Seismic data interpolation based on U-net with texture loss

Seismic data interpolation based on U-net with texture loss Wenqian Fang1, Lihua Fu1, Meng Zhang2, Zhiming Li1* 1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China; 2Department of Computer Science, Central China Normal University, Wuhan 430079, China ABSTRACT: Missing traces in acquired seismic data is a common occurrence during the collection of seismic data. Deep neural network (DNN) has shown considerable promise in restoring incomplete seismic data. However, several DNN-based approaches ignore the specific characteristics of seismic data itself, and only focus on reducing the difference between the recovered and the original signals. In this study, a novel Seismic U-net InterpolaTor (SUIT) is proposed to preserve the seismic texture information while reconstructing the missing traces. Aside from minimizing the reconstruction error, SUIT enhances the texture consistency between the recovery and the original completely seismic data, by designing a pre-trained U-Net to extract the texture information. The experiments show that our method outperforms the classic state-of-art methods in terms of robustness. Keywords: seismic data interpolation; deep learning; U-net; texture loss 1 Introduction Variable operating conditions during seismic surveys frequently result in inadequate trace spacing along spatial axes. The absence of data affects subsequent offset imaging, inversion, and interpretation, as well as the description of geological structures. Therefore, seismic data interpolation is essential in seismic surveys. Seismic data reconstruction techniques can be divided into four categories: prediction filters, wave equations, transform domains, and low-rank theory. Prediction-filter-based methods involve the convolution of seismic data with filters, which mainly include the f-x domain seismic traces interpolation method (Spitz, 1991) and the t-x domain method (Claerbout and Nichols, 1991). Methods based on wave-equations typically use wave propagation to reconstruct seismic data via iterative solution of forward operators and inversion operators (Bagaini and Spagnolini, 1993; Ronen, 1987). Transform-based approaches generally seek ‘optimal’ coefficients in transform domain in terms of least squares; and a good reconstruction can be obtained via inverse transformation. These approaches include Radon transform (Thorson and Claerbout, 1985), Fourier transform (Duijindam et al., 1999; Liu and Sacchi, 2004; Zwartjes and Sacchi, 2007), and Curvelet transform (Herrmann and Hennenfent, 2008; Trickett et al., 2010). Rank-reduction-based methods are based on the assumption that seismic data with a limited number of events are of low rank in the f-x domain, and the missing data and random noise will increase the rank of the matrix or tensor. Therefore, rank-reduction schemes have become a popular tool for seismic data reconstruction (Gao et al., 2013; Naghizadeh and Sacchi, 2012; Kreimer, 2013; Gao et al., 2017). Deep learning (DL) establishes deep neural networks that simulate the human brain for analysis and learning. It has been applied successfully to speech recognition, facial recognition, video classification, and texture recognition. In recent years, DL has attracted increasing attention for addressing the problems pertaining to seismic data interpolation. Wang et al. (2019) used a residual network (He et al., 2016) pre-interpolated by bicubic for seismic data antialiasing interpolation. This approach was demonstrated to achieve better results than the f-x method; however, it was also recognized that the interpolation bias increased as the feature differences between the test dataset and the training dataset increased. Dario et al. (2018) used a conditional generative adversarial network for the interpolation problem in post-stack seismic datasets. They established a network pool for different gap widths of missing traces; this approach was shown to be better than a single network in terms of the Pearson correlation coefficient. However, the limitation of this network pool method is that it requires considerable amounts of data and calculations. Mandelli et al. (2018) applied the U-net network to the random missing interpolation problem of seismic data and they achieved better results than the classical low-rank Singular Spectrum Analysis (SSA) algorithm. Although the DL method has considerable potential in the field of seismic data interpolation, it is also characterized by certain limitations. (1) Majority of the existing methods refer to the results in computer vision but do not focus on the differences in the seismic data. (2) To overcome the challenge of generalizing the learned knowledge to new datasets, a large number of training samples are required. However, seismic exploration is an expensive venture, and seismic data set for deep learning algorithms like the ImageNet dataset (Russakovsky, 2015) in computer vi

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