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Marchenko methods can retrieve 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 indicate 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 behavior of Marchenko-based results on synthetic data subsampled in sources or receivers. With a layered model, we find 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, whereas integrating on the subsampled dimension produces aliasing artifacts but without spatial gaps. Our complex subsalt model indicates that 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 be mitigated to some extent by using more robust iterative solvers, such as least-squares QR. 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.

Summary The correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green’s function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green’s function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2D examples, our exact R/T approach can be extended to 3D and various cases with different interface configurations in arbitrarily complex media, incorporating, e.g., anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow, and so on.