A Gaussian process regression-based denoising method for transient electromagnetic signals

Authors

WANG Peng, College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, ChinaFollow
SHI Jiaxing, College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, China
LU Kai, School of Earth Sciences and Engineering, Xi’an Shiyou University, Xi’an 710065, ChinaFollow
HU Jinru, College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, China
WEN Guangyuan, College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, China
ZHAI Haojie, College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, China

Abstract

Objective The transient electromagnetic (TEM) method serves as a primary geophysical technique for groundwater detection in coalfields at present, with the detection results directly influencing the implementation of water hazard prevention and control in coal mines. Since it is difficult to avoid electromagnetic interference sources such as power lines during data acquisition, TEM signals are prone to be contaminated by electromagnetic noise. Given that primary denoising techniques such as wavelet transform and empirical mode decomposition (EMD) are yet to be further improved, this study developed a novel Gaussian process regression (GPR)-based denoising method for TEM signals. Methods First, time alignment was applied to the noisy TEM signals to ensure roughly equivalent signal magnitudes. Next, non-parametric regression-based fitting was performed for the aligned TEM signals using the radial basis function (RBF), aiming to capture the non-linear trend of the signals and separate noise. Finally, temporal alignment was reversed to obtain the final denoising results. Results For theoretical TEM signals contaminated by four types of individual noise (e.g., sinusoidal, triangular wave, uniform, and Gaussian noise), the proposed method increased their signal-to-noise ratios (SNRs) by 24.61 dB‒36.03 dB and decreased their mean relative errors (MREs) by 5.93%‒9.06%. For TEM signals contaminated by two types of mixed noise, the proposed method increased their SNRs by 28.05 dB and 26.92 dB and decreased their MREs by 5.22% and 8.35%. For field experimental data from a coalfield, the new method increased their SNR by 18.76 dB and decreased their MRE by 175.92%. The oscillatory effects of noise in the induction curves of the survey points were significantly eliminated. Furthermore, the inverted resistivity sections of the survey line exhibited restored longitudinal geoelectric structures and lateral continuity of the strata. The experimental results were roughly consistent with those of noise-free TEM signals. Compared to the wavelet transform, the proposed method exhibited a significant improvement in the denoising results. Conclusions The GPR-based denoising algorithm yields significant denoising results for TEM signals contaminated by theoretical or field experimental noise. For practical applications, its denoising effect can be further improved by improving its covariance function. The results of this study provide a novel, practical solution for the TEM signal denoising.

Keywords

coalfield, transient electromagnetic (TEM) method, Gaussian process regression (GPR), denoising, electromagnetic noise, curve fitting

DOI

10.12363/issn.1001-1986.25.04.0300

Recommended Citation

WANG Peng, SHI Jiaxing, LU Kai, et al. (2026) "A Gaussian process regression-based denoising method for transient electromagnetic signals," Coal Geology & Exploration: Vol. 54: Iss. 2, Article 18.
DOI: 10.12363/issn.1001-1986.25.04.0300
Available at: https://cge.researchcommons.org/journal/vol54/iss2/18

Reference

[1] 曾一凡,武强,赵苏启,等. 我国煤矿水害事故特征、致因与防治对策[J]. 煤炭科学技术,2023,51(7):1−14

ZENG Yifan,WU Qiang,ZHAO Suqi,et al. Characteristics,causes,and prevention measures of coal mine water hazard accidents in China[J]. Coal Science and Technology,2023,51(7):1−14

[2] 刘晓宁. 瞬变电磁技术在工作面顶板水害防治中的应用[J]. 煤矿安全,2020,51(3):153−156

LIU Xiaoning. Application of transient electromagnetic method (TEM) in coal mine roof water hazard prevention and treatment[J]. Safety in Coal Mines,2020,51(3):153−156

[3] 刘伟,吴朝钢,孙俊峰,等. 瞬变电磁法在广昆铁路牧羊村2号隧道岩溶水害治理中的应用[J]. 云南大学学报(自然科学版),2023,45(增刊1):123−128

LIU Wei,WU Chaogang),SUN Junfeng,et al. Application of transient electromagnetic method in the management of karst water damage in Muyangcun 2# tunnel of Guang–Kun railway[J]. Journal of Yunnan University (Natural Sciences Edition),2023,45(Sup.1):123−128

[4] 刘贵忠，邸双亮. 小波分析及其应用[M]. 西安：西安电子科技大学出版社，1992.

