Three-dimensional Modeling of Transient Electromagnetic Responses of Water-bearing Structures in Front of a Tunnel Face

Abstract

We present a finite-difference time-domain (FDTD) approach for the simulation of three-dimensional (3-D) transient electromagnetic diffusion phenomena for the detection of water-bearing structures in front of a tunnel face. The unconditionally-stable du Fort-Frankel difference discrete method is used and an additional fictitious displacement current is introduced into the diffusion equations to form explicit difference equations. We establish a new excitation loop source which considers Maxwell's equations in source media to overcome the limitations of the precondition that the near-surface resistivity of the model is uniform in the well-known 3-D FDTD algorithm demonstrated by Wang and Hohmann in 1993. The algorithm has the ability to simulate any type of transmitting current waveforms and arbitrarily complicated earth structures. A trapezoidal wave is used to simulate a step-off source. The fictitious permittivity is allowed to vary during the computation to ensure the stability and optimize an efficient time step. Homogeneous full-space models with different resistivities are simulated and compared with the analytical solutions to demonstrate the algorithm. Transient electromagnetic (TEM) responses of a tunnel with and without a water-filled vertical fault in front of the tunnel face are simulated and compared. 3-D models with water-filled fault and karst caves in front of a tunnel face are simulated with different parameters considered.