## 3 Vibration Wave Splitting and Loading
### Measured Waveform Calibration  
The vibration velocity \(V_{0}(t)\) of the wave particle, as recorded by the microseismic sensor, is illustrated in Figure 5a. The particle vibration velocity at the seismic wave source, denoted as \(V_{1}(t)\), is calculated using Formula (1).  
\[V_{1}(t)=\frac{PPV_{1}}{PPV_{0}}\times V_{0}(t) \tag{1}\]  
Figure 4: Deformation and failure characteristics of roadway: (**a**) roof settlement; (**b**) roadway spalling; (**c**) bottom drum phenomenon.  
Figure 3: Microseismic energy distribution map.  
In the formula, \(PPV_{0}\) is the PPV of the vibration wave received by the sensor, m/s, and \(PPV_{1}\) is the PPV of the vibration wave particle at the source position, m/s.  
Where \(PPV_{1}\) is estimated by the empirical scaling law, according to the scaling rate proposed by [PERSON], there are [18]:  
\[PPV_{1}=\frac{10^{\frac{6.479+0.57\lg E}{1.9}}}{R} \tag{2}\]  
In the formula, \(E\) represents the dynamic load energy, measured in joules (J), and \(R\) is the distance between the source point and the target point, m.  
Considering that the scaling law is derived from ensemble data related to the global wave attenuation rate, the methodology described may lead to an overestimation of the monitored peak particle. The calibration procedure is delineated as follows: the sensor records the actual vibration wave, referred to as \(PPV_{0}\), which measures 0.21 m/s, while the calculated \(PPV_{1}\) is 1.12 m/s. By employing Formula (1), the input vibration wave, \(V_{1}(t)\), at the source is ascertained, as depicted in Figure 5b.  
The scaling law is predicated on a spherical radiation pattern and is derived from the wave attenuation rates recorded in the global database. It is essential to recognize that the empirical scaling method may lead to an overestimation of the PPV values, as 95% of the data within the global database are positioned below the regression line. Therefore, it is imperative to calibrate the vibration wave in accordance with the attenuation effects specific to different mines. Vibration waves are employed in FLAC\({}^{\text{3D}}\) for computational analyses, and their calibration is conducted using the \(PPV_{2}\) measured at the monitoring location within the roadway. Furthermore, Maxwell damping is utilized to simulate the attenuation of seismic wave intensity [19]. The attenuation ratio N is defined by \(PPV_{2}\) and \(PPV_{0}\):  
\[N=\frac{PPV_{1}-PPV_{2}}{PPV_{1}}\times 100\% \tag{3}\]  
In the formula, \(N\) represents the reduction ratio of the amplitude of the vibration wave from the source to the monitoring point.  
In the current study, the sensor is strategically positioned at a distance of 35 m from the source. The \(PPV_{2}\) recorded at the monitoring location is 0.153 m/s, accompanied by an attenuation ratio (N) of 86.3%. The field-measured \(PPV_{0}\) is 0.21 m/s, whereas the \(PPV_{1}\) at the source, calibrated using Formula (4), is determined to be 1.694 m/s.  
\[PPV_{1}=\frac{PPV_{0}}{1-N} \tag{4}\]  
Figure 5: Vibrating wave velocity curve: (a) \(V_{0}(t)\) is the particle vibration velocity measured at the sensor; (b) \(V_{1}(t)\) is the calculated particle vibration velocity, and \(V_{1}(t)\) is the calibrated particle vibration velocity.  
This calibrated \(PPV/_{1}\) is subsequently integrated into Formula (1) to derive the calibrated vibration wave, as depicted in Figure 5b.