## 2 Materials and Methods
### The Design of the Network Loss Function  
To ensure the synthesis of real reflected waves and achieve the separation of ground rolls and useful signals during the training process of the unsupervised learning network, this paper proposes a total ground roll suppression loss function \(L_{total}\). This loss function consists of two parts: weak ground roll loss \(L_{low}\) and strong ground roll loss \(L_{high}\). The function is represented as follows. \[L_{total}=\lambda_{1}*L_{low}+\lambda_{2}*L_{high} \tag{2}\]  
In this case, \(\lambda_{1}\) and \(\lambda_{2}\) are hyperparameters of the total loss function, representing the scaling coefficients for the weak ground roll loss function and the strong ground roll loss function, respectively. In this section, we will first introduce the characteristics of seismic records after wavelet decomposition and then provide a detailed explanation of each component of the loss function. The wavelet transform is a time-frequency analysis method that can decompose signals into components of different scales and frequencies. In seismic records, by performing wavelet transform on the seismic signal, we can obtain wavelet coefficients at different frequencies. This allows us to concentrate the components and energy of the signal at different frequencies into different wavelet coefficients. Since ground rolls usually have lower frequency characteristics, while body waves in seismic signals often have higher frequency characteristics, we can filter out ground roll noise and retain the body wave signal by selecting appropriate wavelet basis functions and thresholds. Taking synthetic seismic records as an example, as shown in Figure 3, certain wavelet components (indicated by the blue box) exhibit strong ground roll energy, labeled as \(input_{high}\), while other wavelet components (indicated by the green box) have weaker ground roll energy, labeled as \(input_{low}\). Next, let us delve into the individual components of the loss function. (1) Weak ground roll loss \(L_{low}\)  
The weak ground roll loss function aims to compute \(MSE\) (the mean squared error) loss function between the network output and the wavelet decomposition of the input  
Figure 3: Wavelet representation of data. seismic records containing the weak energy ground roll components. It is defined as follows. \[L_{low}=MSE(input_{low},\ output_{low}) \tag{3}\]  
Here, \(input_{low}\) represents the wavelet component obtained through the wavelet decomposition of the original seismic records, which contains very few ground roll components. \(output_{low}\) corresponds to the portion of the wavelet component obtained through the wavelet decomposition of the seismic records that does not contain ground roll components. The significance of the weak ground roll loss function lies in its ability to help the network learn and preserve the information in the input data that is free from ground roll. By increasing the proportion of this component in the loss function and optimizing it, training the network can better suppress ground roll. This contributes to improving the overall performance of the network and the quality of the output results. (2) Strong ground roll loss \(L_{high}\)  
The strong ground roll loss function is designed to compute \(MSE\) loss function between the network output and the wavelet decomposition of the input seismic records, containing the strong energy ground roll components. It is defined as follows. \[L_{high}=MSE\Big{(}input_{high},\ output_{high}\Big{)} \tag{4}\]  
Here, \(input_{high}\) refers to the wavelet component obtained through the wavelet decomposition of the original seismic records, which contains minimal ground roll components. \(output_{high}\) corresponds to the section of the wavelet component obtained through the wavelet decomposition of the seismic records that does not contain any ground roll components.