Low-Frequency Reconstruction for Full Waveform Inversion by Unsupervised Learning

Obtaining reliable low-frequency seismic data is crucial for effectively reducing cycle-skipping in full waveform inversion. However, acquiring high signal-to-noise ratio low-frequency information from field data remains a challenge. An effective solution to mitigate cycle-skipping is to utilize low-frequency information synthesized by neural networks to obtain low-wavenumber initial models. Previous attempts to reconstruct synthetic low-frequency data using supervised learning methods have shown feasibility but were limited to training with synthetic data that required labeled information. In this study, we employed an unsupervised learning method, namely cycle-consistent adversarial networks (CycleGAN), to reconstruct large-scale-feature related low-frequency information based on the high-frequency input data. Unlike supervised learning, CycleGAN allows the use of field data as input to train the network, which is more closely aligned with practical applications. Nevertheless, this approach presents challenges in terms of training complexity and potential output stability. To overcome these challenges, we reconstructed an appropriate target data set that combines high, medium, and low-frequency components and incorporated additional loss functions to enhance the network's output performance. We conducted quantitative evaluations of the method's sensitivity to the target data set and its ability to handle low-quality input data through numerical testing. The final results from field data testing confirmed the feasibility and effectiveness of the proposed method.