In the audio magnetotellurics (AMT) sounding data processing, the absence of sferic signals in some time ranges typically results in a lack of energy in the AMT dead band, which may cause unreliable resistivity estimate. We propose a deep convolutional neural network (CNN) to automatically recognize sferic signals from redundantly recorded data in a long time range and use them to compensate for the resistivity estimation. We train the CNN by using field time series data with different signal to noise rations that were acquired from different regions in mainland China. To solve the potential overfitting problem due to the limited number of sferic labels, we propose a training strategy that randomly generates training samples (with random data augmentations) while optimizing the CNN model parameters. We stop the training process and data generation until the training loss converges. In addition, we use a weighted binary cross-entropy loss function to solve the sample imbalance problem to better optimize the network, use multiple reasonable metrics to evaluate network performance, and carry out ablation experiments to optimally choose the model hyperparameters. Extensive field data applications show that our trained CNN can robustly recognize sferic signals from noisy time series for subsequent impedance estimation. The subsequent processing results show that our method can significantly improve S/N and effectively solve the problem of lack of energy in dead band. Compared to the traditional processing method without sferic compensation, our method can generate a smoother and more reasonable apparent resistivity-phase curves and depolarized phase tensor, correct the estimation error of sudden drop of high-frequency apparent resistivity and abnormal behavior of phase reversal, and finally better restore the real shallow subsurface resistivity structure.