Automated Complex for the Study of Digital Model of Titan

Abstract

This paper aims at considering the issues of regression modeling of the surface of Saturn's moon Titan and at studying the produced model by means of fractal geometry. The fractal analysis allows studying the structure of complex objects, taking into account their qualitative specifics, for example, the relationship between the structure and the processes of its formation. When constructing a harmonic model of Titan, the method of expansion of topographic information into spherical functions was used. As a result, based on the harmonic analysis of the Cassini mission data, a topographic model of Titan was created. In the final form, the model describing Titan's surface includes the expansion of the height parameter depending on the spherical coordinates into a slowly converging regression series of spherical harmonics. It should be emphasized that for modeling surface details of the surface on a scale of 1 degree, the order of expansion should be about 180, which requires an analysis of (180+1)2 harmonic expansion coefficients. An overdetermined topographic information system was solved to meet the regression modelling's conditions. In this case, a number of qualitative stochastic data, such as external measures, were used together with the standard postulation of the harmonic system of the Titan model. As a result of a sampling of self-similar regions (with close values of the self-similarity coefficients) on the surface of Titan, coinciding with the SRGB parameter (characterizes the color fractal dimension), the elements of the moon's surface were determined, which with a high degree of probability were evolutionarily formed under the influence of the same selenochemical processes.