3-D imaging of whole-space environments with electromagnetic induction sensors based on linear approximation

Accurate mapping of the periphery of tunnel has become an essential step in underground mining and engineering. Because of high sensitivity to electric conductivity and magnetic permeability, the whole-space electromagnetic (EM) method has played an important role in geological forecast of groundwater and exploration of mineral ore. However, obtaining a three-dimensional (3-D) image of the whole-space EM method by 3-D inversion is challenging due to the limited observation space and inefficiencies in 3-D forward modeling algorithms. While 1-D inversion algorithms have long been used to map the periphery of the tunnel, various 3-D inversion algorithms have been successfully applied in other scenarios. Recently, the portable frequency domain loop-loop EM induction (EMI) measurement has been considered as an active source magnetic method in near surface surveys, because of the dominance of magnetic permeability in the in-phase (IP) response. The 3-D linear forward modeling method is developed based on the location-specific magnetic sensitivity function, and the 3-D inversion algorithm has been effectively employed for mapping magnetic anomalies in large-scale area. In this study, we intend to demonstrate that the EMI measurement can give 3-D image of the periphery of the tunnel by theory and numerical experiments. The IP response of EMI in whole-space is separated into three parts, and the 3-D linear forward modeling method is examined by analytical solution. The 1-D Fourier transform is used to accelerate the 3-D forward modeling, and the 3-D inversion show a good performance of mapping the magnetic abnormal bodies in underground space.