Finite-difference modeling of electromagnetic wave propagation in dispersive and attenuating media

Realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of Maxwell's equations as well as an adequate description of the material properties. We present a finite difference time-domain (FDTD) solution of Maxwell's equations that allows accounting for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near-surface materials. This algorithm is second-order accurate in time and fourth-order accurate in space, conditionally stable, and computationally only marginally more expensive than its standard equivalent without frequency-dependent material properties. Empirical rules on spatial wavefield sampling are derived through systematic investigations of the influence of various parameter combinations on the numerical dispersion curves. Since this algorithm intrinsically models energy absorption, efficient absorbing boundaries are implemented by surrounding the computational domain by a thin (less than or equal to 2 dominant wavelengths) highly attenuating frame. The importance of accurate modeling in frequency-dependent media is illustrated by applying this algorithm to two-dimensional examples from archaeology and environmental geophysics.