Objective The deep learning-based transient electromagnetic (TEM) forward and inverse modeling methods are data-driven, requiring considerable numerical simulation results as supervisory data to train and assess neural networks. The conventional finite-difference time-domain (FDTD) method for TEM numerical simulation necessitates an iterative solution of time-domain Maxwell's equations. Therefore, this method is time-consuming and computationally intensive, failing to meet the data demand of deep learning-based TEM inversion.
Methods This study introduced deep learning for TEM numerical simulation. Based on the transformer neural network architecture, a neural network for deep learning-based TEM numerical simulation was designed using an encoder-decoder structure. This neural network comprised a 3D gridding module, a patch embedding module, a transformer encoder module, and a linear decoder module. With geoelectric parameters as inputs, this neural network output corresponding TEM responses at the center of the loop source. It was trained for over 200 epochs using the optimization strategy of stochastic gradient descent with momentum combined with adaptive moment estimation (Adam)—an adaptive learning rate algorithm—on a server equipped with four NVIDIA V100 GPUs.
Results and Conclusions The trained network for deep learning-based TEM numerical simulation was employed to predict the TEM responses of the loop sources of four geoelectric models in real time: a homogeneous halfspace model, a layered model, a plate model, and a 3D volume model. The test results of the validation set reveal that the numerical simulation results after the turn-off time derived using the neural network exhibited low mean relative errors (MREs) of less than 2% compared to analytical solutions, linear digital filtering solutions, and FDTD numerical simulation results. Meanwhile, the numerical simulation results were obtained within 1 s. Therefore, the proposed neural network exhibited fast and accurate calculations. This study will provide a theoretical foundation and data support for research on deep learning-based TEM inversion.
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