Scattering coefficient evaluation from a two-dimensional sea fractal surface

This work deals with the problem of electromagnetic scattering from a sea fractal surface. The final goal is to demonstrate that the sea scattered signal retains some fractal characteristic of the two-dimensional (2D) sea fractal surface. To get this final result, the work was organized in four different steps: (1) defining a 2D fractal surface of the sea; (2) computing the electromagnetic (EM) scattered signal; (3) fractally analyzing the EM sea scattered signal; (4) numerically validating the theoretical results. This paper deals with the first two steps of the work, the other ones are reported in a second paper. Some new insights in the field of electromagnetic scattering from fractal surfaces come out from this paper. In detail, for the class of the 2D dynamic Weierstrass-based surfaces with a generic statistical distribution of the amplitude, we provide: (1) a closed-form expression of the scattering coefficient; and (2) the Kirchhoff approximation conditions on the basis of the general criterion of Soto-Crespo and Nieto-Vesperina. These are the main results of this part, and they are very important for the following applications and uses: (1) making a theoretical fractal analysis of the signal, as reported in the second part of this work; (2) defining a numerical algorithm for clutter generation in radar systems; (3) performing a preliminary statistical analysis of the data.