## 1 Introduction  
The accurate prediction of the geological conditions in front of the tunnel during construction is critical. The tunnel seismic forward prospecting is one of the mainstream methods in the current tunnel forward geological prospecting [1]. By projecting seismic waves on the sidewall or face of the tunnel, the seismic waves propagate around and produce reflection, transmission, multiple reflections, etc. at the geological interfaces, which are subsequently received by the receivers arranged on the tunnel. By data processing methods, such as migration and inversion methods, the geological conditions in front of the tunnel can be obtained. However, due to the geological interfaces caused by excavation between the tunnel cavity and the surrounding rock, and the complex geological conditions in front of the tunnel, the seismic wavefield is complex, which leads to difficulty of the interpretation of seismic data. Therefore, it is of great significance to study the characteristics of seismic wavefield and propagation laws under different unfavorable geological conditions. Wavefield analysis is important to research in that it is helpful for the reasonable arrangement of observation devices, understanding of seismic data, and accurate interpretation of seismic data. Researchers have analyzed seismic wavefields and propagation based on numerical modeling or experiments to help in the field of seismic exploration. [PERSON] et al. [2] carried out the analytical studies of body wave propagation and attenuation and gave a better field setup that helps to reduce the detrimental effects of near-field waves. To better obtain the formation of shear velocity, [PERSON] et al. [3] analyzed the acoustic wavefields projected by logging-while-drilling. [PERSON] et al. [4] study the characteristics of the wavefield of crosswell seismic data. The seismic wave propagation cross rock mass has been investigated by [PERSON] et al. [5] and [PERSON] et al. [6]. In the oil-gas exploration field, the characteristic of seismic wavefield in fractured media has been studied [7; 8; 9]. In the field of tunnel construction, [PERSON] et al. [10] studied the seismic wave propagation patterns around mine tunnels for dynamic rock support. [PERSON] et al. [11] studied the seismic response characteristics of the crossing tunnels through experiments and numerical modeling. Among the seismic forward modeling methods, the finite-difference modeling method in the Cartesian coordinate system is the mainstream. [PERSON] et al. [12] used the finite-difference method to simulate the propagation of elastic waves for the first time. Subsequently, the staggered-grid finite-difference scheme in 2D [13] and 3D have been developed [14]. However, there are unavoidable problems in the finite-difference scheme in the Cartesian coordinate system. Because the mesh grid adopts a square grid, the surface of the tunnel, which usually is cylindrical, cannot be accurately divided. Furthermore, when seismic waves pass through the tunnel face, there will be many strong diffraction waves produced at the edges of the tunnel face, which will disturb the actual seismic wave field. Considering that the tunnel is a cylindrical cavity, the finite-difference scheme in the cylindrical coordinate system is a more suitable way to simulate seismic wavefield and study its characteristics in the tunnel. Some related studies have shown its effectiveness. In electromagnetic forward modeling, the finite-difference scheme in the cylindrical coordinate system is widely used to simulate the propagation of electromagnetic waves in cylindrical objects [15; 16] and has shown that it outperforms. In the seismic forward modeling, [PERSON] [17] performed elastic wave forward modeling in cylindrical coordinates to simulate the propagation of elastic waves in sonic logging, but the algorithm uses pseudo-3D equations, which essentially operate in two dimensions. [PERSON] et al. [18] realized the finite-difference simulation of sonic logging using the cylindrical coordinate system. [PERSON] et al.