Fractal theory of sea scattering

We introduce a new dynamic model of the sea surface, based on the fractal Weirstrass-Mandelbroot functions. By using this model, we give a closed form of the scattering coefficient. We show that the scattering coefficient, as a function of time, is a fractal function with the same fractal dimension of the sea surface model. This conclusion is validated by a number of numerical computations, discussed in the paper. The results of the paper can be used as a starting point to give a theoretical development to such problems as: (1) detection theory in a clutter environment by using the fractal dimension of the received signal; (2) theoretical justification of the statistical models which describe the sea clutter for high spatial resolution radar as Weibull or K-distributions; and (3) classification theory of different radar signals based on fractal parameters as the dimension and auto-affinity degree.