[5] 李貅,宋建平,马宇,等. 基于小波分析的TEM信号提取[J]. 煤田地质与勘探,2005,33(2):72−75

LI Xiu,SONG Jianping,MA Yu,et al. The abstract of TEM signal based on the wavelet analysis[J]. Coal Geology & Exploration,2005,33(2):72−75

[6] 刘志新,于景邨,张华,等. 小波变换在矿井瞬变电磁法中的应用[J]. 煤田地质与勘探,2007,35(4):70−72

LIU Zhixin,YU Jingcun,ZHANG Hua,et al. Application of wavelet transfer in coal mine transient electromagnetic method[J]. Coal Geology & Exploration,2007,35(4):70−72

[7] 解海军,李静蕊,董毅,等. 小波基和阈值参数对瞬变电磁信号去噪效果影响[J]. 西安科技大学学报,2020,40(4):682−690

XIE Haijun,LI Jingrui,DONG Yi,et al. Influence of wavelet base and threshold parameters on de–noising effect of transient electromagnetic signal[J]. Journal of Xi’an University of Science and Technology,2020,40(4):682−690

[8] 古瑶,解海军,李璐,等. 基于小波包–神经网络混合算法的瞬变电磁信号降噪研究[J]. 煤炭工程,2023,55(5):147−152

GU Yao,XIE Haijun,LI Lu,et al. Denoising of transient electromagnetic data based on wavelet packet–neural network algorithm[J]. Coal Engineering,2023,55(5):147−152

[9] 杨通田. 坑道等值反磁通瞬变电磁法噪声处理方法技术研究[D]. 长沙：中南大学，2024.

YANG Tongtian. Technical study on noise processing methods of opposing coils transient electromagnetic method in pits[D]. Changsha：Central South University，2024.

[10] 毛鑫鑫,毛立峰,杨聪,等. 半航空瞬变电磁数据小波降噪方法研究[J]. 地球物理学进展,2021,36(3):1287−1296

MAO Xinxin,MAO Lifeng,YANG Cong,et al. Research on wavelet denoising method for semi–airborne transient electromagnetic data[J]. Progress in Geophysics,2021,36(3):1287−1296

[11] 郑梓强. 半航空瞬变电磁运动噪声去除方法研究及数据预处理软件开发[D]. 济南：山东大学，2023.

ZHENG Ziqiang. Research on motion–induced noise removal method of semi–airborne transient electromagnetic and software development for data pre–processing[D]. Jinan：Shandong University，2023.

[12] 陈成栋. 半航空瞬变电磁数据采集设计和数据校正研究[D]. 济南：山东大学，2021.

CHEN Chengdong. Study of data acquisition design and data correction research for semi–airborne transient electromagnetics[D]. Jinan：Shandong University，2021.

[13] 刘帅. 瞬变电磁降噪新方法研究[D]. 桂林：桂林电子科技大学，2020.

LIU Shuai. Research on a new method of transient electromagnetic denoising[D]. Guilin：Guilin University of Electronic Technology，2020.

[14] HUANG N E，ATTOH–OKINE N O. The Hilbert–Huang transform in engineering[M]. Boca Raton：CRC Press，2005.

[15] HUANG N E,LONG S R,WU M L C,et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non–stationary time series analysis[J]. Proceedings of the Royal Society:Mathematical,Physical and Engineering Sciences,1998,454(1971):903−995.

[16] 朱通,杨文明,冯兵. Hilbert–Huang变换在瞬变电磁去噪中的研究与应用[J]. 地球物理学进展,2019,34(6):2389−2397

ZHU Tong,YANG Wenming,FENG Bing. Study on transient electromagnetic method of denoising based on Hilbert–Huang transform[J]. Progress in Geophysics,2019,34(6):2389−2397

[17] 向锡斌. 定源回线地–空瞬变电磁噪声处理研究[D]. 昆明：昆明理工大学，2024.

[18] 彭梦梦. 井下合成瞬变电磁阵列信号重构方法研究[D]. 西安：西安石油大学，2022.

PENG Mengmeng. Research on signal reconstruction method of borehole synthetic transient electromagnetic array[D]. Xi’an：Xi’an Shiyou University，2022.

[19] 戚庭野,卫会汝,冯国瑞,等. 基于WOA–VMD的瞬变电磁探测信号降噪方法[J]. 中南大学学报(自然科学版),2021,52(11):3885−3898

QI Tingye,WEI Huiru,FENG Guorui,et al. Denoising method of transient electromagnetic detection signal based on WOA–VMD algorithm[J]. Journal of Central South University (Science and Technology),2021,52(11):3885−3898

[20] WANG Guofu，DENG Peng，ZHANG Faquan，et al. Noise reduction of the transient electromagnetic weak signal under strong noise based on power detection of EMD[J]. Applied Mechanics and Materials，2011，110/111/112/113/114/115/116：1606–1612.

