## 3 Results and Discussion
### Synthetic Example
In Figure 5, when \(\lambda_{1}=1\) and \(\lambda_{2}=1\), the WPI-SD network simultaneously reconstructs both the effective reflection signal and the ground roll, posing a challenge in distinguishing between the two. The difficulty arises from the values of ground roll and reflected waves, causing the network to struggle in discerning ground roll from reflected waves, leading to mutual interference during the recovery process and hindering complete separation. In Figures 6 and 7, in scenarios where \(\lambda_{1}<\lambda_{2}\), the WPI-SD network prioritizes restoring the effective reflection signals. With the progression of iterations, it subsequently recovers the ground roll. Moreover, as the value of B increases, the disparity in the required number of iterations for recovering ground roll and reflected waves also grows. The preference for restoring effective reflection signals by the WPI-SD network stems from the distinct values of \(\lambda_{1}\) and \(\lambda_{2}\), resulting in varying reconstruction priorities for different signal types. Figure 5: The training process of synthetic seismic data when \(\lambda_{1}=1\) and \(\lambda_{2}=1\) (where (**a**–**i**) represent the output of the network at iterations 0, 80, 100, 140, 160, 180, 340, 800, and 1000 and (**j**) is the loss function after every 1000 iterations of network training). In Figure 8, when \(\lambda_{1}>\lambda_{2}\), the WPI-SD network gives precedence to recovering the ground roll. As the iterations advance, it then proceeds to recover the reflected waves. The network's inclination towards restoring the ground roll is influenced by the differing values of \(\lambda_{1}\) and \(\lambda_{2}\), prompting a higher priority for reconstructing ground roll over reflected waves. According to Figure 9, when using the L2 loss function, deep learning networks tend to prioritize fitting the strong-energy, fast-wave, and smooth waveform of the reflected wave. However, during the iterative training process, due to the strong energy of the ground roll, the network also fits the strong-energy part of the ground roll while fitting the reflected wave, resulting in seismic data with strong-energy ground roll noise and a suboptimal fitting of the weak-energy part of the reflected wave. Additionally, the network's fitting speed is too fast, making it difficult to find the optimal number of iterations to separate the ground roll and reflected wave. In conclusion, the suppression effect of the ground roll is far inferior when using the traditional classic L2 loss function compared to the loss function of the designed WPI-SD ground roll suppression network in this paper. Figure 6: The training process of synthetic seismic data when \(\lambda_{1}=1\) and \(\lambda_{2}=10\) (where (**a**–**i**) represent the output of the network at iterations 0, 80, 100, 140, 160, 180, 340, 800, and 1000 and (j) is the loss function after every 1000 iterations of network training). Figure 7: The training process of synthetic seismic data when \(\lambda_{1}=1\) and \(\lambda_{2}=40\) (where (**a**–**i**) represent the output of the network at iterations 0, 80, 100, 140, 160, 180, 340, 800, and 1000 and (j) is the loss function after every 1000 iterations of network training). Therefore, when setting network parameters, in order to better extract effective reflection signals from actual seismic records, the value of parameter \(\lambda_{1}\) should be greater than parameter \(\lambda_{2}\). Furthermore, to further verify the effectiveness and superiority of the method proposed in this paper, we conducted the following comparative experiments: We compared the ground roll suppression effects of the WPI-SD network with a six-layer skip connection network architecture when using the L2 loss function of \(\lambda_{1}=0.07\) and \(\lambda_{2}=1\), as well as when \(\lambda_{1}=0.04\) and \(\lambda_{2}=1\).