Integrative GPR loss in a discrete random medium model: The effect of rough-surface and subsurface Mie scatterers

In rough geologic media such as alluvial gravels, glacial till, talus or colluvium, the grain sizes may span the range of GPR in situ wavelengths. Here we experimentally and numerically model the combined scattering loss from a rough surface and subsurface dielectric scatterers, the dimensions of which lie within the Mie regime. We compare the GPR signal amplitude and waveform reflected from the bottom of a large tank filled with small boulders, with the numerically computed response from a discrete random medium (DRM) model in which the scatterers are simulated with ellipsoids. In the numerical model the permittivity of the ellipsoids is constant, and their size and orientation are randomized, but with a uniform distribution. The starting in situ dominant pulse wavelength at 900 MHz was about 17 cm, as was the average rock dimension. The major axis of all DRM scatterers ranged from 15-25 cm. Experimentally, the 900-MHz pulse underwent most dispersion within the first in situ wavelength of depth, and then, at 500-700 MHz dominant frequency, the pulses underwent a near inverse range dependency loss rate, as if the media were a pure dielectric. Using a Monte Carlo style approach, we statistically assessed the scattering loss from many realizations and simulations. The model agrees with the experimental data qualitatively by showing the wave propagation features such as the amplitude decay and high frequency content loss with the increase of the reflection depth.