Deep-Learning-Based Low-Frequency Reconstruction in Full-Waveform Inversion

Low frequencies are vital for full-waveform inversion (FWI) to retrieve long-scale features and reliable subsurface properties from seismic data. Unfortunately, low frequencies are missing because of limitations in seismic acquisition steps. Furthermore, there is no explicit expression for transforming high frequencies into low frequencies. Therefore, low-frequency reconstruction (LFR) is imperative. Recently developed deep-learning (DL)-based LFR methods are based on either 1D or 2D convolutional neural networks (CNNs), which cannot take full advantage of the information contained in 3D prestack seismic data. Therefore, we present a DL-based LFR approach in which high frequencies are transformed into low frequencies by training an approximately symmetric encoding-decoding-type bridge-shaped 3D CNN. Our motivation is that the 3D CNN can naturally exploit more information that can be effectively used to improve the LFR result. We designed a Hanning-based window for suppressing the Gibbs effect associated with the hard splitting of the low- and high-frequency data. We report the significance of the convolutional kernel size on the training stage convergence rate and the performance of CNN's generalization ability. CNN with reasonably large kernel sizes has a large receptive field and is beneficial to long-wavelength LFR. Experiments indicate that our approach can accurately reconstruct low frequencies from bandlimited high frequencies. The results of 3D CNN are distinctly superior to those of 2D CNN in terms of precision and highly relevant low-frequency energy. FWI on synthetic data indicates that the DL-predicted low frequencies nearly resemble those of actual low frequencies, and the DL-predicted low frequencies are accurate enough to mitigate the FWI's cycle-skipping problems. Codes and data of this work are shared via a public repository.