Electromagnetic Scattering from Fractional Brownian Motion Surfaces via the Small Slope Approximation

Natural surfaces exhibit scale-invariance properties and power-law spectra over a wide range of scales. For this reason, they are well described in the frame of fractal geometry and, in particular, using fractional Brownian motion (fBm) twodimensional statistical processes. In this paper, we present the derivation of the correlation of Global Navigation Satellite System reflectometry signals scattered by a fBm surface. We here show that this correlation depends on a parameter related to the rootmean-square surface slope as measured at the electromagnetic wavelength scale. When this parameter increases, the correlation smoothly decreases from a value close to unity reaching the value of the roughness-independent expression already available in the literature. In our experiments, based on roughness measurements available in the literature, we firstly show how the description of the roughness of natural surfaces can be conveniently obtained via fBm parameters. Then, we illustrate the behavior of the correlation time for different roughness regimes. For a highaltitude airborne receiver, values ranging from about 6 ms (as predicted by the expression already available in the literature) to several tens of milliseconds are obtained.

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Analytical Formulation of Scattering From Anisotropic Power-Law Spectrum Surfaces: Getting Rid of the Cutoff Wavenumber

Martino,

Simone,

Iodice

2023

IEEE Trans. Geosci. Remote Sensing

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Sea and soil surfaces exhibit power-law spectra over a wide range of spatial frequencies. An analytical formulation of the electromagnetic scattering from such surfaces can be obtained via the two-scale model (TSM). However, this approach requires the definition of a cutoff surface wavenumber, separating the low-and high-frequency parts of the surface spectrum. The final obtained normalized radar cross section (NRCS) value is dependent on the choice of this cutoff wavenumber, which is, to some extent, arbitrary. This problem can be avoided by describing power-law spectrum surfaces via the theory of fractional Brownian motion (fBm) two-dimensional (2-D) random processes. The bistatic NRCS of an fBm surface can be analytically evaluated by using the Kirchhoff approximation (KA) or the first-order small slope approximation (SSA-1): its expression is related to the probability density function (pdf) of an alpha-stable random process, and it can be efficiently evaluated by means of proper asymptotic series expansions. However, fBm surfaces are statistically isotropic, whereas natural surfaces are often anisotropic. Therefore, in this work, we first of all show that an anisotropic power-law spectrum surface can be considered as a generalized anisotropic fBm surface; then, we present an analytical formulation of its NRCS, based on SSA-1; and finally, we compare the obtained results with measured NRCSs of natural surfaces and with NRCS values obtained via more accurate but more computationally demanding methods that require the numerical evaluation of scattering integrals.

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Electromagnetic Scattering from Fractional Brownian Motion Surfaces via the Small Slope Approximation

Cited by 3 publications

References 32 publications

Despeckling of Multifrequency SAR Data Using Electromagnetic Scattering Models

Despeckling of Multifrequency SAR Data Using Electromagnetic Scattering Models

A Novel Analytical Formulation of the Correlation of GNSS-R Signals Scattered by a Natural Fractal Surface

Analytical Formulation of Scattering From Anisotropic Power-Law Spectrum Surfaces: Getting Rid of the Cutoff Wavenumber

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