Introduction

Stacking of multiple datasets to output a final smoothed data is a common research subject in many scientific fields. The stacking can be viewed as the simplest form of random noise attenuation for enhancing multi-dimensional remote sensing datasets (Tian et al., 2014; Zhuang et al., 2015). In seismic data processing, stacking simply means the summation of a collection of seismic traces from different records into a single trace. The quality of stacking greatly affect the performance of many seismic data processing tasks. It can be considered as the simplest way for improving the SNR (Elad and Aharon, 2006; Candès et al., 2006) in prestack seismic data processing. It can quickly obtain a meaningful post-stack seismic image without wavefield continuation. The three steps in the stacking process are normal moveout (NMO) velocity analysis, NMO correction and trace summation.

The original weighted stacking used an SNR-based weighted stacking strategy to minimize random noise. Schoenberger (1996) proposed a different weighted stacking approach that can suppress the multiples effectively by solving a set of optimization equations in order to determine the stacking weights. Neelamani et al. (2006) took the signal structures into consideration and proposed a simultaneous stacking and denoising approach (SAD). Based on the statistics theory, Trickett (2007) proposed to use a maximum-likelihood estimator for weighted stacking by estimating the probability distribution of random noise. Tang (2007) calculated the stacking weights as functions of angle and azimuth and proposed a selective stacking approach.

Li and Gao (2014) proposed a novel method for stacking seismic data in time-frequency domain (Lin et al., 2015; Liu et al., 2016). Liu et al. (2009) proposed a similarity-weighted stacking approach that designs the weights of each trace by calculating the local similarity between each trace and a reference trace, and the method was demonstrated to be superior to the state-of-the-art weighted stacking approaches. The reference trace in the traditional similarity-weighted stacking method is an approximated zero-offset trace directly calculated from the spatial arithmetic mean of data matrix (Rubinstein et al., 2010). When the data matrix contains mis-aligned trace, erratic and non-gaussian random noise, the spatial arithmetic mean of the data matrix is of low fidelity to approximate the zero-offset trace. In this letter, we propose a novel principal component analysis (PCA) (Du and Fowler, 2007; Farrell and Mersereau, 2005) based weighted stacking method. Considering the complicated situations of field seismic data as mentioned above, we propose to extract the principal components of seismic data to approximate a highly accurate zero-offset trace. The principal components of the data matrix are extracted via solving an optimization problem with low-rank constraint. A singular value decomposition can be used to efficiently solve the optimization problem and then the low-rank approximation of the data matrix, which has a high SNR and is close to the ideal NMO-corrected common midpoint (CMP) gather, can be easily obtained. The new stacking method is easy to implement and can obtain significantly better stacked profile with cleaner geological structures. We first use a simple synthetic example to show the principle and then use a real pre-stack field data example to further demonstrate the tremendous improvement over the traditional approaches.