@article{Liu2026, 
author = {Yang Liu and Xiao-Tao Wen and Qing-Jun Yang and Huan Zhu and Yun Zhao and Theo Le Gallais},
title = {Dual-branch wavelet-fusion U-Net for vibroseis harmonic noise attenuation},
year = {2026},
journal = {Petroleum Science},
volume = {23},
number = {10},
pages = {6154-6173},
keywords = {Deep learning, Vibroseis, Harmonic noise attenuation, DW-U-Net, Time-frequency analysis},
url = {https://www.sciopen.com/article/10.1016/j.petsci.2026.04.051},
doi = {10.1016/j.petsci.2026.04.051},
abstract = {Vibroseis is widely used in land surveys, but source-ground coupling and equipment nonlinearities generate second- and higher-order harmonics as well as narrowband resonance lines. These source-related interferences overlap the target reflection band, markedly degrading the signal-to-noise ratio (SNR) and masking weak reflections. We propose a dual-branch wavelet-fusion U-Net (DW-U-Net) for harmonic noise attenuation. The backbone operates in the time domain, while a wavelet side branch explicitly represents low-frequency background and high-frequency details. A differentiable inverse discrete wavelet transform (IDWT) injects the reconstructed wavelet features into the decoder to structurally suppress harmonic streaks while preserving reflections. Training data are generated by adding higher-order harmonics to a reference sweep and then simulating shot records through forward modeling. On the Marmousi2 model under strong harmonic noise, DW-U-Net increases the whole-shot average SNR from 9.92 dB to 29.29 dB, and achieves residual energy 2.44 × 10−3, root mean square error (RMSE) 4.51 × 10−5, and multiscale structural similarity (MS-SSIM) 0.9959. Experiments on the Marmousi2 model and the public Utah FORGE field data demonstrate that DW-U-Net attenuates coherent harmonic streaks and suppresses narrowband resonance lines in shot records. Compared with DnCNN, a standard U-Net, dual residual network (DURN), and multi-input multi-output U-Net (MIMO-U-Net) trained under the same protocol, DW-U-Net delivers consistently higher SNR under strong noise levels. Time-frequency analyses further show that the main reflection band is well preserved in amplitude and bandwidth, while coherent harmonic remnants are substantially reduced.}
}