The use of multi-parameter analysis and fractal geometry for investigating the structure of the lunar surface

A.O. Andreev∗ , Yu.A. Nefedyev∗∗ , L.A. Nefediev∗∗∗ , E.N. Ahmedshina∗∗∗∗ , N.Yu. Demina∗∗∗∗∗ , A.A. Zagidullin∗∗∗∗∗∗

Kazan Federal University, Kazan, 420008 Russia

E-mail: ∗alexey-andreev93@mail.ru, ∗∗star1955@yandex.ru, ∗∗∗nefediev@yandex.ru, ∗∗∗∗ekanika8@gmail.com, ∗∗∗∗∗vnu 357@mail.ru, ∗∗∗∗∗∗arhtur.zagidullin@yandex.ru

Received April 15, 2020

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DOI: 10.26907/2541-7746.2020.2.223-236

For citation : Andreev A.O., Nefedyev Yu.A., Nefediev L.A., Ahmedshina E.N., Demina N.Yu., Zagidullin A.A. The use of multi-parameter analysis and fractal geometry for investigating the structure of the lunar surface. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 2, pp. 223–236. doi: 10.26907/2541-7746.2020.2.223-236. (In Russian)

Abstract

The problems related to the investigation of the lunar surface structure using the methods of multi-parameter analysis and fractal geometry were considered. In order to build a digital model of the lunar surface, we used the data from the Clementine, Kaguya, and LRO space missions. An electronic database of altimetry measurements was constructed. These measurements were confined to a single reference system by robust modeling. For the construction of the digital model, the altimetry satellite data were expanded into harmonic series of the spherical functions. After that, we used the developed model to determine fractal parameters and fractal similarity coefficients of the lunar surface structure and plotted diagrams of their distribution in monochromatic and color modes. The digital cartographic surface was analyzed by the method of fractal geometry aimed at assessing the fractal similarity coefficients and fractal dimensions. The digital model was transformed into a color map with regard to the color height scale. A method was developed to identify SRGB (Square, Red, Green, Blue) dimensions for the model of lunar surface. More than 150 SRGBs were analyzed, and color fractal parameters were found for them. The obtained results can be helpful for creating a global model of the lunar structure.

Keywords: space satellite measurements, digital maps of lunar surface, multi-parameter analysis, fractal geometry

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