Kirchhoff diffractals

Quantitative roughness characterization of geological surfaces and implications for radar signature analysis

“…They can be evaluated from slope and offset of the 1-D spectrum. For fractal surfaces, the curves of the backscattering coefficient as a function of the incidence angle are of variable shape and may in certain cases deviate significantly from the patterns observed for stationary surfaces [23]. Dependent on spectral slope and offset, the function reveals a behavior typical for stationary surfaces (i.e., decreases with increasing ), has a maximum at angles >0 , or even increases with increasing until .…”

“…In the case of the IEM, a solution for surfaces with power-law spectra is not available at present. Yordanov and Ivanova [23] have studied scattering from perfectly conducting surfaces characterized by a powerlaw spectrum with and without large-scale cutoff. They used the Kirchhoff approximation (neglecting multiple scattering) and assumed that the incident e.m. waves were vertically polarized.…”

“…13, lines are drawn to mark the border between nonfractal scattering behavior (to the left) and the diffractal regime (to the right). These lines were determined on the basis of the results shown in [23,Figs. 3 and 5].…”

“…Scattering signatures of stationary surfaces are calculated utilizing the integral equation model (IEM) developed by Fung et al [22]. Scattering from power-law surfaces is addressed on the basis of the work by Yordanov and Ivanova [23]. In this case, roughness parameters that are independent of profile length have to be used to describe the relationship between backscattering signature and surface roughness.…”

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

“…This is often the case at microwave frequencies [41]. First studies on application of KA to fBm surfaces (sometimes approximated by Weierstrass-Mandelbrot functions [42]) date back to the last decades of last century [15,41,43,44]. To summarize the obtained results, we have to preliminarily recall that an fBm surface is a 2D random process whose increments over a fixed distance are zeromean Gaussian with variance…”