**DPS 34th Meeting, October 2002**

*Session 8. Inner Planets*

Oral, Chair(s): T. Widemann and R.M. Nelson, Monday, October 7, 2002, 4:00-5:00pm, Room M
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## [8.06] Validity of Kirchhoff Theory for Electromagnetic Wave Scattering from Random Rough Surfaces with Emphasis on Fractal Models

*A.K. Sultan Salem, G.L. Tyler (Stanford University)*

Understanding of electromagnetic scattering from surfaces is
essential to interpretation of planetary radar observation
of solid bodies, radio wave surface sounding from orbit, and
many planetary remote sensing problems. The validity of
Kirchhoff theory (KT) for analysis of scattering from
fractal surfaces has not been clearly established. KT is
exact for surfaces that are infinite, planar, and smooth.
For other types of surfaces, KT is an approximation that has
limited validity. The first limitation pertains to the local
radius of curvature of the rough surface. The second
pertains to the surface correlation length. By comparing the
results from KT with empirical results, many authors assert
the prime importance of the ratio of the correlation length
to the wavelength (e.g., J.A. Ogilvy, Theory of Wave
Scattering from Random Rough Surfaces, 104-110, Adam Hilger
1991). The larger this ratio, the better KT agrees with
experimental results. We reformulate the second limitation
as follows: The maximum wavelength should not exceed the
correlation length of the surface for a valid application of
KT. Since fractal functions are nowhere differentiable,
band-limited fractals are used as models for physical
surfaces. As first steps, some ad hoc procedures are used to
band-limit the fractal surfaces before calculating the
correlation length and local radius of curvature.
Afterwards, a check is made to make sure that scattering can
be analyzed accurately using KT. This check is extended to
previous works that employ KT with fractal models (G.
Franceschetti et al. 1999, M.K. Shepard and B.A. Campell
1999). The obtained results refer to the rigorous
determination of a hypothesized filtering function
(previously alluded to by Hagfors) to band-limit the
mathematical fractal, transforming it into a physical
representation for scattering calculations. The filtering
function, if found, is expected to be helpful in
understanding scattering from many types of surface models.

If the author provided an email address or URL for general inquiries,
it is as follows:

salatino@stanford.edu

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Bulletin of the American Astronomical Society, **34**, #3<
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© 2002. The American Astronomical Soceity.