Research on three-dimensional full-space transient electromagnetic modeling for advanced prediction

The 3D full-space TEM modeling algorithm was implemented by directly solving diffusion equation using time-domain finite-difference method, calculating field components adopting remedial Liao's absorbing boundary condition, and correspondingly applying Laplace equation and "upper continuation" method to tunnel space and its boundary. Based on analyzed solution of loop source in uniform full-space, full-space "late-time" apparent resistivity formula was derived. And then, advanced prediction of water inrush structure was simulated. The results indicate that, the remedial ABC has a better effect than Dirichlet condition when modeling diffusion of electromagnetic field in 3D infinite medium. Full-space apparent resistivity value is 1.842 times than half-space for the same loop parameters. Transient response at tunnel end is proportional to the resistivity contrast between anomaly structure and its surrounding rock, and reciprocally proportional to the distance of the structure to observation point. However, to the high-resistivity structure, the change of its resistivity has a limited effect to transient response. And also, transient response of the structure is submerged by the response of surrounding rock for the long distance between the structure and observation point.