## 3 Results and Discussion
### Synthetic Example  
This section will first validate the effectiveness of the WPI-SD single model in suppressing synthetic surface wave noise. To create the training set for synthetic seismic records, we utilized the hyperbolic event synthesis method from the crews toolkit. This approach generates data that include reflected waves simulated by hyperbolic common-midpoint gathers and surface waves simulated by linear common-midpoint gathers, leveraging the distinct morphological features of reflection signals and surface wave noise in the lateral-temporal domain. The process of generating seismic data with surface waves involves estimating amplitudes, frequency bands, and velocity ranges of surface waves and effective signals in the pre-stack seismic data of the target area based on actual seismic data. Random seismic signal velocities are then generated, followed by the random generation of fake seismic source wavelets with different dominant frequencies within the effective frequency band range. The observation system was set up based on the sampling interval and trace spacing. By employing the hyperbolic event synthesis method, a significant volume of targeted synthetic seismic data were generated using simulation parameters from the velocity model detailed in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Parameter Setting** & **Parameter** & **Parameter Setting** \\ \hline Model size & 3000 samples \(\times\) 240 traces & Time sampling interval & 2 ms \\ Reflection wave velocity & 800–1000 m/s & Ground roll wave velocity & 200–500 m/s \\ Reflection wave dominant frequency & 25–35 Hz & Ground roll wave dominant frequency & 5–15 Hz \\ Maximum amplitude of effective wave & 2–5 & Maximum amplitude of ground roll wave & 4–10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Synthetic seismic data parameter setting. Figure 4: Illustrates the iterative training process of the network. The parameter settings used in this paper are as follows: the seismic model size is 3000 \(\times\) 240, with 240 seismic traces. The time sampling interval is 2 ms, with a total of 3000 time sample points. The reflection wave velocity ranges from 800 to 1000 m per second, while the ground roll wave velocity ranges from 200 to 500 m per second. Both the reflection wave and ground roll wave source wavelets are of the Ricker type, with the dominant frequency of the reflection wave being 25-35 Hz and the dominant frequency of the ground roll wave being 5-15 Hz. The maximum amplitude range of the effective wave is 2-5, and the maximum amplitude range of the ground roll wave is 4-10. These highly realistic synthetic seismic data are crucial for further analysis and research purposes. This section uses an example of synthetic seismic data composed of real reflected waves modeled by hyperbolic events and surface waves modeled by linear events to detail the situations of the loss function parameters \(\lambda_{1}\) and \(\lambda_{2}\) designed in this paper, as well as the classic traditional L2 loss function under different coefficients. With the increase in the number of iterations, the synthesis of real reflected waves and ground roll in the seismic records also evolves accordingly. As shown in Figures 5-9, synthetic seismic data were recorded during the iterative process of the network within 1000 iterations in the WPI-SD model, for the cases when \(\lambda_{1}=1\) and \(\lambda_{2}=1\), \(\lambda_{1}=1\) and \(\lambda_{2}=10\), \(\lambda_{1}=1\) and \(\lambda_{2}=40\), and \(\lambda_{1}=40\) and \(\lambda_{2}=1\), along with the L2 loss at iteration steps 0, 80, 100, 140, 160, 180, 340, 800, and 1000. As illustrated in Figures 5-8, irrespective of the values of \(\lambda_{1}\) and \(\lambda_{2}\), the WPI-SD model progressively converges towards the original seismic record by iteratively adjusting its network parameters with an increasing number of iterations.