Self-Supervised Seismic Data Interpolation via Frequency Extrapolation

Antialiasing seismic data interpolation algorithms can reconstruct sparse seismic data into dense data, which helps obtaining high-precision migration images and accurately locate reservoirs. Nonlinear seismic interpolation techniques based on deep learning (DL) have become popular in recent years. The majority of supervised techniques, however, depend on large volumes of labeled datasets, which are rarely available for field data interpolation. To overcome the limitations of the labeled data requirement in supervised learning, some unsupervised interpolation techniques, such as the well-known deep image prior (DIP), have been developed. However, these unsupervised techniques often have poor generalization. In order to avoid the complete labeled data requirement and achieve an accurate interpolation result efficiently, we propose a novel self-supervised interpolation via frequency extrapolation (SIFE) algorithm for regularly missing seismic data. The proposed SIFE mainly contains two steps: aliasing-free low-frequency complete data reconstruction via the Nyquist sampling theorem and high-frequency data recovery via self-supervised frequency extrapolation. In the first step, a lowfrequency filter is adopted to obtain aliasing-free sparse data, which can be interpolated into dense low-frequency data via the Nyquist sampling theorem. In the second step, the lowfrequency filtered observation data is mapped to its original full-band observed data via self-supervised learning for frequency extrapolation. After the training convergence, we can obtain an optimized network that can map the reconstructed low-frequency data at the missing locations to the corresponding full-band seismic data via frequency extrapolation, i.e., reconstructing the missing seismic traces. Numerical examples with synthetic and field data show the superiority of the proposed SIFE when compared with DIP.