An Aliasing-Free Low-Frequency Pretrained Model for Seismic Interpolation Using a Small Training Set

High-density seismic data is critical for enhancing the accuracy of subsequent processing. Deep learning is useful in seismic interpolation due to its powerful nonlinear mapping capability based on the extracted high-level features. Most supervised methods, however, rely on a large labeled training set, which is always unavailable due to limited resources and complex acquisition environment. Furthermore, the optimized model with a small training set is prone to poor accuracy and generalization. We pre-train a designed U-net with an adaptive aliasing-free low-frequency dataset, then fine-tune the pre-trained U-net with a tiny original labeled dataset. The low-frequency pre-trained model effectively improves the interpolation accuracy when using a limited labeled training set. We use the aliasing-free low-frequency parts of original regularly sampled sparse data to construct dense low-frequency data based on the Nyquist sampling theorem in the frequency-wavenumber domain, resulting in an adaptive pre-training dataset. Second, we use the adaptively constructed pre-training dataset to pre-train a designed U-net for interpolation, with similar sampling patterns as the original seismic data. Third, based on transfer learning, we use the original small-volume training set to fine-tune the pre-trained U-net, which has captured the macro features of the original data during the pre-training stage. Finally, the fine-tuned U-net is applied to the remaining regularly sampled data for interpolation. The proposed adaptive low-frequency pre-trained model can significantly improve the generalization ability and the interpolation accuracy using the fine-tuned model. Numerical experiments of synthetic and field data validate the superiority of our method in terms of improving interpolation accuracy.