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Moreover, DL has been applied to geologic feature identification ( Huang et al., 2017), seismic lithology detection ( Zhang et al., 2018a), salt detection ( Guillen et al., 2015 Wang et al., 2018a), and velocity inversion ( Wang et al., 2018b). Recently, DL has achieved significant progress in computer vision research, including image classification ( Krizhevsky et al., 2012 He et al., 2016), denoising ( Zhang et al., 2017a), and superresolution ( Dong et al., 2016 Kim et al., 2016). DL offers to learn an amount of parameters through the convolutional neural network (CNN) to capture high-level features in the data. Deep learning (DL), which is a fast developing branch of machine learning, has attracted significant attention from multidisciplinary researchers. For regularly subsampled seismic data with spatial aliasing, associated antialiasing techniques are included in these methods ( Naghizadeh and Sacchi, 2010).Ī machine learning method with support vector regression was successfully applied to seismic data interpolation by Jia and Ma (2017). Most of these interpolation methods are suitable only for random missing cases. (2015) extend the data-driven tight frame (DDTF) method to 3D seismic data interpolation and later proposed the Monte Carlo DDTF method to reduce computation ( Yu et al., 2016). Dictionary learning methods ( Liang et al., 2014) and rank-reduction regularization methods ( Trickett et al., 2010 Gao et al., 2013a Ma, 2013) have also been successfully applied to seismic interpolation. Considering the characteristics of seismic data, the seislet transform was presented by Fomel and Liu (2010) and later used for seismic dealiasing interpolation based on POCS ( Gan et al., 2015). These nonadaptive or highly redundant transforms have strong anisotropic directional selectivity. (2012) propose seismic interpolation using the curvelet transform-based POCS algorithm. In recent years, several directional wavelets, including curvelets and shearlets, have been applied to sparsely present seismic events ( Herrmann and Hennenfent, 2008). A previous example is the project onto convex set (POCS) algorithm based on the Fourier transform method ( Abma and Kabir, 2006). Besides frequency-space ( ⁠ f- x⁠) prediction filtering methods ( Spitz, 1991 Naghizadeh and Sacchi, 2009), other methods based on the sparse representation of seismic data in a transform domain have been popular in the past decade because of their promising frameworks.

To use these incomplete data, many researchers have developed dozens of interpolation methods to restore the missing traces. The primary results of synthetic and field data show promising interpolation performances of the adopted CNN-POCS method in terms of the signal-to-noise ratio, dealiasing, and weak-feature reconstruction, in comparison with the traditional f- x prediction filtering, curvelet transform, and block-matching 3D filtering methods.ĭue to existing terrain obstacles or economic restrictions, missing traces in acquired seismic data, nonuniformly or uniformly, along the spatial coordinate is unavoidable, and this affect seismic inversion, amplitude-versus-angle analysis, and migration. These indicate the high generalizability of the proposed method and a reduction in the necessity of problem-specific training. Additionally, the adopted method is flexible and applicable for different types of missing traces because the missing or down-sampling locations are not involved in the training step thus, it is of a plug-and-play nature. This method alleviates the demands of seismic data that require shared similar features in the applications of end-to-end deep learning for seismic data interpolation. This new method consists of two steps: (1) training a set of CNN denoisers to learn denoising from natural image noisy-clean pairs and (2) integrating the trained CNN denoisers into the project onto convex set (POCS) framework to perform seismic data interpolation. It provides a simple and efficient way to break through the problem of the scarcity of geophysical training labels that are often required by deep learning methods.

We have developed an interpolation method based on the denoising convolutional neural network (CNN) for seismic data.