大地电磁信号中的长周期噪声主要存在于信号的低频、甚低频分段，此类噪声幅值大、随机性强，能将有效的电磁信号完全淹没，导致低频段反演结果出现严重的偏差，为了有效去除大地电磁信号中的长周期噪声，结合变分模态分解（Variational Mode Decomposition，VMD）和多分辨分析的特点，提出了多分辨VMD算法：首先对信号的低频本征模态分量（Intrinsic Mode Function，IMF）进行多层VMD处理，提高长周期噪声在信号低频、甚低频分段的时频分辨率；之后根据噪声的时频特性准确地筛选出包含长周期噪声的IMF分量；最后剔除掉这些IMF分量，达到去除长周期噪声的目的。使用此算法分别对仿真和实测的大地电磁信号进行处理，结果表明：多分辨VMD算法显著的提高了长周期噪声的时频分辨率，通过此算法能够有效的去除大地电磁信号中的长周期方波、三角波噪声，去噪后时域波形的周期性和平滑性明显提高，同时保存了信号的低频有效分量，低频分段的视电阻率、相位图曲线得到了明显优化。

The long-period noise in magnetotelluric signals mainly exists in the low-frequency and very low-frequency segments of the signal. This type of noise has large amplitude and strong randomness,which can completely submerge the effective electromagnetic signal and cause serious deviations in the low-frequency inversion results. In order to effectively remove the long-period noise in the magnetotelluric signal,this paper combines the characteristics of Variational Mode Decomposition (VMD) and multi-resolution analysis,and proposes a multi-resolution VMD algorithm:first,perform multi-layer VMD processing on the low-frequency Intrinsic Mode Function (IMF) of the signal to improve the time-frequency resolution of the low-frequency and very low-frequency segments; then according to the time-frequency characteristics of the noise,the IMF components containing long-period noise are accurately selected; and finally removed these IMF components achieve the purpose of removing long-period noise. Using this algorithm to process the simulated and measured magnetotelluric signals separately,the results show that:the multi-resolution VMD algorithm can significantly improve the time-frequency resolution of long-period noise,and this algorithm can effectively remove the long-period side of the magnetotelluric signal. Wave and triangle wave noise,the periodicity and smoothness of the time-domain waveform after denoising are significantly improved,while the low-frequency effective components of the signal are preserved,and the apparent resistivity and phase diagram curves of the low-frequency segment have been significantly optimized.

0 引言

1 多分辨VMD算法

   1.1 VMD算法原理

   1.2 VMD算法参数组合选取

   1.3 多分辨VMD算法

2 仿真信号处理

3 实测信号处理

   3.1 时域波形去噪结果

   3.2 视电阻率-相位图

4 结论