Separation of simultaneous source data via iterative rank reduction

Abstract

In this paper, we report an inversion algorithm based on singular spectrum analysis (SSA) that is capable of suppressing the interferences generated by simultaneous source acquisition. We derive an iterative scheme that adopts the projected gradient method to solve the source separation problem. The projection operator is the SSA rank reduction filter that suppresses incoherent noise in the frequency-space domain. Convergence of this algorithm can be achieved with appropriate choice of step size and an initial starting point. We use synthetic examples simulated with a data set from the Gulf of Mexico to illustrate this method.

Focal deblending: Marine data processing experiences

“…They do, however, require sorting the elements of the solution into a tensor that exhibits the low‐rank property. A popular choice is to form a Hankel matrix out of monochromatic frequency slices of data in the frequency‐space domain (Cheng & Sacchi, 2013, 2015; Maraschini et al., 2012). Another approach is to sort the data based on mid‐point/half offset coordinates and construct a hierarchically semi‐separable matrix from frequency slices (Wason et al., 2014; Kumar et al., 2015).…”

Source separation via SVD-free rank minimization in the hierarchical semi-separable representation

“…More recently, rank-minimization based techniques have been used for source separation by Maraschini et al (2012) and Cheng and Sacchi (2013). The general idea is to exploit the low-rank structure of seismic data when it is organized in a ma-trix.…”