Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization

Introduction

The simultaneous-source technique aims at removing the limitation of no interference between adjacent shots by allowing more than one source to be shot simultaneously. Thus it can reduce the acquisition period and increase spatial sampling (Berkhout, 2008). Because of its economic benefits and technical challenges, this technique has attracted significant attention of researchers in both industry and academia (Mahdad et al., 2011; Moore et al., 2008; Wapenaar et al., 2012; Abma et al., 2012; Huo et al., 2012). The biggest issue involved in simultaneous-source processing is an intense crosstalk noise between adjacent shots, which poses a challenge for conventional processing. One way to deal with this issue is to use a first-separate and second-process strategy, which is also known as deblending (Doulgeris et al., 2012). The other way is by direct imaging and waveform inversion (Plessix et al., 2012; Choi and Alkhalifah, 2012; Xue et al., 2014; Guitton and Diaz, 2012; Berkhout et al., 2012). In this paper, we focus on the deblending approach.

Different filtering and inversion methods have been applied previously to deblend seismic data. Filtering methods utilize the property that the coherency of the simultaneous-source data varies in different domains. Therefore, one can get unblended data by filtering out randomly distributed blending noise in some transform domains, where one source record is coherent and the others are not (Mahdad et al., 2012; Hampson et al., 2008; Huo et al., 2012). Inversion methods treat the separation problem as an estimation problem, which aims at estimating the desired unknown unblended data. Because of the ill-posed nature of such estimation problems, a regularization term is usually required (Doulgeris and Bube, 2012). The regularization term can be chosen as a sparsity promotion in a sparsifying transformed domain (Abma et al., 2010). van Borselen et al. (2012) proposed to distribute all energy in the shot records by reconstructing individual shot records at their respective locations. Mahdad et al. (2011) introduced an iterative estimation and subtraction scheme that combines the properties of filtering and inversion methods and exploits the fact that the characteristics of the blending noise differ in different domains. One choice is to transform seismic data from the common-shot domain to common-receiver, common-offset or common-midpoint domain. Beasley et al. (2012) proposed a separation technique called the alternating projection method, and demonstrated it to be robust in the presence of aliasing.

In this paper, we propose a novel iterative estimation scheme for the separation of blended seismic data. We construct an augmented estimation problem, then use shaping regularization (Fomel, 2008,2007) to constrain the characteristics of the model during the iteration process for obtaining a suitable estimation result. We adopt seislet-domain (Fomel and Liu, 2010) soft thresholding as a robust shaping operator to remove crosstalk noise and at the same time to preserve useful components of seismic data. Shaping regularization maps each model into a more admissible model at each iteration and allows us to solve the deblending problem with a small number of iterations.

This paper is organized as follows: we first present a formulation of numerical blending using an augmented block-matrix equation. We then incorporate shaping regularization to solve the forward equation iteratively and discuss the selection of the backward operator and shaping operator involved in the shaping-regularization iterative framework. Finally, we test the proposed iterative framework on three numerically blended synthetic datasets and one numerically blended field dataset and compare three different choices of the shaping operator: $f-k$ domain thresholding, $f-x$ predictive filtering, and seislet domain thresholding.

Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization