3D FDTD anisotropic and dispersive modeling for GPR using rotated staggered grid method

Abstract

The finite-difference time-domain (FDTD) method is widely used in numerical modeling of ground penetrating radar (GPR). The well-known Yee's method is the earliest and most popular FDTD method. However, using Yee's method to solve an anisotropic case requires considerable interpolation of electric fields (assuming media to be non-magnetic). In this paper we present a different approach called rotated staggered grid (RSG) method to simulate electromagnetic (EM) wave propagation in anisotropic and dispersive media. RSG-FDTD places electric field components on the same grid system and magnetic field components on the same grid system, however, half a spacing away. The RSG-FDTD method was first used in elastic wave modeling. It requires no interpolations of wave fields and is advantageous for modeling wave propagation in anisotropic media. In this paper, the 3D anisotropic and dispersive EM wave equations are presented, and the RSG-FDTD approximations are derived. The application of the new method is tested using homogeneous media models. To validate the proposed method, results are compared with those of GprMax, and good agreement is achieved. The common offset sections of complex cases with anisotropy and dispersion are also tested and are compared with the corresponding isotropic case.