Three-Dimensional Transient Electromagnetic Modeling Based on Fictitious Wave Domain Methods

Finite-difference time domain (FDTD) methods, which have been widely employed in three-dimensional transient electromagnetic (TEM) modeling, require very small time steps to simulate the electromagnetic fields and this will be time consuming. We present an efficient numerical method for three-dimensional TEM forward modeling. Its key features are based on a correspondence principle between the diffusive and fictitious wave fields. The diffusive Maxwell's equations are transformed and solved in a so-called fictitious wave domain. This scheme allows larger time steps than conventional FDTD methods, allows including air layers, and allows simulating topography. The need for initial field calculations is avoided by including an electric current source in the governing equations. This also avoids a traditional assumption of a flat earth surface in TEM modeling. We test the accuracy of the electromagnetic fields' responses using our method with the spectral differential difference (SLDM) solutions. The results show good agreement even under the existence of air layers and topography in the model.