an inverse problem, which can be highly ill-posed, especially in the presence of noise, incomplete data and limited aperture. We address these issues by combining interferometric redatuming with transform-domain sparsity promotion, leading to a formulation that deals with data imperfections. We show that sparsity promotion improves the retrieval of virtual shot records under a salt flank. To reduce acquisition costs, it can be beneficial to reduce the number of sources or shoot them simultaneously. It is shown that sparse inversion can still provide a stable solution in such cases.