Data-driven low-frequency signal recovery using deep-learning predictions in full-waveform inversion

The lack of low-frequency signals in seismic data makes the full-waveform inversion (FWI) procedure easily fall into local minima leading to unreliable results. To reconstruct the missing low frequency signals more accurately and effectively, we have developed a data-driven low-frequency recovery method based on deep learning from high-frequency signals. In our method, we develop the idea of using a basic data patch of seismic data to build a local data-driven mapping in low-frequency recovery. Energy balancing and data patches are used to prepare highand low-frequency data for training a convolutional neural network (CNN) to establish the relationship between the highand low-frequency data pairs. The trained CNN then can be used to predict low-frequency data from high-frequency data. Our CNN was trained on the Marmousi model and tested on the overthrust model, as well as field data. The synthetic experimental results reveal that the predicted low frequency data match the true low-frequency data very well in the time and frequency domains, and the field results show the successfully extended low-frequency spectra. Furthermore, two FWI tests using the predicted data demonstrate that our approach can reliably recover the low-frequency data.