# Recognition of Tunnel Fracture Zones in Seismic Waves and Ground-Penetrating Radar Data
## 3 Recognition of Tunnel Fracture Zones  
### Recognition of Fracture Zones in Seismic Wave Data  
The seismic wave reflection data and ground-penetrating radar data are used to identify the fracture zones, in combination with the physical properties of the fracture zones. The technical route of the fracture zone identification algorithm is shown in Figure 4.  
In seismic wave detection, the direct wave is considered an interfering signal, while the reflected wave contains the effective signal. The direct wave suppression process is shown in Figure 5. The frequency-wavenumber (F-K) filtering method utilizes the differences in speed and frequency between the direct and reflected waves to suppress the direct signal and retain the effective signal within the reflected wave. The apparent velocity can be described in terms of frequency and wavenumber:  
\[V=\frac{f}{K} \tag{7}\]  
where \(V\) is the apparent velocity, \(f\) is the wave frequency, and \(K\) is the wavenumber.  
Figure 5b presents the frequency-wavenumber domain image of the seismic channel signal, where horizontal lines represent intercepted frequency ranges. The diagonal line  
Figure 4: The technical route of fracture zone identification.  
signifies the apparent velocity calculated by Equation (7). The region delineated by the reflected wave energy cluster is identified by contrasting the direct and reflected wave signals. This facilitates the joint screening of reflected wave signals based on their apparent velocity and frequency characteristics, effectively suppressing the direct wave signal. The outcomes of direct wave suppression are depicted in Figure 5c.  
Velocity scanning and stacking are conducted on the data after applying bandpass and F-K filtering. The correlation between energy clusters and the temporal evolution of reflected signals are calculated from the wave velocity scanning map. This process yields the stacking velocity and the associated propagation velocity at various depths. Figure 6 illustrates the velocity spectrum of the tunnel. The corresponding superimposed velocity is determined by employing the maximum superimposed amplitude of multiple signals. Subsequently, the average velocity between any two points is computed based on the superimposed velocity at different depth positions.  
The designed velocity spectrum reflects the strength of the amplitude superposition of the corresponding time-distance curve according to Equation (1). In the energy cluster, regions with a positive reflection coefficient and significant superposition amplitude are highlighted in red, while negative reflections are distinctly represented in blue.  
Figure 5: F-K filtering process: (**a**) 2D pre-filtered channel; (**b**) spectral analysis with F-K filtering; (**c**) 2D post-filter channel.  
Figure 6: Superposition velocity spectrum.  
Figure 6 illustrates the continuous and dense peaks and valleys in the channel records within the divided area. The calculated velocity spectrum exhibits numerous interference bands, with positive and negative reflections displaying a regional distribution. This suggests that the rock mass in front of the tunnel face is fragmented, impacting the propagation of seismic waves. A three-dimensional image of the tunnel face is obtained by superimposing the three-dimensional seismic wave signals collected by the three-component detector, as shown in Figure 7. This image reveals the spatial locations of the fracture zones.