基于高斯过程回归的瞬变电磁信号去噪方法

Denoising method of transient electromagnetic signal based on Gaussian process regression

  • 摘要: 【目的】 瞬变电磁法是当前探测煤田地下水的主要地球物理方法,探测结果直接影响煤矿防治水工作的开展。针对数据采集过程难以避开输电线路等电磁干扰源,瞬变信号容易混入电磁噪声,而主要的小波变换、经验模态分解去噪技术尚需进一步改进的客观现状,提出一种基于高斯过程回归的瞬变电磁信号去噪新方法。【方法】 对含噪信号进行时间补偿,使信号幅值处于基本相当的幅度;采用径向基函数核对时间补偿后的信号进行非参数回归拟合,捕捉信号非线性趋势并分离噪声;恢复时间补偿得到去噪结果。【结果】 (1)对分别添加正弦噪声、三角波噪声、均匀噪声和高斯噪声4种单类型噪声的瞬变电磁理论信号进行去噪后,信噪比分别提升24.61 dB~36.03 dB,平均相对误差降低5.93%~9.06%;(2)对分别添加2种混合噪声的瞬变电磁信号去噪后,信噪比分别提升28.05 dB、26.92 dB,平均相对误差分别降低5.22%、8.35%;(3)现场实验数据去噪结果相比含噪信号的信噪比提升18.76 dB,平均相对误差降低175.92%,实验点感应曲线中噪声的振荡影响被大幅消除,实验线反演电阻率断面恢复了地层的纵向地电结构和横向连续性,与无噪实验结果基本一致,相对小波变换结果有明显提升。【结论】 基于高斯过程回归的去噪算法对含有理论噪声或现场实验噪声的瞬变电磁信号,均取得了较为明显的去噪效果,可改进其协方差函数以进一步提高去噪效果,并在生产工作中应用。研究成果为瞬变电磁信号去噪提供了新手段并具有实用价值。

     

    Abstract: 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.

     

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