Neural networks (NNs) are efficient tools for rapidly obtaining geoelectric models to solve magnetotelluric (MT) inversion problems. Training an NN with strong predictive power requires numerous training samples to prevent underfitting. To reduce the computational burden of generating a large number of training samples, this work analyzes the influence of the sample features and distribution on the training effect for an NN and proposes an efficient method of sample generation. This innovative method consists of three steps: 1) geoelectrically simplifying the features; 2) removing unnecessary features on the basis of realistic geological characteristics; and 3) mapping the samples to a higher-dimensional space. Numerical examples based on simple stratified models show that the number of samples can be reduced to below one-millionth of the original number while improving the predictive effect of the NN. The performance and effectiveness for processing more complex structures are verified by the inversion results obtained for a public data set, COPROD2. We conclude that this advanced method can generate high-quality training samples at a greatly reduced computational cost. The analysis of the sample features and distribution not only advances the state of research on the use of machine learning in geophysical inversion but also is a forward-looking study on the mechanisms of underfitting, tracing the source of these phenomena back to the training samples used.

As a trenchless detection approach, the transient electromagnetic method (TEM) can effectively detect well-conducted geoelectric structures, such as groundwater structures. The nonlinear TEM inversion process represented by neural network (NN) inversion does not rely on the initial model, which helps it efficiently and accurately obtain geoelectric structures. In this article, a factor analysis (FA)-based deep belief network (DBN) inversion framework built on hybrid memetic pretrained (HMP), HMP-FADBN, is proposed. We construct a DBN with restricted Boltzmann machines (RBMs) and backpropagation NNs (BPNNs) as the base fitting skeleton. FA is used to reduce the dimensionality of the feature space of the DBN. The hybrid memetic (HM) whale optimization algorithm (WOA) pretrains the network parameters and uses the memetic strategy to adjust the coordinated development system of social and individual cognition to enhance the network training effect. Numerical examples show that the prediction accuracy of the proposed HMP-FADBN for TEM geoelectric models is improved from more than 10% to approximately 2%. Moreover, 5%, 10%, and 15% noise tests show that the trained NN has good generalization and denoising abilities, and the prediction accuracy is less than 3% (affected by the maximum noise). Finally, the developed method is successfully applied to a landslide TEM survey, and the predicted quasi-2D geoelectric structure is consistent with the original geological structure.