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 (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.