Seismic data interpolation plays a fundamental role in seismic data processing, which provides the regularly sampled seismic data for the following jobs like 3D SRME and wave equation-based migrations (Xu et al., 2010). There has been a number of effective methods to recover missing seismic traces, these methods can be generally divided into three types. The first kind is based on a convolution operator, which utilizes a prediction filter computed from the low-frequency parts to predict the high-frequency components (Wang, 2002; Spitz, 1991; Porsani, 1999). However, the predictive filtering method can only be applied to regularly sampled seismic data (Naghizadeh and Sacchi, 2007). The second type is a transformed domain method, which is based on a sparsity assumption and makes use of the theory of compressive sensing or compressive sampling (CS) (Donoho, 2006; Mallat, 2009; Herrmann, 2010; Candès et al., 2006) to achieve a successful recovery using highly incomplete available data (Sacchi et al., 1998; Wang, 2003; Zwartjes and Gisolf, 2007; Yang et al., 2013b; Zwartjes and Sacchi, 2007; Yang et al., 2012). Naghizadeh and Sacchi (2007) proposed a multistep autoregressive strategy which combines the first two types of methods to reconstruct irregular seismic data. The third type is based on the integral of continuation operators. This integral is performed based on the traveltime calculation from a velocity model, thus it depends on the known velocity model, which also becomes its limitation (Stolt, 2002; Canning and Gardner, 1996; Bleistein and Jaramillo, 2000; Fomel, 2003).
A recently very popular way for interpolating irregularly sampled seismic data is by using iterative thresholding, such as projection onto convex sets (POCS) and iterative shrinkage thresholding (IST), mainly because of their simple formulations and convenient implementations. Different thresholding approaches will lead to different performances for interpolation.
Because of the advancement of the non-convex optimization algorithms, a half-thresholding algorithm has been proposed both in signal-processing and exploration geophysics communities (Xu et al., 2012; Yang et al., 2013a). In this paper, we summarize a general thresholding framework for IST algorithm. The only difference among soft, hard, and half thresholding lays in the thresholding operator. Thus, a percentile thresholding strategy, which is particularly useful in practice, can be straightforwardly applied to the case of half thresholding. We use both synthetic and field data examples to demonstrate the performance of our proposed percentile-half-thresholding algorithm, compared with other three existing approaches.