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G. L. Tyler, A. K. Sultan-Salem (Stanford U.)
The use of fractal geometry has become increasingly attractive both as a model for natural surfaces and as the basis for a new generation of radio-wave scattering laws. The apparent advantages of the fractal-based (F-B) laws over classical laws, which typically are parameterized by a surface power reflection coefficient and a surface RMS slope-related parameter, are that (i) F-B laws have an additional, physically meaningful roughness parameter, the Hurst exponent, H, which controls the distribution of surface roughness with scale, and (ii) F-B scattering models have an explicit dependence on the sensed surface roughness with wavelength. The latter feature is significant given the actual scale-dependent characteristics of natural surfaces and the observed wavelength dependence of radio-wave scattering from planetary surfaces. When applied to Magellan altimetric scattering data for the surface of Venus, the F-B law with constant H developed by Franceschetti et al.\ ({\em IEEE Trans.\ Ant.\ & Prop.}, 47, 1405--1415, Sept.\ 1999) outperforms the conventional Hagfors and Gaussian laws wherever these represent the best descriptor of scattering behavior, as determined by Tyler et al.\ ({\em J.\ Geophys.\ Res.}, 97(E8), 13,115--13,139, Aug.\ 1992). A conventional exponential scattering law appears to be superior the F-B law for a considerable part of the Venusian surface, however. Motivated by the scale-explicit characteristics of fractal-based laws, we modify the result of Franceschetti et al.\ to expand the range of F-B scattering to approximate the form of the exponential scattering law. With this, we combine the modeling structure of the exponential law with the explicit scale dependence of the fractal-based laws. The method used to approximate the exponential form can be generalized to new families of scattering laws that are explicitly linked to the scales of surface scattering. This work was supported by the NASA PGGP.
The author(s) of this abstract have provided an email address for comments about the abstract: len.tyler@stanford.edu
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Bulletin of the American Astronomical Society, 37 #3
© 2004. The American Astronomical Soceity.