# A Deep Learning Estimation for Probing Depth of Transient Electromagnetic Observation
## 3 Deep Learning Model and Training  
We propose a residual neural network for rapid estimation of the probing depth from TEM data. The performance of deep learning models is greatly influenced by the training datasets; thus, a large number of the subsurface resistivity models and the corresponding TEM responses are often required. We chose a public standard benchmark database from [PERSON] et al. (2022) [20], and this database includes 1 million geologically plausible models and EM resolvable 1-D subsurface resistivity models spanning the resistivity range from 1 \(\Omega\)-m to 2000 \(\Omega\)-m and a depth of 500 m, which is suitable for ground-based and airborne EM systems in a DL context. Here we select a sub-dataset with an intermediate depth of 350 m which consists of 137,000 one-dimensional resistivity models. The vertical-induced electromotive force responses for these models are computed using 1D layered model analytical solutions [9], and the probing depths for each model are calculated using the sensitivity matrix obtained through a 1D electromagnetic field [19]. The training dataset comprises 90,000 samples, while the remaining 10,000 samples are allocated for testing purposes. Simulated TEM responses serve as the input to the neural network, and the computed probing depths are utilized as the network's output. Then, three deep learning models are constructed as shown in Figure 1. CNN (Convolutional Neural Network) is a deep learning model designed for processing data with a grid-like topology, such as images. It primarily consists of convolutional layers that apply filters to extract local features from the input, pooling layers that reduce the spatial dimensions of the feature maps, and fully connected layers that perform classification or regression tasks. RESNET (Residual Network) is a type of deep neural network that addresses the challenges of training very deep networks by incorporating residual blocks. These blocks use shortcut connections to skip one or more layers, allowing gradients to flow more easily through the network and mitigating issues like vanishing and exploding gradients [21]. RNN (Recurrent Neural Network) is a type of neural network designed for sequential data, where connections between nodes can create a cycle, allowing information to persist. RNNs are particularly useful for tasks involving time series or natural language, as they can capture temporal dependencies and patterns in sequences. LSTM (Long Short-Term Memory) is a specialized type of RNN (Recurrent Neural Network) [22] designed to address some of the limitations of traditional RNNs, particularly the vanishing and exploding gradient problems. LSTMs are well-suited for learning long-term dependencies in sequential data. The input of the DL models consists of two channels: the cut-off time and the induced electromotive force (IEF). We take the logarithm of the input to reduce the magnitude difference of the IEF [23]. The last neuron of each channel represents the heights of the transmitter and receiver coils. The final input data shape is 32 \(\times\) 2, where each channel contains 62 neurons for the cut-off time and electromotive force data, and 2 neurons for the height data. Observation elevations of receiving are randomly set to be uniformly distributed in the range [0, 30] m, and the height of the transmitting coil is 10-30 m higher than that of the receiving coil. The number of sampling points is variable and distributed uniformly between 20 and 31. The cut-off time points are distributed logarithmically between the earliest and latest shut-off times, and the earliest and latest cut-off times are also vari able, following a logarithmic uniform distribution: \(t_{late}e[10^{-5},10^{-4}]\), \(t_{early}e[10^{-35},10^{-15}]\), respectively. The output is a Gaussian distribution with a size of \(100\times 1\) representing the probing depth [24]. The maximum probing depth is set to 350 m, which depends on the scale of the models in the training dataset.