This paper illustrates an inversion approach based on matrix rank reduction that separates simultaneous source data. The algorithm operates on each common receiver gather of a multidimensional data set. We propose to minimize the misfit between the observed data and blended predicted data subject to a low-rank constraint that is applied to the data in the frequencyspace domain. The low rank constraint can be implemented via the classical truncated Singular Valued Decomposition (tSVD) or via a new randomized QR decomposition (rQRd) method. Compared to the tSVD, rQRd significantly improves the computational efficiency of the method. In addition, the rQRd algorithm is less stringent on the selection of the rank of the data. This is important as we often have no precise knowledge of the optimal rank that is required to represent the data. We adopt a synthetic 3D VSP data set to test the performance of the proposed deblending algorithm. Through tests under different survey time ratios, we show that the proposed algorithm can effectively eliminate interferences caused by simultaneous shooting.
Simultaneous source acquisition, or blended acquisition, has been attracting a great deal of attention because of the economic potential it brings to seismic data acquisition (Beasley et al., 1998; Berkhout, 2008). The technique aims at improving the acquisition efficiency by allowing continuous recording of overlapping shots. In simultaneous source acquisition, instead of firing one shot each time and waiting for its seismic response, several shots are fired with at close time intervals. In land acquisition, different phase-encoding schemes have been utilized to distinguish the signal from different Vibroseis (Bagaini, 2006). In marine acquisition, simultaneous shooting relies on the randomization of the firing time delays. This is because random time delays would preserve the coherency of desired signal while perturbing the interference in common receiver, offset and midpoint domains (Stefani et al., 2007). The latter is important as it allows separation of simultaneous source data via a coherent-pass constraint (Abma et al., 2010).
Various techniques have been developed for deblending simultaneous source data. Methods that exploit the low-rank property of the unblended data are of special interest to this paper. Maraschini et al. (2012) utilized the SSA low-rank filter, or equivalently the Cadzow filter, in an iterative manner to suppress the incoherent interference in common offset domain. Cheng and Sacchi (2013) posed deblending as a rank constrained inverse problem and solved it via the gradient projection method.