Abstract: Due to the limitation of complex conditions such as topography, the pre-stack seismic data are spatially incomplete or irregularly distributed, resulting in phenomena such as missing or confusing data. In recent years, methods based on convolutional neural networks have been widely used in the reconstruction of missing seismic data. However, the network model of one-step training process is not enough to reconstruct the missing seismic data with a wide amplitude range, and the reconstruction results of the low-amplitude missing part still need to be improved. Therefore,  a coarse-fine network model with a stepwise training process is proposed in this paper. The model consists of a coarse network and a fine network to recover the missing seismic data with a wide amplitude range in a step-by-step process. Discrete wavelet transform is introduced in the fine network instead of pooling operation, and its reversibility facilitates the preservation of detailed features in the up-sampling stage. Using a hybrid loss function, the model reconstructs the true details of the missing signals. The preliminary recovery results of the coarse network are processed by masking operation and input to the fine network, which further accurately recovers the low amplitude signal of the missing part. The experimental results show that compared with the reconstruction methods of residual network (ResNet), U-shaped network (U-Net) and multilevel wavelet convolutional neural network (MWCNN), the method in this paper demonstrates superior reconstruction performance on both synthetic and real data: the signal-to-noise ratio is 18.818 5 dB  on synthetic data with 75% missing, and 12.255 1 dB on real data with 50% missing. In the ablation study, the mean square error of the model reconstruction in this paper is1.689 3×10-4, the signal-to-noise ratio is 19.284 6 dB, the peak signal-to-noise ratio is 43.743 5 dB, and the structural similarity index is 0.984 1, all of which are better than the other three sets of control experiments.

Key words: coarse-refine network, hybrid loss, discrete wavelet transform, seismic data reconstruction