Denoising method of transient electromagnetic signal based on Gaussian process regression

Objective The transient electromagnetic method is currently the primary geophysical technique used for detecting groundwater in coalfields. Its detection results directly influence the implementation of mine water prevention and control measures. The data acquisition process for transient electromagnetic (TEM) methods often struggles to avoid electromagnetic interference sources such as power lines. Consequently, transient signals are susceptible to contamination by electromagnetic noise, while primary denoising techniques like wavelet transform and empirical mode decomposition still require further improvement. This study proposes a novel denoising approach for TEM signals based on Gaussian Process Regression (GPR). Methods The denoising procedure is as follows: (1) Apply time compensation to the noisy signal to normalize its amplitude to a roughly equivalent magnitude; (2) Employ a radial basis function kernel to perform non-parametric regression fitting on the time-compensated signal, capturing the non-linear trend of the signal and separating the noise; (3) Reverse the time compensation to obtain the final denoised result. Results (1) After denoising the transient electromagnetic theory signals with four types of single-type noise (sinusoidal noise, triangular wave noise, uniform noise, and Gaussian noise) added respectively, the SNR is increased by factors of 1.97 to 2.34, and the mean relative error (MRE) is reduced by factors of 25.48 to 55.00. (2) After denoising the transient electromagnetic signals with two types of mixed noise added respectively, the SNR is increased by factors of 2.00 and 2.13, and the MRE is reduced by factors of 33.62 and 27.93, respectively. (3) For the field data, denoising achieves an SNR increase by a factor of 12.49 and an MRE reduction by a factor of 13.34, compared to the noisy signal. The oscillatory effects of noise in experimental point induction curves are significantly eliminated. Moreover, the inverted resistivity section from the experimental line restores the longitudinal geo-electrical structure and the lateral continuity of the strata, showing basic consistency with the noise-free experimental results, and there is a significant improvement compared to the results of the wavelet transform. Conclusions The denoising algorithm based on Gaussian process regression yields significant effectiveness on transient electromagnetic signals containing theoretical noise or field experimental noise. Its kernel function can be further optimized to improve the denoising effect and applied in production work. The research results provide a new means for the denoising of transient electromagnetic signals and have practical value.