FDTD simulation of the angular correlation function of objects buried in continuous random media

Natural media are often inhomogeneous and cannot be described in a deterministic manner, so a statistical model should be employed instead. In analytical studies, statistical models often describe a medium as an effective or mean permittivity (or permeability) with random fluctuations that follow a prescribed correlation function. A single realization (assuming spatial ergodicity) or ensemble of random media with correlation functions chosen to describe the medium of interest are used to study the statistical properties of the scattered and transmitted fields. In this paper, a 3-D finite-difference time-domain (FDTD) scheme is used to model the scattering from an object in a continuous random medium. FDTD techniques have been previously applied to scattering from random rough surfaces and randomly placed objects in a homogeneous background, but little has been done to simulate continuous random media with embedded objects where volume-scattering effects are important. The random medium parameters in this case are approximately based on particular soil models, with subsurface sensing applications in mind. Soil naturally contains fluctuations in density, material, and moisture, which may effect the scattering results. The scattered field from the random medium, with and without an object present, is studied using the angular correlation function (ACF).