Using Wavelet Packet Denoising and a Regularized ELM Algorithm Based on the LOO Approach for Transient Electromagnetic Inversion

Transient electromagnetic method (TEM) inversion is a complex nonlinear problem with high dimensionality and ill-posedness. Using traditional neural networks based on a gradient algorithm to solve the TEM inversion problem might result in a slow convergence where the model falls easily into local minima. To solve these problems, a wavelet packet denoising (WPD) technology and a regularized extreme learning machine (ELM) algorithm based on the leave-one-out cross-validation (LOO) approach are proposed in this article. First, the WPD method is based on the hard threshold, the Shannon entropy with a Sym15 wavelet, which is provided to suppress the noise from the TEM data. Moreover, the learning process of the ELM model is optimized by randomly setting the hidden layer parameters instead of updating based on the gradient algorithm, which accelerates the learning speed. Finally, the LOO methodology is introduced to optimize the regularization factor of the ELM to improve the prediction accuracy and generalization ability of the approach. The inversion results of two typical TEM layered geoelectric models, two anomalous body models, and one field example are provided to prove the validity and feasibility of the proposed approach. In addition, compared with other traditional methods [ELM, backpropagation (BP), radial basis function (RBF), and linear support vector machine (LSVM)], the introduced method achieves higher inversion accuracy, better stability, and stronger forward data fitting ability, enabling it to effectively solve the TEM inversion problem.