Determination of the distribution density of specular points on the sea surface: Formulation of the inverse problem
- 33 Downloads
With reference to the model of a random Gaussian homogeneous cylindrical (one-dimensional) sea surface z = ζ(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 equation 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 written 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.
KeywordsInverse Problem Distribution Density Characteristic Function Oceanic Physic Geometrical Optic
Unable to display preview. Download preview PDF.
- 1.Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Nauka, Moscow, 1980; Springer, Berlin, 1990).Google Scholar
- 2.F. G. Bass and I. M. Fuchs, Wave Scattering from Statistically Rough Surfaces (Nauka, Moscow, 1972; Pergamon, Oxford, 1978).Google Scholar
- 3.K. S. Shifrin and R. G. Gardashov, “Model Computations of Light Reflection from the Sea Surface,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 21, 162–169 (1985).Google Scholar
- 4.T. G. Gardashova and R. G. Gardashov, “Simulation of Statistical Characteristics of Light Reflected by the Sea Surface,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 37, 74–84 (2001) [Izv., Atmos. Ocean. Phys. 37, 67–77 (2001)].Google Scholar
- 5.A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, DC, 1977).Google Scholar