3-D ground-penetrating radar simulation and plane-wave theory in anisotropic media

Modeling ground-penetrating radar (GPR) waves requires simulation of the 3-D full wavefield and the correct description of the electromagnetic (EM) properties. Magnetic and dielectric relaxations are described by relaxation functions associated with each principal component of the respective tensorial property. Anisotropy is modeled up to orthorhombic symmetry, i.e., the principal coordinate systems of the three EM material tensors coincide, and each property is described by three different principal components. The algorithm uses the pseudospectral method for computing the spatial derivatives and a second-order finite difference in time. A complete plane-wave analysis, including energy balance, gives the expressions of measurable quantities such as the EM-wave velocity and the quality factor as a function of frequency and propagation direction. The algorithm reproduces the wavefront shape and attenuation predicted by the plane-wave analysis. In addition, the results are in excellent agreement with an analytical 3-D transient solution. The modeling is applied to evaluation of the EM response of two pipes buried in an anisotropic sand overlying a clay layer. The results demonstrate that anisotropy and loss mechanisms cause significant amplitude and phase distortions.