Elastic full-wave field simulation in 3D tunnel space with the variable staggered-grid finite-difference method in cylindrical coordinates

Tunnel advance detection technology is an important method for determining the structure of complex geological bodies in front of the tunnel face. Among the tunnel advance detection technologies, the seismic method is one of the most accurate methods with long detection distances. In seismic tunnel advance detection, the cylindrical configuration aggravates the complexity of the wave field in the 3D tunnel space and significantly influences the accuracy of the detection results. Thus, it is crucial to simulate an accurate seismic full-wave field of the tunnel space and to understand the propagation and wave-field characteristics of individual seismic waves for seismic tunnel advance detection. Usually, in 3D Cartesian coordinates, the tunnel wall is approximated with a staircase boundary, but it is not sufficiently accurate in shape and generates numerical dispersion in the simulation, especially in the presence of surface waves. Therefore, we developed a variable staggered-grid finitedifference method in cylindrical coordinates to simulate the elastic full-wave field in a 3D tunnel space. Properly setting free-surface boundary conditions solves the propagation of surface waves on the tunnel wall and face. The interference of the instability and discontinuity of the pole axis in the seismic wave field simulation was eliminated using our method. According to practical engineering situations, models containing three types of geological bodies in front of the tunnel face were designed. Their seismic wave propagation and wave field characteristics were analyzed. Compared with the simulation results in Cartesian coordinates, the results in cylindrical coordinates show that numerical dispersion is negligible and conclude that a higher signal-to-noise ratio and more accurate seismic wave field can be simulated with cylindrical coordinates in the 3D tunnel space. Our simulation method provides theoretical and practical guidance for analyzing and interpreting seismic wave fields in tunnel advance detection.