## 3 Experimental Validation
The forward-model-simulated results obtained using neural network models \(\textsl{g}_{20000}\) and the ray method are shown in Figure 8. Figure 8c shows the residual comparison between forward modeling using neural networks \(\textsl{g}_{20000}\) and the ray method. It can be seen that the accuracy of the simulated result based on \(\textsl{g}_{20000}\) is superior to that yielded by the ray method. Errors in forward modeling will affect the inversion results and reduce their accuracy. The MCMC method can be used to statistically analyze the model errors of forward model methods, explain the model errors during the inversion process, and reduce the impact of model errors on the inversion results. In this study, we used 1000 samples to statistically analyze model errors, and the one-dimensional distribution results regarding model errors for different forward models are shown in Figure 9. To further compare different forward models, Figure 10 shows the covariance matrices corresponding to each forward model. \(\textsl{g}_{10000}\) and \(\textsl{g}_{20000}\) lead to a less-correlated covariance model as opposed to that obtained using the ray method, as seen in the (lack of) off-diagonal elements of the estimated covariance model. The posterior probability density function samples obtained by using the trained neural network instead of the forward model and using the Monte Carlo method are shown in Figure 11. In Figure 11, the first model in each row is the reference velocity model, and the remaining four models are samples of a posterior distribution obtained using the corresponding forward-modeling method. The figure shows that as the amount of training  
Figure 5: Observation data: 702 travel times. increases, the inversion results gradually approach the reference model. This proves the effectiveness of using the SE-CNN neural network method for MCMC inversion. Figure 12 shows the mean of the posterior distribution samples of the inversion results. From Figure 12, it can be seen that for the mean model, as the training size increases, the details of the mean value of the research results also increases, and it is closer to the reference model. But even for SE-CNN networks with small training sizes, their mean model can still reflect the characteristics of the reference model, such as training sizes of 1000 and 5000. Figure 6: (**a-d**) Four different sampling models obtained using prior information. Figure 7: (**a**) Traveltime data simulated based on \(g_{1000}\); (**b**) traveltime data simulated based on \(g_{5000}\); (**c**) traveltime data simulated based on \(g_{10000}\). Figure 8: (**a**) Traveltime data simulated based on \(g_{20000}\); (**b**) traveltime data simulated based on ray method; (**c**) residual of \(g_{20000}\) and ray method. Figure 4:0 (**a-e**) Covariance matrix of five forward methods using trained neural network and ray method. Figure 4:1 1D distribution of the modeling errors using neural network and ray method. Figure 4:2 (**a–e**) Four samples of the a posterior probability density of the forward models using trained neural network and ray method. To further compare the inversion results, we subtracted the mean of the inversion results of each method from the reference model to obtain the corresponding residual distribution, as shown in Figure 4:3 As the size of the trained neural network increases, the residual gradually decreases, which is consistent with our analysis of the inversion results in Figures 11 and 12. In order to test the efficiency of the different methods, different forward models were tested with regard to forward time, and the time taken for 100 forward simulations of different forward models was recorded. The results are shown in Figure 4:4 Compared with the most accurate model, both the forward models based on neural networks and that based on the ray method significantly improve computational efficiency.