Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm

Recently an efficient pseudospectral time-domain (PSTD) algorithm has been developed to solve partial differential equations in computational electromagnetics and acoustics. It uses the fast Fourier transform (FFT) algorithm to approximate spatial derivatives, and the perfectly matched layer (PML) to eliminate the wraparound effect. Due to its high accuracy in the spatial derivatives, this method requires a significantly smaller number of unknowns than a conventional finite-difference time-domain (FDTD) method when solving large-scale problems. In this work, we further extend the PSTD algorithm to frequency-dependent media and apply the algorithm to simulate ground-penetrating radar (GPR) measurements in a dispersive earth. The dispersion of the soil is treated by the recursive convolution approaches. The convergence property of the PSTD algorithm is investigated for the scattering of a dispersive cylinder. Multidimensional large-scale problems in GPR measurements are presented to demonstrate the efficiency of this frequency-dependent PSTD algorithm.