**37th DPS Meeting, 4-9 September 2005**

*Session 57 Moon, Mercury and Venus*

Poster, Thursday, September 8, 2005, 6:00-7:15pm, Music Recital Room
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## [57.15] Fractal-Based Modeling of Radio-Wave Scattering from the Surface of Venus

*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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