# Fault Imaging of Seismic Data Based on a Modified U-Net with Dilated Convolution
## 1 Introduction
[14] used results of the skeletonized seismic coherent self-correction method as training samples to train a CNN model to identify seismic faults. In 2019, [PERSON] et al. [15] realized the identification of small-scale faults by using U-Net network. [PERSON] et al. [6] used a full-convolutional neural network, FCN, to achieve a better characterization of faults. Among these networks, the U-Net architecture is currently very popular, due to its shortcut operation which concatenates attribute maps from the low-level feature (shallow layer) to maps of high-level feature (deep layer), and it can be seen as a special kind of CNN [16; 17; 18]. In addition, the U-Net does not have strict requirements on the size of training sets, and smaller training sets can also provide satisfactory results. However, most networks including the U-Net uniformly process all feature maps of the same layer, resulting in the same receptive field of the network in the same layer, thus obtaining relatively single local information. Moreover, with the continuous down-sampling of the network and the convolution operation with step size, the defect that only a single size information can be obtained at the same layer becomes more and more obvious, resulting in the inaccurate identification of faults by the neural network. To address these issues, this paper introduces a new neural network model, which takes U-Net as the basic network and uses inter-group channel dilated convolution module (GCM) to connect each cross-connection layer between encoding path and decoding path, and uses inter-group space dilated convolution module (GSM) to connect layers after each deconvolution layer in decoding path. Both GCM and GSM use dilated convolution. Dilated Convolution, also known as hole convolution or expanded convolution, is to inject cavities into the standard convolution kernel to increase the reception field of the model. In the CNN structure, convolution and pooling drive most layers, convolution performs feature extraction, while pooling performs feature aggregation. For an image classification task, this network structure has good feature extraction capability, among which the most classical structure is VGGNet (a convolutional neural network was developed by the University of Oxford's Visual Geometry Group and Google DeepMind in 2014). However, this structure has some problems for target detection and image segmentation. For example, the size of receptive field is very important in target detection and image segmentation, and the guarantee of receptive field depends on down-sampling. However, down-sampling will make small targets difficult to detect. If down-sampling is not completed and the number of convolutional layers is only increased, the computation of the network will increase. In addition, if pooling is not carried out for features, the final feature extraction effect will also be affected, and there will be no change in the receptive field. In order to solve these problems in CNN, this paper introduces dilated convolution to increase the receptive field without sacrificing the size of the feature map. Compared with the conventional convolution operation, dilation rate is added to the dilated convolution, which refers to the number of intervals of points in the convolution kernel [19; 20; 21]. When dilatation rate is 1, the dilated convolution will degenerate into conventional convolution. The similarity between dilated convolution and conventional convolution lies in that the size of convolution kernel is the same, that is, the number of parameters of neural network remains unchanged [22; 23]. The difference lies in that dilated convolution has a larger receptive field and can preserve the structure of internal data [24; 25].