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.

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