# A Deep Learning Estimation for Probing Depth of Transient Electromagnetic Observation
## 6 Discussion  
Recently, several research studies have successfully applied deep learning algorithms to one-dimensional transient electromagnetic (TEM) rapid inversion [9; 10; 11; 12]. Despite achieving encouraging progress, most of these studies have primarily focused on neural network structure and data preprocessing, with less discussion on how to set up a reasonable training dataset. As a data-driven approach, deep learning algorithms heavily rely on the rationality of the training dataset. The design of the training dataset not only needs to cover as many underground structures as possible but also needs to comply with the characteristics of the geophysical field itself. For instance, if the resistivity models in the training dataset exceed the resolution of the TEM method, the neural network cannot identify high-resolution structures from the corresponding observed data. As a result, the loss function may not decrease adequately, leading to a decline in prediction capability. Similarly, for certain low-resistivity models, the probing depth of TEM is limited and may  
Figure 4: Probing depth prediction of field data using different DL models. The map shows the location of the study area at Fort Irwin, California, USA. The resistivity section along line L10450 is gained by stitching together the 1-D models obtained from [PERSON] et al. (2014) [27]. The black, green, and red dots represent the probing depth predicted by the ResNet, CNN, and RNN, respectively. not be sufficient to identify structures below the probing depth. In such cases, the neural network also fails to provide accurate predictions. Conventional inversion methods for TEM typically employ regularization algorithms [28; 29] ([PERSON] and [PERSON], 1977; [PERSON] et al., 1995), which means that models without resolution are mainly determined by the regularization smooth term in the objective function. However, neural networks do not possess this characteristic, resulting in weaker prediction capability below the probing depth. To address this issue, we utilize the proposed rapid prediction algorithm to constrain the probing depth of the publicly available resistivity model repository from [PERSON] et al. (2022) ([PERSON] et al., 2022). Then, we conduct TEM one-dimensional inversion based on UNet (Figure 5) for both the unconstrained and constrained model repositories, and compare the prediction results of the two to validate the effectiveness. As the TEM inversion problem requires a more advanced architecture than probing depth prediction to learn more complicated characteristics, we adapt the prevalent CNN-based UNet ([PERSON] et al., 2017) architecture to directly learn the mapping from input (TEM response) to output (Resistivity model). The input data structure of UNet in Figure 5 is completely identical to that of ResNet in Figure 1, which means UNet is capable of handling various data of ground and airborne transient electromagnetics, including different cut-off times and different numbers of sampling points. We employ two types of processing for the output data labels: 1 Datasets1: The resistivity models at a fixed depth of 350 m are obtained from the standard benchmark database. 2 Datasets2: ResNet is utilized to predict the probing depth for each model in 1, and then the portion above the predicted detection depth is extracted as new labeled data. Additionally, a spline interpolation algorithm is employed to maintain the same number of layers as the original model, ensuring compatibility with the output dimensions of the neural network. Then, two training sets are used to train two models, which are defined as \(UNet_{1}\) and \(UNet_{2}\). Figure 6 illustrates the evolution of the loss function during the training process for the two training sets. It can be observed that the errors of both training sets gradually decrease and stabilize with increasing iterations, and the error curve of the constrained training set shows a greater reduction compared to the unconstrained training set.