Fractal Analysis of The Lunar Bouguer Gravity Field

  • Rosen Iliev Institute for Space Research and Technology
  • Boyko Ranguelov
  • Antoaneta Frantzova
  • Tzanko Tzankov
Keywords: Moon, Bouguer, gravity, anomalies, fractals, GIS

Abstract

Recent dedicated lunar gravity measure mission provided high-resolution data for the Moon. The collected data are the starting material for the construction of the latest gravity model.  Like all celestial bodies, our natural satellite, is not a perfectly spherical object and its internal structure is not formed of homogeneous layers of equal thickness and gravity field varies from place to place. By measuring variations in lunar gravity can determine the density variations and deduce its internal structure. Gravity anomalies of the Moon are caused by concentrations of huge masses of material known as "mascons". Mascons are a symbol of the periods of creation and destruction in the course of the turbulent geological history of the Moon. This article present the results of the fractal analysis of the lunar Bouguer gravity field. The results obtained in the course of the study confirm the fractal geometry of the lunar Bouguer gravity field. The resulting fractal dimensions (D) varies from 1,4-1,5 to 2,4-2,5 and indicate a high level of gravity values fragmentation. Also, the spatial relationship between Bouguer gravity anomalies, "free-air" gravity anomalies and lunar digital elevation model (DEM) are considered. 

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Author Biographies

Rosen Iliev, Institute for Space Research and Technology

Institute for Space Research and Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

Boyko Ranguelov

Department of Applied Geophysics, University of Mining and Geology “St. Ivan Rilski”, Sofia, Bulgaria

Antoaneta Frantzova

Climate, Atmosphere and Water Research Institute (CAWRI), Bulgarian Academy of Sciences, Sofia, Bulgaria

Tzanko Tzankov

Department of Geography and Methodology of Teaching Geography, University of Shumen „Bishop Konstantin Preslavsky, Shumen”, Bulgaria

References

Ranguelov, B., Iliev, R., Tzankov, Tz., Spassov, E. (2019) Fractal analysis of the lunar free-air gravity field. To Physics Journal, 2, 126-133.

Mancinelli, P., Pauselli, C., Perugini, D., Lupattelli, A., Federico, C. (2014) Fractal Dimension of Geologically Constrained Crater Populations of Mercury. Pure and Applied Geophysics, Springer Verlag, Volume 172, Issue 7, 1999–2008.

Turcotte, D. (1987) A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars. Journal of Geophysical Research, 92, 597-601.

Demin, S.A., Andreev, A.O., Demina, N.Y., Nefedyev, Y.A. (2017) The fractal analysis of the gravitational field and topography of the Mars. J. Phys.: Conf. Ser. 929 012002, 1-7. Doi :10.1088/1742-6596/929/1/012002

Demin, S.A., Andreev, A.O., Demina, N.Y., Nefedyev, Y.A. (2018) The fractal analysis of the topography and gravitational field of Venus. J. Phys.: Conf. Ser. 1038 012020, 1-6. Doi :10.1088/1742-6596/1038/1/012020

Nefedjev, A.Y. (2003) Lunar Surface Research Using Fractal Analysis. The Journal of the Eurasian Astronomical Society, 22, 4-5, 631-632. Doi.org/10.1080/1055679031000139460

Baldassarri,A., Montuori,M., Prieto-Ballesteros,O., Manrubia, S.C. (2008) Fractal properties of isolines at varying altitude revealing different dominant geological processes on Earth. J. Geophys. Res., 113, E09002, doi:10.1029/2007JE003066.

Huang, X, Jiang, X., Yu, Т., Yin, H. (2009) Fractal-Based Lunar Terrain Surface Modeling for the Soft Landing Navigation. Second International Conference on Intelligent Computation Technology and Automation, Changsha, Hunan, China, 53-56. doi: 10.1109/ICICTA.2009.250

Kumar, A.V.S., Sekhar, R.P.R., Tiwari, R.M. (2016) Fractal Analysis of lunar Gravity anomalies over the Basins of Lunar Farside. 19th National Space Science Symposium (NSSS-2016), Poster Session, Kerala, India.

