Seismic data interpolation using deeply supervised U-Net plus plus with natural seismic training sets

Interpolation techniques provide an effective method for recovery of missing traces. In recent years, many researchers have applied deep learning methods to seismic data interpolation. Generally, one can choose synthetic data as a training set; however, the features of synthetic data are always inconsistent with those of field data, which may lead to inaccurate interpolation. Meanwhile, U-Net is a common network structure used in seismic data interpolation; however, the four downsampling and upsampling structures of U-Net have limited adaptability for different data. In this study, the deep learning method based on U-Net++ was proposed for seismic data interpolation, which contains U-Net with different depths. The different depths were connected by skip pathways, and the best depth of the network was chosen for different seismic data by deep supervision. Furthermore, a new strategy for training sets was designed: frequency-wavenumber (f-k) bandpass filters were used to convert natural images into a natural seismic training set, which has a stronger generalization capability than synthetic data as the training set. The characteristics of the new training set can effectively improve the accuracy of missing data reconstruction. Compared with the conventional U-Net and traditional interpolation techniques, for example, the Fourier Bregman method, the proposed method produces more accurate and reasonable interpolation results. Further, it can reconstruct both irregular and regular missing seismic data, even in the presence of strong random noise and aliasing. Synthetic and field data tests showed the effectiveness, robustness and generalization of the proposed method.