Frequency dependence of scattering by dense media of small particles based on Monte Carlo simulation of Maxwell´s equations

The frequency dependence of scattering by geophysical media at microwave frequencies is an important issue because multi-frequency measurements are useful for remote sensing applications. Classically, the independent scattering theory states that if the particles are small, scattering is proportional to the fourth power in 3-D scattering and the third power in 2-D scattering. In this paper, we study rigorously the frequency dependence of scattering by dense media by Monte Carlo simulations of the solutions of both 2- and 3-dimensional Maxwell´s equations. The particle positions are generated by deposition and bonding techniques. The sparse-matrix canonical-grid method has been applied to speed up the simulation of scattering by 2D small particles. Numerical solutions of Maxwell´s equations indicate that the frequency dependence of densely packed sticky small particles is much weaker than that of independent scattering. The results are illustrated using parameters of snow in microwave remote sensing.