Deblending using the focal transformation with an efficient greedy inversion solver

Nowadays, using simultaneous source seismic acquisition is becoming popular in order to achieve a denser source spacing in an efficient manner. For further processing these data need to be deblended, meaning that they have to be separated in their non-overlapping constituents. In this work, we adopt a novel greedy inversion solver to design a faster version of the double focal transform, which we can use to eliminate blending noise in simultaneous source acquisition. The greedy inversion introduces a coherence-oriented mechanism to enhance focusing of the significant model space, leading to a sparse model space and fast convergence rate. Although the convergence rate of greedy inversion is larger than that of the Spectral Projected Gradient for l(1) minimization (SPGL1) solver, the greedy solver is still not fast enough. We propose to use a relative tolerance strategy to speed up the greedy solver: the LSQR (Sparse Equations and Least Squares) algorithm in the inner loop of the greedy solver is stopped when the misfit change between inner iterations is less than a pre-defined relative tolerance value or when it reaches a maximum number of iterations. Synthetics and numerically blended field data examples demonstrate the validity of its application for deblending. We also investigate the effect of random noise on the deblending process, which shows that it is better to apply a denoising process before deblending in order to get an optimum result. (C) 2019 Published by Elsevier B.V.