A Self‐Supervised Learning Framework for Seismic Low‐Frequency Extrapolation - Cheng, Shijun; Wang, Yi; Zhang, Qingchen; Harsuko, Randy; Alkhalifah, Tariq (Journal of geophysical research. Machine learning and computation, 2024)
Full waveform inversion (FWI) is capable of generating high‐resolution subsurface parameter models, but it is susceptible to cycle‐skipping when the data lack low‐frequency components. Unfortunately, such components (<5.0 Hz) are often tainted by noise in real seismic exploration, which hinders the application of FWI. To address this issue, we develop a novel self‐supervised low‐frequency extrapolation method that does not require labeled data, enabling neural networks to be trained directly on real data. In the proposed approach, the neural network training is divided into two stages: warm‐up and iterative data refinement (IDR). In the IDR stage, the pseudo‐labels for the current epoch are derived from the predictions made by the network trained in the previous epoch on the original observed data. The IDR stage gradually narrows the gap between the predicted pseudo‐label and the ideal ground truth, thereby enhancing the network's low‐frequency extrapolation performance. This paradigm effectively addresses the significant generalization gap often encountered using supervised learning techniques, which are typically trained on synthetic data. We validate the effectiveness of our method on both synthetic and field data. The results demonstrate that our method effectively extrapolates low‐frequency components, aiding in circumventing the challenges of cycle‐skipping in FWI. Meanwhile, by integrating a self‐supervised denoiser, our method effectively and simultaneously performs denoising and low‐frequency extrapolation on noisy data. Furthermore, we showcase the potential application of our method in extending the ultralow frequency components of the large‐scale collected earthquake seismogram. Plain Language Summary Full waveform inversion (FWI) is a method used to provide detailed underground images for efforts in oil exploration or studying earthquakes. However, the method is prone to a problem known as “cycle‐skipping,” caused by the lack of low frequencies in the data, and as a result, the inversion converges to an inaccurate velocity model. We propose a new way to extrapolate the low‐frequency components using a neural network‐based self‐supervised approach. This means our method learns directly from real data rather than relying on artificially created data, which is a common limitation in the supervised paradigm. Our method not only helps to overcome the issue of skipping cycles but also demonstrates robustness against noisy data, enhancing its practical application potential. The tests on exploration data validate its ability to predict the low‐frequency components, helping to avoid local minima and thus improving the accuracy of FWI. Also, we demonstrate how our method can be applied to invert earthquake data, where it can extend the ultralow frequency information. This research could contribute to providing a better and a more reliable way to obtain images of the Earth's interior. Key Points We develop a self‐supervised seismic low‐frequency extrapolation algorithm that can be applied to exploration and earthquake seismograms The predicted low‐frequencies can help fill in the model the wavenumber spectrum and help avoid cycle‐skipping in full waveform inversion Our method, by integrating a self‐supervised denoiser, is robust against noisy observed data