Deblended-data Reconstruction Using Generalized Blending and Deblending Models

We introduce a generalized concept of blending and deblending, and establish the generalized-blending 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 and inhomogeneous shooting, signature stamping, non-uniform and under sampling. Similarly, the generalized deblending includes data reconstruction that works all for shot-generated-wavefields separation, spectrum recovery and balancing, designature, 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, we consider an iterative optimization scheme using a so-called closed-loop approach with the generalized-blending and -deblending models, in which the former works for the forward modelling and the latter for the inverse modelling in the closed loop. We established and applied this method to synthetic datasets. The results show that our method succeeded to fully reconstruct deblended data from the fully generalized blended data.