## 3 Inversion Experiments and Results
### Inversion of Synthetic Data
Especially for the case wherein 1 million training samples were used, the RMSE curves of the training and validation subsets are more stable, indicating that the learning process of the model is more stable and that the prediction performance is more reliable. Therefore, on the basis of sufficient computing resources, it is undoubtedly a recommended strategy to select a larger training sample set for model training. This not only helps to improve the prediction accuracy of the model but also optimizes the training efficiency to a certain extent. However, we should also be wary that excessively increasing the sample size may lead to an increased risk of model overfitting and unnecessary waste of computational resources. Based on the above analysis, in the subsequent actual data inversion work, we used a dataset containing 1 million training samples for model training and inversion in order to ensure the prediction accuracy, training efficiency, and effective utilization of computing resources. In order to further verify the effectiveness of the CNN inversion algorithm proposed in this paper, two types of simulation data, namely the forward modelling data of four simple models and four smooth models, respectively, were used to conduct exhaustive \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset Size**} & \multirow{2}{*}{**Epochs**} & \multirow{2}{*}{**Training Time**} & \multicolumn{2}{c}{**Training RMSE (log(S/m))**} & \multicolumn{2}{c}{**Validation RMSE (log(S/m))**} \\ \cline{3-7}  & & & **First Epoch** & **Last Epoch** & **First Epoch** & **Last Epoch** \\ \hline
10,000 & 128 & 770 s & 0.17429195 & 0.01394231 & 0.12349591 & 0.01427501 \\
100,000 & 116 & 6178 s & 0.08908294 & 0.00843343 & 0.04441574 & 0.00922912 \\
200,000 & 127 & 12,053 s & 0.06410906 & 0.00717885 & 0.03920344 & 0.00807352 \\
500,000 & 123 & 32,659 s & 0.04031481 & 0.00624532 & 0.01976297 & 0.00702438 \\
1,000,000 & 94 & 45,179 s & 0.02804457 & 0.00566881 & 0.0149168 & 0.00637553 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training time and RMSE values of five training experiments. Figure 2: RMSE change curves of the training and validation subsets. The data in (**a**) pertain to a case wherein 50,000 training samples were used; the data in (**b**) pertain to a case wherein 1 million training samples were used. inversion tests. The settings of thickness (T) or center depth (D) and conductivity (\(\sigma\)) for each layer of the simple and smooth models are shown in Tables 2 and 3, respectively. Figures 3 and 4 visually show the results of the CNN inversion (a CNN constructed based on 1 million training samples) compared with the regularization inversion [20]. From the inversion results, it can be clearly observed that the CNN inversion algorithm can reconstruct the layered structure of the theoretical model well, especially in the area of the high-resistivity layer. CNN inversion shows better performance than regularization inversion and can more accurately restore the real appearance of the stratigraphic structure. For simple models (as shown in Figure 3), the CNN inversion algorithm can accurately distinguish the boundary between different strata and reveal the hierarchical differences in the geological structure. For the more complex smooth model (as shown in Figure 4), the CNN inversion also performs well and is able to reconstruct the gently varying conductivity distribution in the strata, which further proves its capability in dealing with complex geological structures. Table 4 shows the RMSE between the inversion results and the theoretical model. It can also be seen from the RMSE data that the results obtained via CNN inversion are better than those obtained via regularization inversion. These excellent inversion results are attributed to the hybrid generation approach used in constructing the training sample data.