In a simultaneous source survey, the source firing time interval is not limited by the shot record recording time and thus a huge acquisition efficiency can be obtained. However, the price to be paid is that the recorded seismic data is contaminated by strong blending interference and extra processing effort is needed to separated the blended wavefields. Central to the deblending approach described in this paper is the seislet transform, which is used to map the blended data such that, under a sparseness constraint, the blended components are mapped to different regions in the seislet domain and can be separated. Within the seislet transform, the local slope map needs to be calculated for the prediction and updating operations. However, it is difficult to estimate local slopes in the presence of strong noise, especially for blended data. Therefore, in this paper, we propose a novel deblending flowchart based on an iterative seislet deblending process. A real blended marine data example demonstrates its effectiveness for the purpose of deblending.

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 ℓ₁ 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.