Simulation of ground penetrating radar on dispersive media by a finite element time domain algorithm

This paper presents a two-dimensional finite element time domain (FETD) algorithm for simulation of ground penetrating radar (GPR) on dispersive and lossy media. The medium of linear dispersion is modeled by a multi-pole Debye model, which is incorporated into the FETD scheme through the Fourier transform. We apply the finite element Galerkin method to discretize the computation domain using triangular elements. A perfectly matched layer is extended to match the dispersive media and is used as an absorbing boundary condition to truncate the computation domain. The proposed FETD algorithm is proven to have comparable accuracy with the finite difference time domain (FDTD) method by comparing the simulated electromagnetic waves propagating in a homogeneous dispersive medium with the corresponding analytical solution. At an expense of computational costs, the FETD approach can yield more accurate results when simulating a complex geometry than the FDTD approach, which suffers from the staircase error. Moreover, we analyze the influence of material dispersion on GPR data acquired by different survey geometries. The results demonstrate that material dispersion will bring a great challenge for quantitative interpretation of GPR data. Numerical simulation of GPR data with dispersion does help in accurate interpretation of GPR data.