## 4 Numerical Examples  
To verify the effectiveness of the iterative virtual events internal multiple suppression method, first of all, we use a simple horizontal layered model as a test case, with the velocity model displayed in Figure 5. The velocity model size is 4000 m \(\times\) 1600 m, and forward modeling is carried out using the higher order finite difference method based on the acoustic equation. An absorption boundary is applied at the top of the model. At the acquisition surface, seismic data are modeled with 501 sources and 501 receivers on a fixed spread with a spacing of 20 m, and the grid size is 2.5 m \(\times\) 2.5 m. The source emits a Ricker wavelet with a 25 Hz center frequency. The number of time sampling points is 1024, and the time sampling interval is 4 ms. Figure 6 shows the seismic record of one shot, including primaries and internal multiples in forward modeling, with the direct wave removed. Since the primary focus of this paper is the suppression of internal multiples in post-stack data, zero offset gathers are extracted from the forward shot records for internal multiple suppression. The extracted zero offset gathers are shown in Figure 7a. The iterative virtual event multiple suppression method is applied to suppress the internal multiples, and the resulting zero offset gathers are displayed in Figure 7b. The figure reveals that all internal multiples are essentially suppressed without damaging the primaries, indicating that the iterative virtual event method can effectively suppress stacked multiples in model data. Figure 8a displays the predicted initial internal multiples model, while Figure 8b shows the internal multiples after iteration. The internal multiple information after iteration is more abundant and matches the actual multiples better. The suppression effect is sufficiently ideal, demonstrating that the iterative virtual event multiple suppression method can effectively suppress the internal multiples in synthetic data. Figure 5: Velocity model. Figure 6: Original seismic data with the internal multiple. Figure 9 shows the profile comparison before and after the internal multiple suppression. Figure 9a displays the partial stack profile before internal multiple suppression, while Figure 9b shows the corresponding stack profile after the internal multiple suppression. As seen in Figure 9b, the internal multiples below 6 s are mostly suppressed, and the horizontal difference in energy and frequency of the events below 6 s is smaller after the internal multiples are suppressed, particularly at the position indicated by the red arrow. To more clearly observe the effect of internal multiple suppression before and after, the part in the yellow box in Figure 9 is enlarged, as shown in Figure 10. In Figure 10, the event, which is similar to the upper strong reflection waveform with the opposite phase, periodic appearance, and significant lateral variation, is essentially suppressed. This is consistent with the analysis and identification results of multiples discussed earlier (Figures 2 and 3). The results demonstrate that the iterative virtual event multiple suppression method can effectively suppress the internal multiples in field data. Figure 9: Profile comparison before and after the internal multiple suppression. (**a**) Original stacked profile; (**b**) stacked section after the internal multiple suppression. To further analyze the suppression effect and accuracy of internal multiples, some sections before and after internal multiple suppression are selected for spectrum analysis, as shown in Figure 11. Figure 11a is the partial superimposed section before internal multiple suppression, Figure 11b is the partial superimposed section after internal multiple suppression, and Figure 11c shows the frequency distribution curve before and after internal multiple suppression. It can be seen from the figure that after suppressing internal multiples, the frequency spectrum is significantly broadened, and the spectral energy of the seismic profile is increased.