## 1 Introduction  
Brittle failure of rock masses triggered by engineering activities and natural changes results in the energy release with the spreading of a seismic wave, which is called a microseismic (MS) event [1]. To better understand the relationship between rock fracturing and production activities, MS monitoring, a real-time monitoring technique, has been widely applied in various rock engineering projects, such as mining engineering [2], underground caverns [3, 4], slope stability [5, 6], oil and gas extraction [7, 8], etc. The technique utilizes multiple sensors installed in the monitoring borehole to record MS signals for the exploration of internal development characteristics of rock rupture. However, due to the complex construction environment and geological conditions, the collected signal is often contaminated by random background noise. Due to the complicated causes, its frequency and amplitude are distributed across the whole period. The existence of noise in time serials will interfere subsequent analysis, such as the automatic recognition of signal types [9], and the inversion and location of seismic events [10]. Therefore, it is crucial to extract the MS signal from various kinds of noise for obtaining reasonable analysis results. To effectively improve the quality of the collected signal, numerous classical algorithms have been introduced and further developed for better suitability to engineering conditions, such as t-x prediction filtering [11], wavelet transform (WT) [12; 13; 14], singular value decomposition (SVD) [15; 16], empirical mode decomposition (EMD) [17; 18; 19; 20], mathematical morphology [21], shearlet transform [22; 23], compressed sensing [24], machine learning [25; 26; 27], and the short time Fourier transform [28], [PERSON] and [PERSON] [29] took advantage of a rank reduction algorithm called multichannel singular spectrum analysis (MSSA) to alleviate the influence of random noise in seismic records. For reducing low-frequency noise, [PERSON] et al. [21] introduced the mathematical morphology theory to MS signals, but the selection of structural elements in this method requires some experience. By dividing the MS data matrix into many small blocks, [PERSON] [16] used SVD to quickly reconstruct multi-channel seismic data. [PERSON] and [PERSON] [25] constructed the unsupervised nonparametric machine learning model by obtaining a reasonable dictionary from the noisy data, thereby recovering the missing seismic traces. Due to more excellent localization ability than Fourier transform, WT was also introduced to transform a signal into multiple wavelet coefficients through the mother wavelet [30]. For further improving the resolution in time-frequency domain, [PERSON] et al. [13] proposed applying synchrosqueezed continuous wavelet transform (SS-CWT) to detect small events buried in the nonstationary noise. The test results showed that a larger part of noise was eliminated from small-amplitude MS signal in contrast to conventional denoising methods. By adjusting the parameters of the hybrid block thresholding (BT) to the inferred signal property, [PERSON] and [PERSON] [12] combined BT with the continuous wavelet transform to improve the quality of the real seismic signal. In addition to the above methods, another dominant algorithm to suppress noise is the EMD method. It is a recursive approach proposed by [PERSON] et al. [31], which can adaptively decompose a nonstationary signal into a group of intrinsic mode functions (IMFs). It is not necessary to preset the basic function of EMD and the decomposition procedure is completely automatic, both of which are different from the well-known WT. [PERSON] et al. [17] successfully applied it to remove cable interference from seismic data, and [PERSON] and [PERSON] [18] proposed a f-x EMD method to suppress the random and coherent noise in complex geologic sections.