# Fault Imaging of Seismic Data Based on a Modified U-Net with Dilated Convolution
## 3 The Architecture of the Modified U-Net  
The proposed neural network adopts a U-Net of a 4-layer structure as the basic network. In the coding path, feature maps of each layer are connected to the corresponding decoding layer by GCM, in which each layer adopts two 3 \(\times\) 3 convolution layers and maximum pooling layer for feature extraction. Then, in the decoding path, feature maps of each layer are connected to the corresponding decoding layer by GSM. Each layer adopts a 3 \(\times\) 3 convolution layer, up-sampling layer and 1 \(\times\) 1 convolution layer to restore, and the output layer adopts a 3 \(\times\) 3 convolution layer and 1 \(\times\) 1 convolution layer to output. In this modified U-Net, the batch regularization (BN) and modified linear units (ReLU) are added to all convolution layers to correct data distribution, except for the output layer. GCM and GSM modules play a key role in the modified U-Net, and their operation mechanism is similar. GCM module can divide the input feature map into four groups on average, and then carry out the dilated convolution operation with dilation rates of 1, 2, 3 and 5, respectively. In addition, the module extracts and outputs the features of the input feature map through pooling, convolution, batch regularization, activation, softmax and other conventional operations, and finally obtains the channel information of all groups. For the GSM module, it can divide the input feature map into three groups on average, and each group carries out the dilated convolution operation with dilation rates of 1, 2 and 4, respectively. This module carries out feature extraction and output in sequence by down-sampling, convolution, batch regularization, activation, up-sampling, convolution, batch regularization, activation and softmax, and finally obtains the spatial information of all groups. Figure 3: The dilated convolution with dilation rate of 1, 2 and 3, respectively. (**a**) dilation rate = 1; (**b**) dilation rate = 2; (**c**) dilation rate = 3. Figure 2: The dilated convolution with the same dilation rate of 2, respectively. There are grid effects in all three graphs. (**a**) the first convolution with dilation rate of 2; (**b**) the second convolution with dilation rate of 2; (**c**) the third convolution with dilation rate of 2. Figure 4 shows the structure of GCM in the modified U-Net. This module divides the input feature map into four groups evenly, and each group performs dilated convolution operations with dilation rates of 1, 2, 3, and 5. The size of the target area of fault identification determines the value of the dilation rate. After dilated convolution, four groups of feature maps with different scales are obtained. Besides, four groups of channel information are returned by softmax, which were taken as weights and multiplied by four groups of feature maps with different scales obtained via dilated convolutions to acquire new feature maps. The receptive field corresponding to the group with the largest weight contributed the most to the final network prediction. Finally, the four groups of new feature maps are spliced together and then a residual operation is performed with the input feature map to obtain the final prediction result. The GCM module uses the idea of grouping and realizes the automatic selection of inter-group multi-scale information under the guidance of channel information. Figure 5 shows the structure of GSM, which realizes the selection of multi-scale information between groups in another way and enhances the consistency of receptive field and target region recognition. In this module, the input feature map was divided into three groups, and then three groups of feature maps with different scales are obtained by the dilated convolution with dilation rates of 1, 2 and 4. At the same time, three feature maps with spatial weights are cropped from the input feature map through a series of conventional operations.