# Three-Component Microseismic Data Denoising Based on Re-Constrain Variational Mode Decomposition
## 1 Introduction  
Microseismic monitoring is a technology used to monitor the subsurface fracturing of rocks due to human activities [1; 2; 3; 4]. This is the first step in recognizing microseismic event signals for microseismic monitoring. However, owing to the characteristics of microseismic event signals (e.g., low energy, high frequency, and short duration) they are easily disrupted by various factors, which increases the difficulty of the subsequent processing and interpretation. Therefore, it is necessary to denoise the monitoring record. The denoising process for microseismic data is mainly divided into two basic strategies according to the type of data: multi-channel denoising and single-channel denoising [5]. For the multi-channel strategy, microseismic data are denoised by the spatial distribution information of the geophone. [PERSON] et al. [6] used a median filter based on the seismic profile structure to suppress blending noise. [PERSON] et al. [7] used a method based on the correlation between the three components of microseismic to identify the 3D shearlet transform coefficient and effectively remove the noise. [PERSON] et al. [8] established a model based on the least squares method to decompose seismic data using the spatial and temporal relationships among multi-channel seismic data. The single-channel strategy is mainly used for denoising via time-frequency transformation and signal decomposition. [PERSON] et al. [9] used wavelet time-frequency analysis to suppress the seismic noise. [PERSON] et al. [10] combined the synchrosqueezed continuous wavelet transform and a detection function to remove noise from the signal. Noise reduction methods based on decomposition and reconstruction are widely used in single-channel noise reduction [11], such as empirical mode decomposition (EMD) [12; 13]which is used to process the real and imaginary parts of the frequency domain of the signal in the time window to reduce random and coherent noise. [PERSON] et al. [14] applied an AR mode to process the results of EMD in the frequency domain to reduce random noise. However, EMD has some drawbacks in practical applications, such as mode mixing [15], [PERSON] et al. [16] used ensemble empirical mode decomposition (EEMD), which was proposed by [PERSON] et al. [17] to overcome the problem of mode mixing and to process the real and imaginary parts of the frequency domain of the signal in the time window to reduce the noise. [PERSON] et al. [18] applied wavelet threshold filtering to process the high-frequency intrinsic mode function (IMF) of the EEMD, and then reconstructed the high frequency and low frequency to reduce the noise. [PERSON] et al. [19] combined the complex curvelet transform and complementary ensemble empirical mode decomposition (CEEMD) which was proposed by [PERSON] et al. [20] to improve the effect of decomposition. [PERSON] et al. [21] selected the IMFs of the CEEMD using the self-correlation coefficient, then used the wavelet packet threshold to process the IMFs, and finally reconstructed the IMFs to suppress the noise. [PERSON] et al. [22] selected the EEMD mode by the variance contribution rates (VCRs), which removed the modes with VCR < 0.01 and others retained. Then, each retained mode was constructed as a Hankel matrix, and it was processed by principal component analysis (PCA) to complete denoising. Compared with EMD, EEMD, and CEEMD, VMD can further decrease the redundant modes and solve the mode-mixing problem, and has a more powerful anti-noise performance [23]. Since then, many studies have applied VMD to reduce noise. [PERSON] et al. [24] used VMD to perform time-frequency analysis of seismic data to suppress noise and highlight the geologic characteristics. [PERSON] et al. [25] selected IMFs to reconstruct a signal based on detrended fluctuation analysis (DFA). [PERSON] et al. [26] performed a correlation analysis on the IMFs of the VMD to suppress the noise. [PERSON] et al. [27] combined VMD and odd spectrum analysis to remove the remaining low-frequency noise of the VMD. [PERSON] et al.