## 4 Case Study  
In order to verify the feasibility of the method on field MS signals, the noisy data from the underground powerhouse of Shuangjiangkou Hydropower Station was processed by the above methods. Shuangjiangkou Hydropower Station, located in Aba Tibetan and Qiang Autonomous Prefecture, Sichuan Province, China, has the world's highest dam at 312 m under construction. Its underground caverns have a minimum horizontal burial depth of about 400m and a vertical burial depth of about 320 m-500 m. Due to high ground stress and unstable structural plane, the MS monitoring system produced by the Engineering Seismology Group (ESG) of Canada has been applied to monitor the main powerhouse and the main transformer chamber for 24 h. The system is composed of 10 single-axis acceleration sensors, two Paladin signal acquisition system, a Hyperion signal processing system, and some cables. The accelerometer with a sensitivity of 25 V/g has a frequency response between 50 Hz and 5 kHz, and the sampling frequency of the acquisition system is 10 kHz [3; 4]. In this section, a noisy MS signal collected from the excavation of the underground powerhouse in April 2019 is selected for analysis. Figure 9 shows the waveforms and the time-frequency diagrams of the signal before and after noise reduction. Figure 10 illustrates applying the multi-step AIC method to determine the interval of the MS signal. Figure 10a is the AIC time series of the entire waveform, and Figure 10b,c are the revised AIC values of the front and back time window segments, respectively. It can be seen from the figure that there is a minimum value before and after the maximum value, and the global minimum of AIC is not a local minimum. The start position of MS is slightly adjusted from 9742 to 9740, while the end position has moved a lot from 14,821 to 16,172. As can be seen from the waveform diagram in Figure 9e, the repositioning result is more in line with the fluctuation of the MS signal. According to the time-frequency results of the above methods, their key parts from 9000 ms to 15,000 ms have hardly changed, while the instantaneous frequencies of other parts weaken in various degrees. The noise with a frequency above 500 Hz is largely eliminated by EEMD or CEEMD, leaving other parts with a certain degree of attenuation. Apart from the frequency components above 300 Hz almost disappearing, a considerable portion below 300 Hz has also been reduced by VMD. VMD-AIC further reduces the unimportant frequency remaining in the VMD denoising result, and only retains the fluctuation in the range [9742; 9743; 9744; 9745; 9746; 9747; 9748; 9749; 975; 976; 977; 978; 979; 980; 981; 982; 983; 984; 985; 986; 987; 988; 989; 990; 991; 992; 993; 994; 995; 9  
To further test the performance of the proposed method, 40 noisy signals are also selected for the above comparative analysis. Due to the complex interference factors, the time series of pure MS signal cannot be definitively determined in the field signal. In order to reasonably evaluate the denoising effect of unknown signal, an easily implemented evaluation method is developed in this paper. With reference to the definition of \(SNR\), the noise ratio (\(NR\)) for evaluating unknown field signals is defined as follows:  
\[NR=100+10\log\left(\frac{\sum\limits_{i=1}^{N}{(x_{i}^{\prime}-\overline{x}_{i })^{2}}}{\sum\limits_{i=1}^{N}{(x_{i}^{\prime})^{2}}}\right) \tag{15}\]  
where \(x_{i}^{\prime}\) is the \(i\)-th amplitude of the original noisy signal, and \(\overline{x}_{i}\) is its new amplitude after noise suppression. The ratio is an indicator to assess the relationship between the noise variation and the original signal. The more random noise is extracted, the smaller the amplitude of the corresponding position of \(\overline{x}_{i}\) becomes. Admittedly, its \(NR\) will present a pretty big value. In general, \(NR\) is greater than 0 and less than 100. If a negative value occurs, it means the signal after noise reduction is almost unchanged.