Finite element reverse time migration imaging in tunnels using an unstructured mesh

Abstract

Wave field extrapolation is critical in reverse time migration (RTM). At present, wavefield extrapolation in RTM imaging for tunnels is mostly carried out via the finite difference method. However, complex tunnel models, such as those for karst and fault fracture zones, are constructed using regular grids with straight curves which can easily cause numerical dispersion and reduce imaging accuracy. In this study, the wavefield extrapolation for tunnel RTM was conducted using the finite element method, where an unstructured mesh is employed as the body-fitted partition in a complex model. The Poynting vector calculation equation suitable for the unstructured mesh finite element method was established to suppress low-frequency noise interference. The tunnel space was considered during the wavefield extrapolation to suppress mirror artefacts by using the flexibility of mesh generation. Finally, the influence of the survey layouts (one-sidewall and two-sidewall) on the tunnel imaging results was explored. The RTM results for a simple tunnel model with an inclined interface show that the method based on unstructured meshes can effectively suppress low-frequency noise and mirror artefacts, thus obtaining clearer imaging results. Also, the two-sidewall tunnel survey layout more accurately obtains the real position of the inclined interface ahead of the tunnel face. Complex tunnel numerical modelling and actual data migration results further illustrate the effectiveness of the finite element unstructured mesh method.