Due to different reasons, seismic data may have missing traces. Seismic data reconstruction is such a procedure to remove sampling artifacts, and to improve amplitude analysis, which are very important for subsequent processing steps including high-resolution processing, wave-equation migration, multiple suppression, amplitude-versus-offset (AVO) or amplitude-versus-azimuth (AVAZ) analysis, and time-lapse studies Wang et al. (2010); Liu and Sacchi (2004); Zhong et al. (2015); Trad et al. (2002); Naghizadeh and Sacchi (2010); Abma and Kabir (2005). In recent years, due to the development of compressive sensing framework, there are a lot of sparsity-based methods for interpolating irregularly sampled seismic data. However, for regularly missing traces, sparsity-based methods Abma and Kabir (2006); Li et al. (2012); Chen et al. (2014a) can not obtain satisfying results because of the strong aliasing noise in the transform domain. Instead, the prediction-based approaches Naghizadeh and Sacchi (2007); Spitz (1991) are still the best approaches for interpolating regularly missing traces.
In this paper, we propose to use seislet transform to perform a sparsity-based reconstruction, based on the well-established projection onto convex sets (POCS) framework Abma and Kabir (2006). Many numerical studies show that the local slope is the main factor affecting the sparsity and anti-aliasing ability of the seislet transform. Even though with the original aliased data, we can not obtain precise dip estimation, we can use low-pass filtered data (below 15 Hz) to estimate local slope in order to construct the seislet transform of the full-band seismic data and perform thresholding. Synthetic data and field data examples show nearly perfect results using the proposed approach. The traditional prediction based approach and the based POCS approach are both compared with the proposed approach and are demonstrated to be less effective.