Separation and reconstruction of simultaneous source data via iterative rank reduction

Abstract

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.

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

“…According to the regularization constraints, there are several different iterative approaches. Most of the successful regularizations (Akerberg et al, 2008;Abma et al, 2010;Chen et al, 2014a;Cheng and Sacchi, 2015) are based on the sparsity constraint in some sparse transform domains. Compared with the filtering methods, deblending via inversion methods usually leads to better separation results (van Borselen et al, 2012).…”

“…Zu et al (2015) design a periodically varying code to achieve a better deblending performance than random code. Li et al (2013) and Cheng and Sacchi (2015) set a hybrid sampling and blending operator to deal with the problem of simultaneous source separation and reconstruction.…”

Applications of low-rank compressed seismic data to full-waveform inversion and extended image volumes

“…There has been a surge of interest in recent years in applying low-rank techniques to seismic data problems, including interpolation (Ma, 2013;Kumar et al, 2015;Aravkin et al, 2014;Trickett et al, 2010), noise attenuation (Freire and Ulrych, 1988;Bekara and Van der Baan, 2007;Nazari Siahsar et al, 2016), estimation of primaries by sparse inversion (Jumah and Herrmann, 2014), simultaneous source deblending (Cheng and Sacchi, 2015;Kumar et al, 2016), and travel-time tomography (Stork, 1992). Extensions of these low-rank ideas to multi-dimensional tensors in the seismic context can be found in, e.g., Kreimer and Sacchi (2012), Kreimer et al (2013), Trickett et al (2013), Da .…”

Blended‐acquisition design of irregular geometries towards faster, cheaper, safer and better seismic surveying

“…For example, Kutscha and Verschuur () and Kontakis and Verschuur () dealt with data reconstruction and deblending respectively using similar inversion frameworks. Some recent studies have jointly handled both deblending and data reconstruction (Cheng and Sacchi ; Ishiyama et al . ; Li et al .…”

“…For example, Kutscha and Verschuur (2012) and Kontakis and Verschuur (2015) dealt with data reconstruction and deblending respectively using similar inversion frameworks. Some recent studies have jointly handled both deblending and data reconstruction (Cheng and Sacchi 2015;Ishiyama et al 2017;Li et al 2013). In principle, deblended and reconstructed data are iteratively estimated in the transform domain together with prior knowledge and/or constraints to data.…”