# A Deep Learning Estimation for Probing Depth of Transient Electromagnetic Observation
###### Abstract  
The probing depth of the transient electromagnetic method (TEM) refers to the depth range at which the underground conductivity changes can be effectively detected. It typically ranges from tens of meters to several kilometers and is influenced by factors such as instrument parameters and the conductivity of the subsurface structure. Rapid and accurate probing depth is useful for the selection of appropriate inversion parameters and improving survey accuracy. However, mainstream methods suffer from issues such as low computational precision, large uncertainties, or high computational requirements, making them unsuitable for processing massive airborne electromagnetic data. In this study, we propose a prediction model based on deep learning that can directly compute the probing depth from the TEM responses, and its effectiveness and accuracy are validated through synthetic models and field measurements. We compared the performance of classic deep learning models, including CNN, RESNET, and RNN, and found that RNN performed the best overall on both synthetic and field data. Furthermore, we apply this algorithm to deep learning-based ATEM inversion by constraining the one-dimensional resistivity model depths in the training set, to reduce the non-uniqueness of the inversion, accelerate the convergence, and improve its prediction accuracy. deep learning; transient electromagnetic method; probing depth prediction +
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of non-uniform resistivity structures and the number of sampling points. It relies on reasonable estimates of the half-space model, which introduces considerable uncertainty. The second method involves calculating the probing depth based on the Jacobian matrix derived from the inversion model [8]. This method allows for the calculation of probing depth for any model and takes into account the influences of noise and the number of sampling points. However, the second approach requires the availability of a well-defined inversion model, which itself depends on the predetermined probing depth. Additionally, the inversion process is inherently subject to non-uniqueness and affected by various parameters, leading to potential errors. Moreover, for large-scale datasets, such as airborne transient electromagnetic data, the Jacobian-matrix-based method entails a significant computational burden, making it unsuitable for real-time data processing [9]. A better approach is to directly calculate the probing depth based on the transient electromagnetic curve. To date, there is currently no developed algorithm for this purpose, but it is theoretically feasible since the probing depth depends on the resistivity model, which directly influences the observed data. In recent years, several studies have successfully applied deep learning (DL) algorithms to the one-dimensional inversion of ATEM [10, 11, 12]. These studies attempt to construct a \"fully mapping\" inversion operator that directly transforms observed data into predicted models [9, 10, 13, 14, 15] by minimizing the loss function of the predicted model based on the training data to obtain data-driven trained models [16, 17]. The training process allows neural network algorithms to abstract high-dimensional feature maps and learns complex mapping functions, thereby avoiding issues associated with linearized inversion, such as convergence to local minima. This study firstly proposes a new method for estimating TEM probing depth based on deep learning models. The method takes the cut-off time and induced electromotive force (IEF) as inputs and the probability distribution of the probing depth as output. It establishes a direct predictive model from the measurements to the probing depth, eliminating the need for inversion calculations and sensitivity matrix estimation. This approach reduces the subjective influence of manually setting involved parameters and improves the computational efficiency of the probing depth calculation.