## 4 Results and Analysis
### Numerical Simulation Results and Analysis
#### 4.1.3 Kirchhoff Integral Pre-Stack Depth Migration Imaging of Synthetic Model  
Figures 6 and 7 show the imaging results of the pre-stack depth migration of the data obtained from the forward modeling of the model in Figure 2 by using the Kirchhoff integral pre-stack depth migration imaging method. Figure 6 shows the pre-stack depth migration imaging result of the Kirchhoff integral method without removing the direct wave, and Figure 7 shows the migration imaging result after removing the direct wave. It can be seen from Figures 6 and 7 that the actual velocity model is used as the migration velocity field in the imaging process, and the migration results can effectively restore the geological structure of the target layer boundary. The imaging section shows that the shape of the five-layer geological interface is basically consistent with the input model. The continuity of the reflected wave event is good, the energy distribution of each interface is uniform, and the resolution is high. By comparing the offset seismic profiles, the offset  
Figure 4: Ricker wavelet source.  
Figure 5: Seismic profile of the synthetic model.  
results significantly eliminate the interference of direct and multiple waves, and the imaging clarity and accuracy are effectively improved, which verifies the accuracy of the method.  
As shown in Figure 6, for the Kirchhoff pre-stack depth migration imaging results affected by unremoved direct waves, the interference of direct waves significantly affects the imaging accuracy of shallow and deep reflection events. There is discontinuity in  
Figure 6: Kirchhoff pre-stack depth migration imaging results without removing direct waves: (**a**) Kirchhoff pre-stack depth migration imaging; (**b**) illumination compensation; (**c**) compensated Kirchhoff pre-stack depth migration imaging.  
Figure 7: Kirchhoff pre-stack depth migration imaging results with removing direct waves: (**a**) Kirchhoff pre-stack depth migration imaging; (**b**) illumination compensation; (**c**) compensated Kirchhoff pre-stack depth migration imaging.  
shallow reflection events, and the signal-to-noise ratio of the deep reflection interface is low, resulting in a decrease in the resolution of the formation interface.  
As shown in Figure 7, the results of Kirchhoff pre-stack offset imaging with the effects of the excised direct wave show that after the interference of the direct wave is excised by the wavefield separation method, Kirchhoff pre-stack depth offset processing is performed again, and the results show that the reflection events of the shallow interfaces are clear and continuous, and the signal-to-noise ratio of the deep interfaces is significantly improved, and the imaging accuracy is significantly improved. The results of migration imaging restore the stratigraphic morphology and interface characteristics of the input model well, and the waveform continuity and energy distribution of each interface are enhanced.  
The final results show that the existence of the direct wave is one of the main factors affecting the accuracy of Kirchhoff pre-stack migration imaging. After removing the influence of direct waves, the interface characteristics of the imaging section in the shallow and deep parts are significantly improved, which provides method support and a theoretical basis for improving imaging accuracy under complex geological conditions in actual exploration.  
Figure 8 shows a comparison of the Kirchhoff pre-stack depth offset imaging results with the addition of model constraints (Figure 8a) and without (Figure 8b). As can be seen in Figure 8, the offset imaging results with model constraints added are clearer, the results match the modeled structural morphology, and the resolution of the laminar interface is higher than that of the imaging results without model constraints, which verifies the accuracy of the method.