Local slopes carry useful information about the directionality of the predominant events in a seismic dataset and therefore can be used to steer the reconstruction process of sparsely sampled data. However, in the presence of spatial aliasing (for example, in the crossline direction of streamer data), conventional algorithms fail to provide a reliable estimate of such slopes and only low-frequency, smooth versions of the slope field can be produced. We show that provided the availability of multi-component data, and more precisely the pressure wavefield and its first-order gradient, such slopes are naturally embedded in the data and can be easily obtained by smoothed division of those wavefields. We further show that the estimated slopes can be used as regularization in a multi-channel sparse interpolation problem, providing additional guidance to the reconstruction process compared just using the pressure data and its gradient at the available traces. Numerical examples on 2D and 3D datasets confirm the effectiveness of the proposed two-stage process for multi-channel seismic data reconstruction.

The Marchenko redatuming approach reconstructs wavefields at depth that contain not only primary reflections, but also multiply-scattered waves. While such fields in principle contain additional subsurface information, conventional imaging approaches cannot tap into the information encoded in internal multiples in a trivial manner. We discuss a new approach that uses the full information contained in Marchenko-redatumed fields, whose output are local reflection and transmission responses that fully enclose a target volume at depth, without contributions from over- or under-burden structures. To obtain the Target-Enclosing Extended Images (TEEIs) we solve a multi-dimensional deconvolution (MDD) problem that can be severely ill-posed, so we offer stable estimates to the MDD problem that rely on the physics of the Marchenko scheme. We validate our method on ocean-bottom field data from the North Sea. In our field data example, we show that the TEEIs can be used for reservoir-targeted imaging using reflection and, for the first time, local transmission responses, shown to be the direct by-product of using internal multiples in the redatuming scheme. Finally, we present local, TEEI-derived reflection and transmission images of the target volume at depth that are structurally consistent with a benchmark image from conventional migration of surface data.