[21] LIU Fubo,LI Jutao,LIU Lihua,et al. Application of the EEMD method for distinction and suppression of motion–induced noise in grounded electrical source airborne TEM system[J]. Journal of Applied Geophysics,2017,139:109−116.

[22] 李杰. 基于经验模态分解与独立成分分析的航空瞬变电磁去噪方法研究[D]. 西安：长安大学，2020.

LI Jie. Study on airborne transient electromagnetic method of denoising based on empirical mode decomposition and independent component analysis[D]. Xi’an：Chang’an University，2020.

[23] 张清河,吴欣悦,刘含,等. 一种新颖的探地雷达快速正演模拟及埋地目标探测机器学习方法[J]. 地球物理学报,2023,66(8):3482−3492

ZHANG Qinghe,WU Xinyue,LIU Han,et al. A novel method for fast forward simulation of ground penetrating radar and buried target detection based on machine learning[J]. Chinese Journal of Geophysics,2023,66(8):3482−3492

[24] 刘晨阳. 基于深度学习的时间域航空瞬变电磁数据处理方法研究[D]. 长春：吉林大学，2024.

LIU Chenyang. Research on time–domain airborne transient electromagnetic data processing methods based on deep learning[D]. Changchun：Jilin University，2024.

[25] 赵腾远,宋超,何欢. 小样本条件下江苏软土路基回弹模量的贝叶斯估计:基于静力触探数据与高斯过程回归的建模分析[J]. 岩土工程学报,2021,43(增刊2):137−141

ZHAO Tengyuan,SONG Chao,HE Huan. Bayesian estimation of resilient modulus of Jiangsu soft soils from sparse data:Gaussian process regression and cone penetration test data–based modelling and analysis[J]. Chinese Journal of Geotechnical Engineering,2021,43(Sup.2):137−141

[26] 刘怡茹,陈龙舟,林兴元. 高斯过程回归在航空瞬变电磁去噪中的应用[J]. 工程地球物理学报,2018,15(6):771−779

LIU Yiru,CHEN Longzhou,LIN Xingyuan. The application of Gaussian process regression in aviation transient electromagnetic denoising[J]. Chinese Journal of Engineering Geophysics,2018,15(6):771−779

[27] 刘怡茹. 基于高斯过程回归的时间域航空电磁去噪方法研究[D]. 成都：成都理工大学，2019.

LIU Yiru. Research on the denoising methods based on Gaussian process regression for time domain airborne electromagnetic data[D]. Chengdu：Chengdu University of Technology，2019.

[28] 胡承林. 综合物探技术在煤矿采空区的应用研究[D]. 成都：成都理工大学，2011.

HU Chenglin. The appliance research of integrated geophysical techniques on colliery gob[D]. Chengdu：Chengdu University of Technology，2011.

[29] SCHULZ E,SPEEKENBRINK M,KRAUSE A. A tutorial on Gaussian process regression:Modelling,exploring,and exploiting functions[J]. Journal of Mathematical Psychology,2018,85:1−16.

[30] ROBERTS S J,OSBORNE M A,EBDEN M,et al. Gaussian processes for time–series modelling[J]. Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,2013,371(1984):20110550.

[31] WANG Shenlong，ZHANG Lei，URTASUN R. Transductive Gaussian processes for image denoising[C]//2014 IEEE International Conference on Computational Photography (ICCP). Santa Clara：IEEE，2014：1–8.

[32] CRESSIE N，WIKLE C K. Statistics for spatio–temporal data[M]. Hoboken：Wiley，2011.

[33] HASTIE T，TIBSHIRANI R，FRIEDMAN J. The elements of statistical learning：Data mining，inference，and prediction (2^nd Edition)[M]. New York：Springer New York，2009.

[34] GHASSEMI N H，DEISENROTH M P. Analytic long–term forecasting with periodic Gaussian processes[C]//Artificial Intelligence and Statistics. PMLR，2014：303–311.

[35] THOMAS E,SARIN V. Augmented low–rank methods for Gaussian process regression[J]. Applied Intelligence,2022,52(2):1254−1267.

[36] KAUFMAN A A，KELLER G V. Frequency and transient soundings[M]. Amsterdam：Elsevier，1983.

[37] WANG Peng,WANG Qing,WANG Yi,et al. Detection of abandoned coal mine goaf in China’s Ordos Basin using the transient electromagnetic method[J]. Mine Water and the Environment,2021,40(2):415−425.