Determination of the Distribution Density of Specular Points
on the Sea Surface: Formulation of the Inverse Problem

R. G. Gardashov

Istanbul University, Turkey
e-mail: rauf_gardashov@yahoo.co.uk

Received July 7, 2005

Abstract—With reference to the model of a random Gaussian homogeneous cylindrical (one-dimensional) sea
surface z = (x), the inverse problem is formulated in the form of the integral Fredholm equation of the first kind
to determine the distribution density of the number of specular points on the sea surface. The kernel of the equa-
tion is determined in terms of the Fourier transform of the distribution density of radii of surface curvature at
the points of specular reflection. The equation derived by the author earlier for the distribution density and writ-
ten for the dimensionless radius of curvature contains no parameters, a result that is indicative of the universal
character of this distribution for an arbitrary Gaussian surface. The validity of the original formulas obtained in
this paper was verified by simulations.

DOI: 10.1134/S0001433806050094


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