An analysis of acquisition-related subsampling effects on Marchenko focusing, redatuming, and primary estimation

Marchenko methods can retrieve both Green’s functions and focusing functions from single-sided reflection data and a smooth velocity model, as essential components of a redatuming process. Recent studies also show that a modified Marchenko scheme can reconstruct primary-only reflection responses directly from reflection data without requiring a priori model information. To provide insight into the artifacts that arise when input data are not ideally sampled, we study the effects of subsampling in both types of Marchenko methods in 2D earth and data — by analyzing the behaviour of Marchenko-based results on synthetic data subsampled in sources or receivers. We show with a layered model that for Marchenko redatuming, subsampling effects jointly depend on the choice of integration variable and the subsampling dimension, originated from the integrand gather in the multidimensional convolution process. When reflection data are subsampled in a single dimension, integrating on the other yields spatial gaps together with artifacts while integrating on the subsampled dimension produces aliasing artifacts but without spatial gaps. Our complex subsalt model shows the subsampling may lead to very strong artifacts, which can be further complicated by having limited apertures. For Marchenko-based primary estimation (MPE), subsampling below a certain fraction of the fully-sampled data can cause MPE iterations to diverge, which can to some extent be mitigated by using more robust iterative solvers, such as LSQR. Our results, covering redatuming and primary estimation in a range of subsampling scenarios, provide insights that can inform acquisition sampling choices as well as processing parameterization and quality control, e.g., to set up appropriate data filters and scaling to accommodate the effects of dipole fields, or to help ensuring that the data interpolation achieves the desired levels of reconstruction quality that minimize subsampling artifacts in Marchenko-derived fields and images.