重庆邮电大学学报（自然科学版）2025，Vol.37Issue(2)：204-214,11.DOI:10.3979/j.issn.1673-825X.202312280438
VMD与时间-空间分数阶扩散模型联合分段TEM滤波
Segmented TEM filtering combined with VMD and time-space fractional-order diffusion model
摘要
Abstract
To eliminate noise in transient electromagnetic(TEM)signals,this paper proposes a segmented filtering method based on variational mode decomposition(VMD)and a time-space fractional nonlinear diffusion model(TSFDM).Consid-ering the characteristics of TEM signals,the sampled signal is dynamically segmented using a threshold-based approach.VMD is then applied to each segment for adaptive decomposition,retaining the first intrinsic mode function(IMF1)as the initial filtered data.The time Caputo fractional derivative and spatial Riemann-Liouville fractional derivative in the time-space fractional diffusion equation are approximated using the discrete difference method and the displaced Grunwald-Letni-kov approximation method,respectively.An iterative convergence difference equation is established,and a smoothing oper-ator is applied to construct the TSFDM filter.The second-stage filtered signals obtained through TSFDM iterative computa-tion are stitched together using the superposition averaging method to reconstruct the complete TEM signal.Simulation re-sults show that the proposed method improves overall signal quality by approximately 22 dB and enhances the signal-to-noise ratio(SNR)of later-stage signals by approximately 38 dB,bringing it close to the original signal.Compared to traditional methods,the proposed approach achieves superior evaluation metrics.Additionally,the attenuation characteristics of meas-ured TEM signals are preserved,effectively restoring the variation trend of the frequency-domain curve.关键词
瞬变电磁信号(TEM)滤波/变分模态分解/阈值分段/时间-空间分数阶扩散模型(TSFDM)/差分方程Key words
transient electromagnetic method(TEM)signal filtering/variational mode decomposition(VMD)/threshold segmentation/time-space fractional-order diffusion model(TSFDM)/discrete difference equation分类
信息技术与安全科学引用本文复制引用
谭超,谭继伟,沈艳军,袁永榜,欧星作,闵薪宇,孙其浩..VMD与时间-空间分数阶扩散模型联合分段TEM滤波[J].重庆邮电大学学报（自然科学版）,2025,37(2):204-214,11.基金项目
国家自然科学基金项目(62273200) National Natural Science Foundation of China(62273200) （62273200）
