## 2 Principles and Methods  
### Analysis of Magnetotelluric Noise  
The MT method is based on the theory of plane electromagnetic waves being perpendicularly incident along a horizontally uniform layered medium. When the measurement area is relatively far from the field source, the scale of horizontal inhomogeneity in the area's structure is small, and the exploration depth is not particularly deep, the plane wave assumption remains valid [18]. In the MT method, plane electromagnetic waves serve as effective field sources, whereas field sources that do not satisfy the characteristics of plane waves are referred to as noise [19]. Interference noise is mainly categorized into source, geological, and cultural noise, each with different causes and mechanisms of electromagnetic signal generation, resulting in varying impacts on geomagnetic observation data [20].  
Source noise is primarily caused by natural electromagnetic fields outside the Earth. Geological noise arises from the influence of geological factors in the measurement area on the electrical properties of Earth's medium, mainly including static displacement distortions caused by locally inhomogeneous bodies near the surface and topographical effects due to terrain variations [21]. Although both source noise and geological noise can affect various frequency bands of the MT signals, they can be corrected and eliminated using various calibration methods [22]. Therefore, this paper will not delve deeply into geological noise and source noise, but will focus on analyzing and processing strong cultural noise in MT signals. Cultural noise is electromagnetic noise generated by artificial electromagnetic field sources [23], including power transmission systems, electrical equipment, industrial stray currents, railways, and highways. The signal intensity of such noise can be several times or even several orders of magnitude higher than that of normal signals, leading to the obliteration of MT signals and resulting in serious deviations in the computed apparent resistivity and phase curve data. When these cultural electromagnetic wave noises are vertically incident to the ground, they can be regarded, in a sense, as field source signals for MT. However, this electromagnetic noise is often close to the observation point and is highly variable, failing to meet the conditions of vertical incidence. Thus, it is classified as non-plane waves, not conforming to the requirements of MT for field sources; hence, cultural noise is typically categorized as noise signals [24].  
According to on-site investigations, the area is traversed by highways, national roads, and rural roads with frequent trains and high-speed railway. Additionally, high-voltage power lines and transmission towers are densely distributed in the region, factors that are expected to significantly interfere with the field MT signals. An analysis of the field time series signals has confirmed the existence of such interference. The analysis revealed a variety of noise types in the area, with common strong cultural noise categorized by waveform characteristics into impulse noise, square wave noise, triangular wave noise, and periodic noise. To examine the denoising performance of the VMD algorithm on strong cultural noise and further investigate the impact of the initial parameter settings on the decomposition results, this paper conducted simulation experiments on typical strong cultural noise. A complete segment of time series data was extracted from the field data file TS3 at the S6-5000 measurement point to serve as a clean signal, resulting in a clean-signal time-domain waveform. Based on this, four types of strong cultural noise were simulated, ultimately producing a simulated time-domain waveform of strong cultural noise, as shown in Figure 1.