We introduce a generalized concept of the so-called blending and deblending, and establish the generalizedblending and -deblending models. Accordingly, we establish a method of deblending, or deblended-data reconstruction, using these models. The generalized blending can handle real-life situations; this includes random encoding both in the space and time domain, both at the source and receiver side, thus all incoherent shooting, inhomogeneous shooting, non-uniform and under sampling. Similarly, the generalized deblending includes data reconstruction that works for all shot-generated-wavefields separation, spectrum recovery and balancing, regularization and interpolation, again both at the source and receiver side. However, we do face a challenging question: how to fully reconstruct deblended data from the fully generalized blended data. To address this challenge, we consider an iterative optimization scheme using a so-called closed-loop approach. We use the properties of blended signal specified by the blending code: the coherency of blended signal versus the incoherency of blending noise in the pseudo-deblended domain. This can be posed as an inverse problem with quantifying the coherency and its solutions by selecting optimal metrics of the coherency. We applied this method to synthetic datasets. The results show that our method succeeded to fully reconstruct deblended data from the fully generalized blended data. We discuss its applicability to time-lapse seismic monitoring as it ensures high repeatability of the surveys. Our methodology should reduce the repeatability problem because reconstructing deblended data in monitor surveys is much more realistic and reliable than positioning sources and receivers exactly as the baseline survey.

Surface waves in seismic data are often dominant in a land or shallow-water environment. Separating them from primaries is of great importance either for removing them as noise for reservoir imaging and characterization or for extracting them as signal for near-surface characterization. However, their complex properties make the surface-wave separation significantly challenging in seismic processing. To address the challenges, we propose a method of three-dimensional surface-wave estimation and separation using an iterative closed-loop approach. The closed loop contains a relatively simple forward model of surface waves and adaptive subtraction of the forward-modelled surface waves from the observed surface waves, making it possible to evaluate the residual between them. In this approach, the surface-wave model is parameterized by the frequency-dependent slowness and source properties for each surface-wave mode. The optimal parameters are estimated in such a way that the residual is minimized and, consequently, this approach solves the inverse problem. Through real data examples, we demonstrate that the proposed method successfully estimates the surface waves and separates them out from the seismic data. In addition, it is demonstrated that our method can also be applied to undersampled, irregularly sampled, and blended seismic data.