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

Abstract

Magnetotelluric (MT) transfer-function estimation is severely challenged by strong industrial interference and random noise in complex observation environments. Here, we introduce a hybrid denoising framework that integrates Transformer-based interference identification with particle swarm optimization–variational mode decomposition (PSO-VMD). The Transformer identifies and suppresses strong high-frequency interference while preserving and reconstructing low-frequency signals. PSO-VMD adaptively optimizes the decomposition parameters to isolate and remove noise-dominated components and recover high-frequency signals. By integrating the complementary outputs of the two stages, the proposed framework achieves broadband reconstruction of MT time series. Experiments using synthetic and field data demonstrate that the method robustly suppresses complex interference and noise and substantially improves the accuracy and stability of MT transfer-function estimation. These results demonstrate that the proposed framework provides an effective approach for MT data processing in complex noise environments.