# Recognition of Tunnel Fracture Zones in Seismic Waves and Ground-Penetrating Radar Data
## 2 Characteristics of the Detected Signal in Fracture Zones  
### Characteristics of Seismic Wave Data in Fracture Zones  
Seismic waves are reflected when they encounter different wave impedance interfaces during propagation. The principle of seismic wave detection is shown in Figure 1. Geological changes in front of the tunnel face, as well as the distribution and nature of hazardous bodies, can be detected according to changes in the amplitude and wave velocity of seismic wave reflection signals. Because a reflected wave takes longer to travel, the receiving point first receives a direct wave signal, and the amplitude of the reflected wave becomes smaller than that of the direct wave, separating the reflected wave from the direct wave and other interfering signals, further enabling the identification of fracture zones by analyzing changes in reflected wave signals. Figure 1: Principles of reflection at fracture zones for seismic wave detection. The changes in reflected waves depend on the reflection coefficient, which is expressed as  
\[R=\frac{\rho_{2}V_{P2}-\rho_{1}V_{P1}}{\rho_{2}V_{P2}+\rho_{1}V_{P1}} \tag{1}\]  
where \(\rho_{1}\) and \(\rho_{2}\) are the rock densities on both sides of the reflecting interface, and \(V_{P1}\) and \(V_{P2}\) are the seismic wave propagation velocities on both sides of the reflecting interface. The reflection coefficient varies as seismic waves encounter interfaces with different wave impedances during propagation according to Equation (1). Positive reflection occurs when seismic waves transition from interfaces with low wave impedance to those with high wave impedance. Conversely, negative reflection is observed when they transition from interfaces with high wave impedance to those with low wave impedance. Spatial imaging of the collected 3D signal data in front of the tunnel face enables the visualization of information about the location of abnormal reflected interfaces based on the principles of the seismic wave common reflection surface (CRS) and diffraction scanning offset superposition. The principle of diffraction scanning offset superposition is shown in Figure 2.  
The diffraction scanning offset superposition principle involves relocating the reflected waves to their actual positions. The exploration area is divided into a grid to achieve this, with each point treated as a reflection point. The process entails a systematic scan along the grid points. Let \(P\) represent a reflection point on the reflecting interface, where the travel time \(t_{ij}\) of the reflected wave, generated by the source point \(S_{i}\) and received by the detection point \(R_{j}\), can be determined as follows:  
\[t_{ij}=\frac{\left(\sqrt{H^{2}+\left(X_{P}-X_{S_{i}}\right)^{2}}+\sqrt{H^{2}+ \left(X_{R_{j}}-X_{P}\right)^{2}}\right)}{V} \tag{2}\]  
where \(H\) is the vertical depth of the scanning point \(P\); \(X_{P}\), \(X_{S_{i}}\), and \(X_{R_{j}}\) are the horizontal coordinates of scanning point \(P\), source point \(S_{i}\), and detector \(R_{j}\); and \(t_{ij}\) is the vertical two-way travel time of scanning point \(P\). The amplitude values \(a_{t_{ij}}\) of \(n\) receiver channels from \(m\) different sources passing through the same scanning point \(P\) are superimposed, and the total amplitude is calculated:  
\[a_{\Sigma}=\sum_{i=1}^{m}\sum_{j=1}^{n}\left(a_{t_{ij}}\right)_{p} \tag{3}\]  
Drawing upon the principles of CRS theory, Equation (3) highlights the cumulative amplitude augmentation of points along the reflection interface, contrasting with the  
Figure 2: Diffraction scanning offset superposition principle. relatively diminished total amplitude of points away from the reflection interface. Consequently, the reflection interface is prominently highlighted and accurately repositioned in three-dimensional space, delineating the spatial distribution of fracture zones. This approach aims to discern and enhance information on subsurface structures in seismic data, thereby amplifying the efficacy of signals.