Goossens, S., Lemoine, F.G., Sabaka, T.J., Nicholas, J.B., Mazarico, E., Rowlands, D.D., Loomis, B.D., Chinn, D.S., Neumann, G.A., Smith, D.E., Zuber, M.T. (2016) A Global Degree and Order 1200 Model of the Lunar Gravity Field using GRAIL Mission Data. 47th Lunar and Planetary Science Conference, Houston, TX, Abstract #1484.

Mandelbrot B. (1982) The Fractal Geometry of Nature. San Francisco: W.H. Freeman & Co., San Francisco, 68 p.

Mandelbrot, B.B. (1967) How long is the Coast of Britannia? Statistical self-similarity and fractional dimension. Science, 156, 636-638.

Korvin, G. (1992) Fractal models in the Earth Sciences. New York: Elsevier, 236 p.

Turcotte, D. (1986) Fractals and Fragmentation. Journal of Geophysical Research. 91, B2, 1921-1926.

Hirata T. (1989) Fractal dimension of fault system in Japan: Fractal structure in Rock geometry at various scales. Pure and Applied Geophysics, 131, 157-173.

Turcotte, D. (1986) A fractal model of crustal deformation. Tectonophysics, 132, 361-369.

Prashker, S. (2009) An anti-aliasing algorithm for calculating the perimeter of raster polygons. Geotec, Ottawa & Geomtics Atlantic, Wolfville, NS, CD-ROM

Prashker, S. (1999) An improved algorithm for calculating the perimeter and area of raster polygons. Proceedings of the 4th International Conference on GeoComputation Mary Washington College Fredericksburg, Virginia,USA, 25 - 28 July 1999, "GeoComputation CD-ROM".

Smith, D.E., Zuber, M.T., Neumann, G.A., Mazarico, E., Head, J.W., III, Torrence, M.H. and the LOLA Science Team (2011) Results from the Lunar Orbiter Laser Altimeter (LOLA): global, high-resolution topographic mapping of the Moon, Lunar Planetary Science Conference XLII, Abstract 2350.

Tooley, C.R., Houghton, M.B., Saylor, R.S., Peddie, C., Everett, D.F., Baker, C.L. and Safdie, K.N. (2010) Lunar Reconnaissance Orbiter mission and spacecraft design, Space Sci. Rev., 150, 23–62, doi:10.1007/s11214-009-9624-4.

Archinal, B.A. (Chair), A’Hearn, M.F., Bowell, E., Conrad, A., Consolmagno, G.J., Courtin, R., Fukushima, T., Hestroffer, D., Hilton, J.L., Krasinsky, G.A., Neumann, G.A., Oberst, J., Seidelmann, P.K., Stooke, P., Tholen, D.J., Thomas, P.C. and Williams, I.P. (2011) Report of the IAU Working Group on cartographic coordinates and rotational elements: 2009, Celestial Mechanics and Dynamical Astronomy, 109, 2, 101-135, doi 10.1007/s10569-010-9320-4.

Conrad, O., Bechtel, B., Bock, M., Dietrich, H., Fischer, E., Gerlitz, L., Wehberg, J., Wichmann, V. and Boehner, J. (2015) System for Automated Geoscientific Analyses (SAGA) v. 2.1.4. Geosci. Model Dev., 8, 1991-2007, doi:10.5194/gmd-8-1991-201

Thiede, R., Sutton, T., Düster, H., Sutton, M. (2014) Quantum GIS Training Manual. Locate Press, 388 p.

Wieczorek, M. A., Neumann, G.A., Nimmo, F., Kiefer, W.S., Taylor, G.J., Melosh, H.J., Phillips, R.J., Solomon, S.C., Andrews-Hanna, J.C., Asmar, S.W., Konopliv, A.S., Lemoine, F.G., Smith, D.E., Watkins, M.M., Williams, J.G. and Zuber, M.T. (2013) The crust of the Moon as seen by GRAIL, Science, 339, 671-675. Doi:10.1126/science.1231530.

Published
2019-08-30
How to Cite
Iliev, R., Ranguelov, B., Frantzova, A., & Tzankov, T. (2019). Fractal Analysis of The Lunar Bouguer Gravity Field. To Physics Journal, 3, 77-88. Retrieved from http://purkh.com/index.php/tophy/article/view/452
Section
Research Articles