oa Finite-difference ground-penetrating radar modeling in frequency-dependent media

Realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of Maxwell's equations as well as a complete description of the material properties. We present a two-dimensional (2-D) flnite-difference time-domain solution of Maxwell's equations that allows to account for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near-surface materials. In close analogy with the viscoacoustic case, the governing equations are obtained by assuming dielectric and conducting relaxation functions. The finite-difference solution 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. The algorithm is applied to a realistic problem illustrating the respective damping effects of conductivity and frequency-dependent dielectricity.