Scattering from natural soils modeled by dielectric fractal profiles: the forward-backward approach

The forward-backward (FB) method is an efficient technique for numerical evaluation of electromagnetic scattering from rough surfaces. In its usual formulation, this technique can be only applied to perfectly or highly conducting surfaces. In addition, up to now FB has been employed to compute scattering from surfaces modeled by Gaussian stochastic processes with Gaussian or Pierson-Moscowitz spectra. Accordingly, this technique can be fruitfully used for numerical simulations of scattering from sea surfaces. However, in order to properly deal with natural soil surfaces, extension to the dielectric interface case and to fractal surface models is needed. Extension of the FB method to the dielectric interface case has been recently presented, whereas application to fractal surface models is presented here. Original contribution of the present paper is twofold. First of all, the FB method for dielectric profiles is framed within the theory of iterative methods for the solution of linear systems. In addition, application of the FB method to dielectric band-limited fractional Brownian motion fractal one-dimensional surfaces is explored. Numerical experiments show that, for most of realistic values of dielectric constant and fractal parameters actually encountered for natural soil profiles, the FB method is very rapidly convergent, and its results are in perfect agreement with "exact" ones (i.e. with results of method of moments solved via a direct method).