An Improved Finite‐difference Time‐domain Solution for Three‐dimensional Transient Electromagnetic Modeling in Source‐free Media

An improved finite-difference time-domain (FDTD) solution is developed for three-dimensional transient electromagnetic modeling in source-free media. Based on Guptasarma's linear filtering method and the fast Hankel transform, the improved method selects the electric fields (E) at the first two time-steps, and the time derivative of the magnetic induction (∂B/∂t) at the second time-step as initial conditions. This selection can avoid approximating ∂E/∂t at initial times and improve initial accuracies. During the iterations, the electric fields and ∂B/∂t are both defined at the same integer time indices and the deriving equations are modified based on the FDTD method. Consequently, it can avoid the approximation of the electric fields at intermediate time indices and magnetic fields at integer time indices, and improve the iteration precisions. The convolutional perfectly matched layer (C-PML) boundary condition is employed to reduce the reflection errors and the effects are verified. At last the proposed approach is checked via homogeneous half-space models, layered models and 3D anomalous models with complex backgrounds. The results show that the improved method can reduce simulation errors twice or thrice and deepen effective exploration depth by 20%, which has verified the effectiveness of the improved method for three-dimensional transient electromagnetic modeling, especially for long-time and high-resistance modeling.