Reconstruction of irregular missing seismic data using conditional generative adversarial networks

During acquisition, due to economic and natural reasons, irregular missing seismic data are always observed. To improve accuracy in subsequent processing, the missing data should be interpolated. A conditional generative adversarial network (cGAN) consisting of two networks, a generator and a discriminator, is a deep-learning model that can be used to interpolate the missing data. However, because cGAN is typically data set oriented, the trained network is unable to interpolate a data set from an area different from that of the training data set. We design a cGAN based on Pix2Pix GAN to interpolate irregular missing seismic data. A synthetic data set synthesized from two models is used to train the network. Furthermore, we add a Gaussian-noise layer in the discriminator to fix a vanishing gradient, allowing us to train a more powerful generator. Two synthetic data sets synthesized by two new geologic models and two field data sets are used to test the trained cGAN. The test results and the calculated recovered signal-to-noise ratios indicate that although the cGAN is trained using synthetic data, the network can reconstruct irregular missing field seismic data with high accuracy using the Gaussian-noise layer. We test the performances of cGANs trained with different patch sizes in the discriminator to determine the best structure, and we train the networks using different training data sets for different missing rates, demonstrating the best training data set. Compared with conventional methods, the cGAN-based interpolation method does not need different parameter selections for different data sets to obtain the best interpolation data. Furthermore, it is also an efficient technique as the cost is because of the training, and after training, the processing time is negligible.