Abstract: In order to realize time domain difference method(FDTD) modeling in slowly varying transient electromagnetic fields,we introduce the virtual displacement current that lets FDTD iteration carried out with time step.For the quite simple model,propagation of the field in time domain needs time,which can be used to transform exciting source into the initial conditions.However,The previous method is no longer suitable for calculating the complex 3D model and the source and the boundary condition should be reconsidered.The exciting source can be injected practically due to its "slope form".The subsurface boundary condition is determined by behavior that electromagnetic waves attenuated in the earth,and the modified perfect match layer is for air boundary.The analysis show that the alternating direction implicit FDTD is a viable approach to time stability problem brought by uniform grids in the air and the earth.