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. Unfortunately, the low-frequency 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. This paradigm effectively addresses the significant generalization gap often encountered by 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 performs simultaneously denoising and low-frequency extrapolation on noisy data. Furthermore, we showcase the potential application of our method in extending the ultra-low frequency components of the large-scale collected earthquake seismogram.
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