Ground-penetrating radar: Wave theory and numerical simulation in lossy anisotropic media

Subsurface georadar is a high-resolution technique based on the propagation of high-frequency radio waves. Modeling radio waves in a realistic medium requires the simulation of the complete wavefield and the correct description of the petrophysical properties, such as conductivity and dielectric relaxation. Here, the theory is developed for 2-D transverse magnetic (TM) waves, with a different relaxation function associated to each principal permittivity and conductivity component. In this way, the wave characteristics (e.g., wavefront and attenuation) are anisotropic and have a general frequency dependence. These characteristics are investigated through a plane-wave analysis that gives the expressions of measurable quantities such as the quality factor and the energy velocity. The numerical solution for arbitrary heterogeneous media is obtained by a grid method that uses a time-splitting algorithm to circumvent the stiffness of the differential equations. The modeling correctly reproduces the amplitude and the wavefront shape predicted by the plane-wave analysis for homogeneous media, confirming, in this way, both the theoretical analysis and the numerical algorithm. Finally, the modeling is applied to the evaluation of the electromagnetic response of contaminant pools in a sand aquifer. The results indicate the degree of resolution (radar frequency) necessary to identify the pools and the differences between the anisotropic and isotropic radargrams versus the source-receiver distance.