## 4 Processing of Field Data  
This paper utilizes the V8 satellite synchronous MT acquisition system developed by Phoenix Geophysics, Canada, to analyze and process MT data collected from Datong in Shanxi province. The duration of data collection at the measurement points was approximately 4 h. Owing to the large volume of data, this paper focuses only on the complete sampling cycle time series segment of the electric field component Ex from the TS3 file at measurement point S7-19000, which exhibits various strong cultural noise interferences. The proposed PSO-optimized VMD method was employed for denoising, resulting in the visualization of the denoising effect of the field MT data time series signal shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Types of Noise**} & **Impulse** & **Square Wave** & **Triangular Wave** & **Periodic** \\ \hline \multirow{2}{*}{EMD} & NCC & 0.943 & 0.949 & 0.937 & 0.986 \\  & SNR & 9.548 & 10.491 & 10.174 & 18.408 \\ \hline \multirow{2}{*}{ITD} & NCC & 0.932 & 0.938 & 0.922 & 0.925 \\  & SNR & 9.327 & 10.367 & 9.863 & 10.794 \\ \hline \multirow{2}{*}{VMD} & NCC & 0.948 & 0.954 & 0.958 & 0.973 \\  & SNR & 9.809 & 10.515 & 10.361 & 12.802 \\ \hline \multirow{2}{*}{PSO-VMD} & NCC & 0.967 & 0.967 & 0.970 & 0.999 \\  & SNR & 11.773 & 11.869 & 12.110 & 26.482 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quantitative comparison of different denoising methods.  
The figure shows that the noise in the original signal is complex and diverse, with various typical strong cultural noises overlapping to different extents, resulting in complex signal characteristics. The energy amplitude of this noise is several orders of magnitude higher than that of the normal useful signal. After processing with the proposed method, the strong cultural noise superimposed on the original signal was effectively extracted, and the original trend in the data was retained, leading to a more accurate restoration of the genuinely useful MT information.  
To further evaluate the denoising effectiveness of the proposed method, this paper conducts a comprehensive analysis and assessment of the PSO-optimized VMD method using apparent resistivity and phase curves.  
In order to study the relationship between the resistivity of a homogeneous isotropic earth medium and the measured value of the magnetotelluric field on the ground, the impedance was introduced. The magnetotelluric field data were collected in four time series in Ex, Ey, Hx, and Hy channels, which were divided into a number of segments and Fourier transformed to obtain the frequency domain data for electric field strength (E) and magnetic field strength (H). Impedance (Z) reflects the electrical structure of the subsurface, linking the electric and magnetic channels in the frequency domain.  
By processing the field data, a comparative visualization of the apparent resistivity and phase curves was generated, as shown in Figure 6. The figure indicates that after simple power spectrum selection, the quality of the low-frequency data in the processed curves is significantly improved compared to that before denoising. The curves are smoother and more continuous, closely resembling the curves from the interference-free time periods.  
Figure 5: Denoising representation of time series signal of field MT data. Horizontal coordinates indicate sampling points and vertical coordinates indicate amplitude. The first line in blue indicates the initial signal, the second line in red indicates the extracted noise signal, and the third line in blue indicates the reconstructed denoised signal. (**a**) Field signal; (**b**) noise contours extracted using the VMD method; (**c**) reconstructed signal.