3D forward modeling of mine transient electromagnetic by time-domain vector finite element

In order to expand the applicability of mine transient electromagnetic (MTEM) forward modeling to complex geological models, a 3D forward modeling method based on time-domain vector finite element was developed. Firstly, the Helmholtz equation of magnetic vector potential based on Coulomb's gauge was derived from Maxwell's equations in time domain. On this basis, combining the perfect conductor boundary conditions, the corresponding weak form equation was derived by Galerkin method. The first order tetrahedral vector element that has extensive applicability was used to analyze the weak form equation, and the loop source was regarded as many current elements to overcome the singularity of the source. The backward differentiation with increasing step size was used for time discretization. Thus the full waveform MTEM response of any complex geological model could be calculated. Secondly, the root mean square percentage error between FEM solution of homogeneous whole space and analytical solution was 0.84%, which validates the proposed algorithm. Thirdly, the influence of ramp current was calculated. The results show that the ramp current will increase the induced voltage, the influence of linear ramp current will be stronger than exponential one when their turn-off time are same, and under the same turn-off waveform, the longer turn-off time the influence extends later. Under the linear ramp current, the induced voltage before the turn-off time is mainly caused by the change of current in the transmitting loop. Fourthly, the influence of tunnel was calculated, the results show that when the turn-off time is zero, the tunnel will reduce the induced voltage in early time, but has barely influence in late time, and the influence is stronger when the transmitting loop is in the center of tunnel comparing to that when the loop is at the heading face, when the loop is toward roof/floor or side comparing to that when the loop is toward heading face, but considering the practical turn-off time the influence can be ignored. Finally, the responses in the horizontal and vertical section of ahead rectangular watery goaf were simulated, the modeling results show that the watery goaf will increase the induced voltage, and in horizontal section the strongest anomalous response will occur when the transmitting loop points to the center of the anomalous body, but in vertical section it will occur when the transmitting loop points to the roof/floor. © 2019, Editorial Office of Journal of China Coal Society. All right reserved.