During shale gas exploitation, a distributed optical fiber acoustic sensing system (DAS) based on phase-sensitive optical time domain reflectometry (Φ-OTDR) is a commonly employed solution for monitoring microseismic waves generated during hydraulic fracturing operations. Signal-to-noise ratio (SNR) is an important parameter reflecting the performance of the Φ-OTDR system, and obtaining microseismic signals with good SNR is the basis for monitoring the fracturing effect of shale gas. However, due to the thermal noise and scattering noise of the photodetector, the phase noise and frequency drift of the laser, and the environmental noise, the SNR of the Φ-OTDR system will deteriorate, resulting in difficult vibration localization and distorted phase signal obtained by demodulation. The solution to this problem is essential for broad applications of Φ-OTDR systems in the engineering field.

To improve the SNR of vibration signals measured by Φ-OTDR systems, we propose a vibration signal denoising method based on variational mode decomposition (VMD) and mutual information (MI). The in-phase orthogonality (I/Q) demodulated phase signal is further processed, and the number of VMD layers K is determined by the scaling index calculated by detrended fluctuation analysis (DFA). The process of the DFA method is as follows. First, the input noisy signal is decomposed into K(K=1,2,3…) IMF components by VMD, and then the scaling index of each mode is estimated by DFA. The relationship between the number of decomposition layers K and the scaling index is K=argmaxKnum(α1:K≥θ)=J,K=1,2,3,⋯, where the parameter Jis determined by the scaling index of the input noisy signal. When the value of K is determined, the MI between the IMF components generated by the K-layer VMD and the input noisy signal is calculated. The mean value of the normalized MI of each component and the input signal is taken as the threshold value. Additionally, when the normalized MI of a component and the input signal is greater than this threshold value, the component is considered to be a correlated mode, otherwise it is a non-correlated one. The distortion and noise of the phase signal are suppressed by discarding the non-correlated modes determined by the MI method.

A coherent detection Φ-OTDR system is set up to verify the denoising effect of the VMD-MI method. The 500 Hz single-frequency vibration signal (Fig. 6) and the 500, 1000, and 1500 Hz multi-frequency vibration signals (Fig. 10) are processed by VMD, wavelet denoising (Wavelet), empirical mode decomposition (EMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). For the 500 Hz single-frequency vibration signal, the number of decomposition layers K is determined as 4 by the DFA method, and the MI between each component and the original phase signal is calculated (Fig. 7) to determine IMF3 as the correlated mode to be retained, and the remaining components are discarded as non-correlated modes. For the original phase signal with the SNR of 18.34 dB (Fig. 6), the proposed method improves the SNR to 41.45 dB, which is significantly better than the 18.46, 34.87, and 38.60 dB of the Wavelet, EMD, and CEEMDAN methods, respectively (Fig. 8). For the multi-frequency vibration signals of 500, 1000, and 1500 Hz, the number of decomposition layers K is determined to be 7 by the DFA method, and the IMF3, IMF4, IMF5, and IMF6 are determined to be correlated modes and the remaining components are non-correlated modes by the MI method (Fig. 9). Meanwhile, the noise reduction is reduced by discarding the non-correlated modes. For the original phase signal with SNR of 18.82, 20.38, and 17.41 dB, the proposed method improves the SNR to 32.28, 33.77, and 30.68 dB respectively, significantly better than Wavelet, EMD, and CEEMDAN methods (Fig. 10).

The DAS system based on Φ-OTDR is a promising detection device in the microseismic monitoring of shale gas fractures. The SNR is an important criterion to evaluate the quality of the detection signal, and enhancing the SNR is significant to improve the overall sensing performance of the DAS system. We propose a method to improve the SNR of Φ-OTDR based on VMD. The DFA method is adopted to determine the appropriate number of decomposition layers, and the correlated modes are selected and retained by calculating the MI between the components obtained from VMD and the original phase signal to achieve noise removal. The experimental results show that the VMD-MI algorithm is significantly better than Wavelet, EMD, and CEEMDAN in improving the SNR of 500 Hz single-frequency vibration signal, and 500, 1000, and 1500 Hz multi-frequency vibration signals. This proves the effectiveness and superiority of the proposed method in improving the measurement performance of the Φ-OTDR system. Meanwhile, this method can help acquire high-fidelity microseismic information in microseismic monitoring of shale gas.