Improved Variational Mode Decomposition for Magnetotelluric Data Denoising Combined with Transformer Neural Network

Magnetotelluric (MT) signals are easily contaminated by strong cultural interference and random noise in complex observation environments, leading to distortion of estimated transfer functions. We proposed a joint denoising method integrating Transformer-based noise identification and particle swarm optimization-based variational mode decomposition (PSO-VMD). The Transformer model is first used to identify and locate strong interference noise in the original MT time series, after which abnormal segments are removed and reconstructed to suppress impulsive interference. Meanwhile, VMD is performed on the original signal, with PSO introduced to adaptively optimize the mode number K and penalty factor α, enabling the automatic search for the optimal parameter combination and the acquisition of the best decomposition result. Based on the optimized VMD results, the lower frequency mode components dominated by noise characteristics are removed, and the reconstructed signal from the remaining modes are further filtered to reduce random high-frequency noise. Finally, the filtered PSO-VMD components are superimposed on the Transformer output signal to reconstruct the final denoised MT time series. Both synthetic and observed experimental results show that the proposed method effectively improves the signal-to-noise ratio of MT time series, and further enhances the robustness of transfer functions, providing an effective technical approach for MT data processing in complex noise environments.