## 2 The ARDU Denoising Model
### Middle Layer of the ARDU Model: The Role of Atrous Convolution  
The middle layer of the ARDU model is a symmetrical U-shaped structure, which is composed of an encoder, a decoder, and feature concatenating. The main function of the encoder is to extract seismic signal features through downsampling. It is composed of five groups of feature extraction units and the atrous convolution of the bottom layer. Each group of feature extraction units is composed of atrous convolution, an activation function, batch normalization, and a residual dense block, in which the activation function and batch normalization are the same as those of the input layer. The down-sampling of the encoder is realized by reducing the characteristic image of the seismic signal, which inevitably loses the detailed information about signal characteristics. The atrous convolution can expand the receptive field of the convolution layer without increasing the network parameters to obtain more feature information about the seismic signals [28]. In the ARDU model, after many experimental results, the denoising effect is the best when the dilated coefficient of the atrous convolution is set to 2, so the dilated coefficient of the atrous convolution used by the model encoder was set to 2. The atrous convolution of the bottom layer is also used to expand the receptive field of the convolution kernel, enhance the neighborhood information learning of the seismic signal feature map, and contact the signal context information so as to better restore the structural feature of the seismic signal. After atrous convolution, batch normalization and the activation function are also added, and their effect is consistent with the input layer of the model. The implementation principle of atrous convolution is shown in Figure 3. Figure 3a shows a common convolution with a receptive field size of 3 \(\times\) 3. In Figure 3b, atrous convolution with a dilated coefficient \(r\) of 2 is added on the basis of the common convolution with a 3 \(\times\) 3 receptive field, and the field of the convolution kernel is increased to 5 \(\times\) 5. Let the convolution kernel size of the convolution layer be \(k\times k\); when the dilated coefficient of the atrous convolution is \(r\), the calculation form of its receptive field size \(v\) is shown in Formula (3). \[v=[(r-1)\times(k-1)+k]\times[(r-1)\times(k-1)+k] \tag{3}\]  
Figure 2: ReLU function. The residual dense block is mainly composed of dense connections and global residual learning, and the structure is shown in Figure 4. The dense skip connection connects each current convolutional layer to all convolutional layers, realizing the interconnection between all layers, as shown by the blue arrows in Figure 4. This method deepens the depth and width of the network to a certain extent, integrates the information about all layers as far as possible, forms a continuous memory mechanism, and enhances the feature extraction ability of the model. The global residual learning gives the ability of backoff to the residual dense block by adding a directly connected skip connection between input and output, as shown by the red arrow in Figure 4. In this way, the residual learning can automatically select whether to perform feature extraction through the three convolution layers according to the effect of gradient descent, directly skip the convolution layer and select the skip connection to perform feature flow, or combine the features of the three convolution layers and the skip connection to perform output, thereby mitigating the problems of gradient vanishing and gradient exploding caused by deepening of the number of network layers and making the network easier to train. For each unit of the residual dense block, as shown in the green dashed-line box in Figure 4, batch normalization and the activation function are added after the convolution layer so that the input of each layer has a stable distribution, which can effectively avoid gradient diffusion and improve the generalization ability and convergence speed of the network.