Separation and reconstruction of simultaneous source data via iterative rank reduction

We have developed a rank-reduction algorithm based on singular spectrum analysis (SSA) that is capable of suppressing the interferences generated by simultaneous source acquisition. We evaluated an inversion scheme that minimizes the misfit between predicted and observed blended data in t-x domain subject to a low-rank constraint that is applied to data in the f-x domain. In particular, we developed an iterative algorithm by adopting the projected gradient method with the SSA filter acting as the projection operator. This method entails extracting small patches of data from a common receiver gather and organizing the spatial data at a given monochromatic frequency into a Hankel matrix. For the ideal unblended data, Hankel matrices extracted from the data are of low rank. The incoherent interferences in common-receiver domain caused by simultaneously fired shots increase the rank of the aforementioned Hankel matrices. Therefore, rank-reduction filtering is an effective way to annihilate source interferences while preserving the unblended signal. Through tests with synthetic examples, we found that the interference can be effectively suppressed by the proposed method. In addition, we found that the proposed algorithm can be modified to simultaneously cope with deblending and data recovery. A real survey acquired in the Gulf of Mexico was used to mimic a simultaneous-source acquisition with missing shot locations. The algorithm was able to recover the missing shot gathers from the blended acquisition with an improvement of the signal quality of approximately 12 dB.