Simulation Topographical Surfaces Geographical and Geological Using Differential Geometry

Mohammedi Ferhat, Bensaada Said

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DOI: 10.4236/ijg.2011.24070                

Abstract

By applying differential geometry to analogue models developed such a model is calculated for the geometrical shape. Dip measurements are critical data for geologists, and in particular for structural studies. They enable quantifying geologic features observed across the surface in order to model the sub-surface. Dip measurements are provided by direct or indirect sources: geological maps, fieldwork data, Digital Elevation Model (DEM). This quantification then allows for comparison of such models to measured field data and supplants the use interferometry Radar describes and compares 3-D deformations. This example supplements and is based on the material found in L.S.S.I.T. Theory as well as some of the experimental results with the new method are delineated.

Keywords

Structural Geology, Topography Surfaces, Differential Geometry, Modeling Images Optically

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. Léna, “Méthodes Physiques de l’Observation,” Inter Editions/ Edition du CNRS, 1986.
[2]	M. Berger and B. Gostiaux, “Géométrie Différentielle, Courbes et Surfaces,” Ed. PUF, Paris, 1987.
[3]	F. Mohammedi, “Thèse de Doctorat, Etudes topographiques des Surfaces,” Louis Pasteur University, Strasbourg, 1993.
[4]	K. Patorski and M. Kujawinska, “Handbook of the Moiré Fringe Technique,” Elsevier Science Publishers, New York, 1993.
[5]	Y. Menard, “Topographie de la mer à Partir des Données Altimétriques Sea-Sat,” L’océanologie spatiale, CNES, 1982, pp. 701-721.
[6]	M. Robin, “la Télédétection, Nathan Université,” Série Géographie, 1995.
[7]	B. Han, “Recent Advancements of Moiré and Microscopic Moiré Interferometry for Thermal Deformation Analyses of Microelectronics Devices,” Experimental Mechanics, Vol. 38, No. 4, 1998, pp. 278-328.
[8]	S. De Nicola and P. Ferraro, “Fourier Transform Method of Fringe Analysis for Moiré Interferometry,” Journal of Optics A: Pure and Applied Optics, Vol. 2, No. 3, 2000, pp. 228-233.
[9]	L. D’Acquisto, L. Fratini, A. M. Siddiolo, “A Modified Moiré Technique for Three-dimensional Surface Topog- raphy,” Measurement Science and Technology, Vol. 13, No. 4, 2002, pp. 613-622. doi:10.1088/0957-0233/13/4/326
[10]	L. Salvi, J. Pagès and L. Batlle, “Pattern Codification Strategies in Structured Light Systems,” Pattern Recog- nition, Vol. 37, No. 4, 2004, pp. 827-849. doi:10.1016/j.patcog.2003.10.002
[11]	A. Antal and D. Paveleva, “Projection Method of Resolving Ambiguities by Determining the Order of Colors in Moiré fringes,” Applied Optics, Vol. 44, No. 36, 2005, pp. 7709-7713. doi:10.1364/AO.44.007709
[12]	J. Pares and. Toscer, “les systèmes de télé- communications par satellites,” Masson & Cie, ENSTA, 1975:
[13]	F. Mohammedi, “Modelling by a Method for Automating Moiré Images for Application in 2D-3D,” I.Re.Phy, Vol. 3, No. 2, 2009, pp. 129-134.