Fractal surface synthesis for remote sensing

In this paper we present a physical approach for the synthesis of fractional Brownian motion (fBm) with the use of Weierstrass-Mandelbrot functions (WM). The quantitative equivalence between WM and fBm is still an open problem, and it is here faced by showing that a WM can be seen as a spectral sampling of an fBm process. The presented physical framework provides the quantitative definition of the sampling frequency as a function of the physical properties of the fractal surface. The obtained results can be employed for the evaluation of the electromagnetic field scattered from natural surfaces, which is a topic of broad interest for the remote sensing community. The comparison domain and the results for the sampling frequency parameter will change, in agreement with the physical mechanisms that govern the scattered field formation.