## 3 Inversion Experiments and Results
### Inversion of Synthetic Data  
To illustrate the effectiveness of our inversion method, we first tested it on synthetic data. In the process of generating the forward model sample set, the conductivity value range was set between 0.0001 S/m and 1 S/m to simulate the electrical characteristics under different geological conditions, and the maximum depth of the model was set to 200 m to cover the common detection depth range for ATEM. The coil height was randomly selected to be in the range of 20 m to 50 m. For the simple forward modeling model, we limited the maximum number of layers to five layers in order to simulate relatively simple geological structures. The thickness of each layer was randomly determined to be in the range of 5 m to 100 m to reflect the variation in thickness of different geological layers. For the smooth forward modeling model, the number of model layers was fixed at 20 layers, and the thickness of each layer was 10 m, to ensure that the model is insensitive to the change in inter-layer conductivity. Of these 20 layers, 1 to 5 layers were randomly selected, and conductivity values were assigned to these selected layers using the same conductivity random generation method as the simple model. The conductivity values of the remaining unselected layers were calculated by interpolation. In order to unify the training data format, we used interpolation technology to convert all forward modeling models into 25-layer models of fixed thickness, and the conductivity values of each layer were extracted to form a vector with a length value of 25 (25 \(\times\) 1) as the output of deep learning network training. In the forward simulation stage, we selected 24 electromagnetic response data points at logarithmic intervals from 0.06 ms to 6.64 ms after the current was turned off. The electromagnetic response data, together with the height of the transmitting coil, formed a vector with a length value of 25 (25 \(\times\) 1), which was used as an input to train the deep learning network. The number of training samples has a great influence on the training of the CNN. For this paper, we conducted five training experiments to analyze the influence of dataset size on the network model, and the number of training samples was 10,000, 100,000, 200,000, 500,000, and 1 million. The data were split into training and validation subsets using 80 and 20 percent of the data, respectively. The training subset was used to train the network, while the validation subset was used to evaluate the performance of the CNN model during the training procedure. The Adam optimization algorithm was used for model training, and the optimization process was performed using a predefined number of iterations (epochs). In this study, the predefined number of epochs was 1000, and in order to avoid overfitting or underfitting problems caused by an excessive or insufficient number of epochs, the early stopping regularization method was used. When the loss value on the validation subset was not improved for 10 consecutive iterations, the training process automatically stopped. Table 1 shows the training time and RMSE values of the five training experiments. As seen from Table 1, with an increase in the number of training samples, the RMSE of both training and validation subsets gradually decreased, but the training time gradually increased. When the number of training samples increased from 500,000 to 1 million, although the number of samples increased by 100%, the number of iterations decreased by 23.6%, and the training time only increased by 38.3%. Figure 2 shows the RMSE change curves of the training and validation subsets during the training process for 500,000 and 1 million training samples. From the changes in the curves, it can be seen that the network training process shows good convergence.