# A Deep Learning Estimation for Probing Depth of Transient Electromagnetic Observation
## 5 Field Example  
To investigate the practical applicability of the algorithm proposed in this study, airborne transient electromagnetic data collected by the United States Geological Survey (USGS) in Leach Lake Basin, California, Fort Irwin, were utilized for testing ([[http://dx.doi.org/10.3133/off20131024G](http://dx.doi.org/10.3133/off20131024G)]([http://dx.doi.org/10.3133/off20131024G](http://dx.doi.org/10.3133/off20131024G))). The survey area is a geologically complex, internally drained basin bisected and flanked by a number of faults, as shown in Figure 4.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **MAE** & **MAPE** & **RMSE** & **Cross-Entropy** \\ \hline CNN & 0.032 & 0.56\% & 0.105 & 0.056 \\ RESNET & 0.039 & 1.94\% & 0.118 & 0.064 \\ RNN & 0.031 & 0.34\% & 0.102 & 0.055 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance of different deep learning models on test datasets.  
Figure 3: **(a)** Model I. The numbers indicate resistivity (\(\Omega\cdot\)m). **(b)** Model II. **(c)** The probing depth derived from the 1D inverted model I (white with regularization parameter 0.2 and green curves with 1.0). Dotted and orange curves show the probing depth derived from true model and ResNet. **(d)** The brown points show the probing depth derived from the 100 1D inverted model II, which are obtained from 100 synthetic IEFs with 10% random Gaussian noise. The background model was obtained from a noise-free 1D inversion. The cyan points show the probing depth derived from ResNet using the same 100 synthetic IEFs with 10% random Gaussian noise. The vertical orange line length on each scatter point represents the standard deviation.  
Inverting a large volume of AEM data and calculating probing depth is very time-consuming by conventional inversion techniques. A conventional 1D inversion and Jacobian matrix computation typically require around 20 to 30 s for a single TEM measurement. Using well-trained ResNet in our study, however, it takes less than 2 s to obtain over 2000 probing depth estimations. This is of great significance for handling a large volume of field-measured airborne TEM data. The inversion profile in Figure 4 is from [PERSON] et al. (2014) [27], and the probing depth is obtained through the inversion model. The dots in the profile represent the probing depth predicted by the DL models. The variation trends of the predicted probing depth by the three DL models are generally consistent with the probing depth calculated through the inverted model. Specifically, in areas with lower overall resistivity, the predicted probing depth is shallow, while in areas with higher overall resistivity, the predicted probing depth is greater. This alignment confirms the effectiveness of the DL models in predicting the probing depth based on the field airborne transient electromagnetic measurements.  
The predictions from RNN and RESNET are essentially overlapping, while the depth predicted by CNN is relatively shallower. Since the predictions from RNN and RESNET are closer to the traditional methods, we believe that RNN and RESNET better capture the nonlinear relationship between the observations and probing depth, resulting in superior prediction performance. This is particularly interesting although RESNET does not seem to outperform CNN on the test set (Table 1, Figure S1), it exhibits better generalization ability on field data. In general, RNN performed the best overall on both synthetic and field data. Due to the more complex architectures of the RNN and RESNET models compared to CNN, these findings suggest that advanced models have an advantage in data transferability.