# Random Noise Suppression Method of Micro-Seismic Data Based on CEEMDAN-FE-TFPF
## 1 Introduction  
Micro-seismic events are rock rupture phenomena caused by geological engineering activities or natural micro-earthquakes. As the existence of random noise will affect the signal recognition, first arrival time pickup, accuracy of micro-seismic source location, and energy estimation, it is necessary to attenuate the random noise of micro-seismic signals before further operation. In the actual micro-seismic data, the events generated by the impact pressure of minerals have the characteristics of large released energy, relatively low frequency, and short duration, so their signal-to-noise ratio (SNR) is lower than other conventional seismic data. Moreover, the propagation direction, frequency, and speed of random noise are not regular, which is not ideal for sufficiently suppressing random noise only using the time domain method. There are many denoising methods for micro-seismic data, such as frequency-domain filtering, the standard deviation method, and the MAD method. However, for complex non-stationary micro-seismic signals, these methods cannot effectively attenuate random noise and protect the effective signals from damage. Therefore, other denoising methods have been developed, including FIR (non-recursive filter)/IIR (recursive filter) filter, wavelet transform, Curvelet transform, F-K transform, Singular Value Decomposition (SVD), TFPF, and so on. However, each method has its drawbacks. The IIR filter cannot control the phase characteristics of the filter, while the FIR filter is more complex to design. Although the transform domain method can well distinguish the abrupt part of non-stationary signals, the denoising results are influenced by the basis function and the Gibbs effect. The SVD transform requires many assumptions. As a new time-frequency analysis method, TFPF can recover non-stationary signals without any assumptions. With its unique advantages, TFPF has been gradually applied to suppress the random noise of one-dimensional micro-seismic data. However, TFPF also has some shortcomings. The selection of its window length directly influences the denoising result. [PERSON] et al. put forward the application of TFPF in actual seismic exploration, and systematically analyzed the influence of fixed window length and window type [1; 2; 3; 4; 5; 6]. In the 1990s, [PERSON] et al. [7; 8; 9; 10] proposed the Empirical Mode Decomposition (EMD) method to solve the problem of unstable micro-seismic signals. This method is an adaptive decomposition method. It can not only decompose the signal into several IMFs without any assumptions, but also highlight the physical characteristics of the signal. [PERSON] et al. proposed a denoising method based on EMD and the improved wavelet threshold, which achieved good results [11]. However, the traditional EMD method brings the problem of modal aliasing. In addition, in the threshold denoising method of EMD, it is difficult to achieve a balance between amplitude preservation and random noise suppression. To solve the above problems, CEEMDAN [12; 13; 14; 15] is proposed. This method solves the problem of mode aliasing by adding adaptive white noise, and decomposes the signal into approximate stationary IMFs with different frequencies. [PERSON] et al. combined EMD and TFPF for seismic denoising and demonstrated the better performance of the new method compared with the conventional TFPF [16]. [PERSON] studied the basic principles and the problems existing in the algorithm itself of EMD, EEMD, CEEMD, and CEEMDAN deeply, and proposed a threshold denoising method using signal entropy [17]. [PERSON] et al. combined CEEMDAN with TFPF, and used sample entropy to screen IMFs, so as to further improve the denoising effect [18]. Based on the characteristics of TFPF and CEEMDAN, this paper proposes a CEEMDAN-TFPF denoising method by using discriminant factors to screen the processing IMFs. The main process and innovation of this paper are summarized as follows:  
1.