Modeling of Multilayered Media Green’s Functions With Rough Interfaces

Horizontally stratified media are commonly used to represent naturally occurring and manmade structures, such as soils, roads, and pavements, when probed by ground-penetrating radar (GPR). Electromagnetic (EM) wave scattering from such multilayered media is dependent on the roughness of the interfaces. In this study, we developed a closed-form asymptotic EM model taking into account random rough layers based on the scalar Kirchhoff-tangent plane approximation (SKA) model, which we combined with planar multilayered media Green’s functions. In order to validate our extended SKA model, we conducted simulations using a numerical EM solver based on the finite-difference time-domain (FDTD) method. We modeled a medium with three layers – a base layer of perfect electric conductor (PEC), overlaid by two layers of different materials with rough interfaces. The reflections at the first and at the second interface were both well reproduced by the SKA model for each roughness condition. For the reflection at the PEC surface, the extended SKA model slightly overestimated the reflection, and this overestimation increased with the roughness amplitude. A good agreement was also obtained between the FDTD simulation input values and inverted root mean square (RMS) height estimates of the top interface, while the inverted RMS heights of the second interface were slightly overestimated. The accuracy and the performances of our asymptotic forward model demonstrate promising perspectives for simulating rough multilayered media, and hence, for the full waveform inversion of GPR data to non-invasively characterize soils and materials.