## 2 Materials and Methods
### Network Architecture of WPI-SD  
The WPI-SD network proposed in this article is built upon a six-layer skip connection network, as illustrated in Figure 2. The skip connection network incorporates cross-layer feature reconstruction, wherein the decoder combines high-level convolutional features with low-level convolutional features. This fusion process aims to retain crucial feature information from the higher-level convolutions, consequently enhancing the network's accuracy in non-linear modeling and its ability to generalize.  
Figure 1: The methodological roadmap of the WPI-SD unsupervised learning-based deep pre-stack ground roll noise suppression method.  
Clearly, the upsampling process in deep learning networks requires filling in a lot of missing content, generating something from nothing, which lacks sufficient auxiliary information. Therefore, based on the encoder-decoder structure of the main pathway, we introduce the skip connection pathway. As the network propagates, with an increasing depth, the receptive field of the corresponding feature maps becomes larger, but the preserved detailed information decreases. For the task of extracting effective signals from seismic data, the rich detailed information preserved by high-level convolutions is very valuable. Based on the symmetrical encoder-decoder structure, we use concatenation layers to concatenate the feature maps extracted through downsampling in the encoding process with the new feature maps obtained through upsampling in the decoding process, corresponding one by one in the channel dimension. By introducing feature information at corresponding scales into the upsampling process, multi-scale and multi-level information is provided for the  
Figure 2: Structure diagram of skip connection network. The basic structure of the skip connection network consists of two parts: the main pathway and the skip connection pathway. The main pathway of the network includes encoding and decoding layers. The encoding layer contains six scales, with feature map channel numbers ranging from 16 to 128 across scales 1 to 6. Each scale is composed of a convolutional layer followed by a stride convolutional layer. The convolutional layers consist of a padding layer with a padding size of 2, a convolutional layer with a stride of 1 and a kernel size of \(5\times 5\), a batch normalization layer, and a LeakyReLU (Leaky Rectified Linear Unit) activation function layer. The stride convolutional downsampling layers consist of a padding layer with a padding size of 2, a stride convolutional layer with a stride of 2 and a kernel size of \(5\times 5\), a batch normalization layer, and a LeakyReLU activation function layer; they downsample the length and width of the input feature map by half. The encoding and decoding layers of the network are symmetrical, with each scale consisting of a convolutional layer followed by an upsampling layer. The convolutional layers include a batch normalization layer, a padding layer with a padding size of 1, a convolutional layer with a stride of 1 and a kernel size of \(3\times 3\), a batch normalization layer, and a LeakyReLU activation function layer. The upsampling layers mainly consist of an upsampling operation using bilinear interpolation; they upsample the length and width of the input feature map by 2 times.  
effective restoration of seismic signals, thereby improving the reconstruction quality and reducing information loss.