Iterative deblending with multiple constraints based on shaping regularization

Introduction

Modern seismic acquisition requires a high-density, wide-azimuth coverage for improving the subsurface illumination. Large acquisition systems require a highly efficient acquisition deployment. The principal purpose of simultaneous source acquisition is to accelerate the acquisition of a large-density seismic dataset, which can save acquisition cost and increase data quality. The benefits are compromised by the intense interference between different shots Abma and Yan (2009); Berkhout (2008); Beasley et al. (1998). Fig 1 shows a demonstration of the marine multi-source acquisition (two sources involved). The two sources shoot with a small random time dithering and thus will cause strong interference to the other source. The shooting time of each shot (shot schedules) are predefined in a separation-guided fashion and should be recorded correctly in order to formulated the inverse problem for source separation.

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Figure 1. A demonstration of the marine two-source acquisition.

One approach to solve the problem caused by interference is by a first-separate and second-process strategy Chen et al. (2014a); Berkhout (2008); Abma and Yan (2009); Beasley et al. (1998), which is also called deblending. Another way is by direct imaging and inversion of the blended data by attenuating the interference during the inversion process Verschuur and Berkhout (2011); Berkhout (2008); Xue et al. (2014); Chen et al. (2015).

There are generally two types of deblending approaches that have been investigated in the literature: (1) treating deblending as a noise filtering or attenuation problem Chen et al. (2014b); Qu et al. (2015); Huo et al. (2012); Chen (2014), (2) treating deblending as an inversion problem Chen et al. (2014a); Abma et al. (2010); Cheng and Sacchi (2015). Most of the filtering based approaches are based on median filtering (MF). Huo et al. (2012) used a multidirectional vector median filter after resorting the data into common midpoint gathers. Chen et al. (2014b) proposed using the common midpoint domain for deblending using a simple MF, because of the better coherency of useful signals than that in other domains and also because the useful near-offset events follow the hyperbolic assumption and can thus be flattened using normal moveout (NMO) correction. Chen (2014) proposed a type of MF with spatially varying window length. The space-varying median filter (SVMF) does not require the events to be flattened. For inversion based approaches, the ill-posed property of the inversion problem requires some constraint to regularize the inversion problem. Akerberg et al. (2008) used sparsity constraints in the Radon domain to regularize the inversion. Abma et al. (2010) proposed using $f-k$ domain sparsity as a constraint. Bagaini et al. (2012) compared two separation techniques for the dithered slip-sweep (DSS) data using the sparse inversion method and f-x predictive filtering Chen and Ma (2014); Gan et al. (2015); Canales (1984), and pointed out the advantage of the inversion methods over the filtering based approaches. In order to deal with the aliasing problem, Beasley et al. (2012) proposed the alternating projection method (APM), which chooses corrective projections to exploit data characteristics and appears to be less sensitive to aliasing than other approaches.

Currently, deblending is the crucial subject for obtaining a successful marine simultaneous-source acquisition. While the industry has obtained encouraging success in 3D deblending problem (e.g. OBN based 3D acquisition), the 2D deblending problem (e.g. marine towed-streamer acquisition) is still in trouble mainly because of the limited constraints that one can put onto the inversion problem. Chen et al. (2014a) proposed a general iterative deblending framework via shaping regularization Fomel (2007). The constraint for the ill-posed inversion problem is applied via the shaping operator which amounts to thresholding in the transformed domain. In this paper, I propose a new iterative deblending approach based on shaping regularization. Instead of simply enforcing the sparsity constraint in the sparse transform domain, I propose to use iterative orthogonalization to compensate the energy loss during the sparsity-constrained inversion. I iteratively threshold each deblended data in the seislet transform domain Fomel and Liu (2010) and orthogonalize the deblended data and blending interference in order to mitigate the energy loss during each iteration. The proposed approach differs from the conventional deblending approaches by applying multiple constraints based on the shaping regularization framework. I apply this approach to both synthetic and field data example and demonstrate its superior performance in obtaining more precise deblended results.

Iterative deblending with multiple constraints based on shaping regularization