Pre-stack elastic reverse time migration in tunnels based on cylindrical coordinates

Seismic forward-prospecting in tunnels is an important step to ensure excavation safety. Nowadays, most advanced imaging techniques in seismic exploration involve calculating the solution of elastic wave equation in a certain coordinate system. However, considering the cylindrical geometry of common tunnel body, Cartesian coordinate system seemingly has limited applicability in tunnel seismic forward-prospecting. To accurately simulate the seismic signal received in tunnels, previous imaging method using decoupled non-conversion elastic wave equation is extended from Cartesian coordinates to cylindrical coordinates. The proposed method preserves the general finite-difference time-domain (FDTD) scheme in Cartesian coordinates, except for a novel wavefield calculation strategy addressing the singularity issue inherited at the cylindrical axis. Moreover, the procedure of cylindrical elastic reverse time migration (CERTM) in tunnels is introduced based on the decoupled non-conversion elastic wavefield. Its imaging effect is further validated via numerical experiments on typical tunnel models. As indicated in the synthetic examples, both the PP- and SS-images could clearly show the geological structure in front of the tunnel face without obvious crosstalk artifacts. Migration imaging using PP-waves can present satisfactory results with higher resolution information supplemented by the SS-images. The potential of applying the proposed method in real-world cases is demonstrated in a water diversion tunnel. In the end, we share our insights regarding the singularity treatment and further improvement of the proposed method.