Polar 3D Transformation of the Full Gradient of Attractive Potential
ABSTRACT
The method of 3D polar transformation of full gravity potential gradient vectors is based on the geometric properties of the crossing points of complete gradient of the potential to localize the source region that causes the observed anomaly. The cross-points—poles—are defined for rectangular polygons of different sizes where the full gradient vector is defined at every vertex. The polygon size range could be specified. The set of poles, positive and negative, is then represented on the 3D chart in the form of clusters of dots or cubes and can be considered as a model image of the sources, intended for visual analysis and further interpretation.
The method of 3D polar transformation of full gravity potential gradient vectors is based on the geometric properties of the crossing points of complete gradient of the potential to localize the source region that causes the observed anomaly. The cross-points—poles—are defined for rectangular polygons of different sizes where the full gradient vector is defined at every vertex. The polygon size range could be specified. The set of poles, positive and negative, is then represented on the 3D chart in the form of clusters of dots or cubes and can be considered as a model image of the sources, intended for visual analysis and further interpretation.
Cite this paper
G. Prostolupov and M. Tarantin, "Polar 3D Transformation of the Full Gradient of Attractive Potential," International Journal of Geosciences, Vol. 3 No. 2, 2012, pp. 329-332. doi: 10.4236/ijg.2012.32035.
G. Prostolupov and M. Tarantin, "Polar 3D Transformation of the Full Gradient of Attractive Potential," International Journal of Geosciences, Vol. 3 No. 2, 2012, pp. 329-332. doi: 10.4236/ijg.2012.32035.
References
[1] C. Zhang, M. F. Mushayandebvu, A. B. Reid, J. D. Fairhead and M. E. Odegard, “Euler Deconvolution of Gravity Tensor Gradient Data,” Geophysics, 2000, Vol. 65, No. 2, pp. 512-520. doi:10.1190/1.1444745 [2] V. O. Mikhailov and M. Diament, “Some Aspects of Interpretation of Tensor Gradiometry Data,” Izvestiya, Physics of the Solid Earth, Vol. 42, No. 12, 2006, pp. 971-978. doi:10.1134/S1069351306120019 [3] A. S. Dolgal, “Geopotential Fields Approximation for Practical Tasks Using Equivalent Sources,” Geophysical Journal, Vol. 21, No. 4, 1999, pp. 71-80. [4] A. D. Gvishiani, S. M. Agayan, Sh. R. Bogoutdinov and A. A. Solovyov, “Discrete Mathematical Analysis and Applications Geology and Geophysics,” Bulletin of Kamchatka Regional Association “Educational-Scientific Center”. Earth Sciences, Vol. 16, No. 2, 2010, pp. 109-125 [5] G. V. Prostolupov and M. V. Tarantin, “Attractive Potential Full Gradient Vectors Transformation,” Proceedings of 38th Uspensky Simposium on Theoretical and Practical Aspects of Geologycal Interpretation of Geophysical Fields., Perm, 2011, pp. 245-248
[1] C. Zhang, M. F. Mushayandebvu, A. B. Reid, J. D. Fairhead and M. E. Odegard, “Euler Deconvolution of Gravity Tensor Gradient Data,” Geophysics, 2000, Vol. 65, No. 2, pp. 512-520. doi:10.1190/1.1444745 [2] V. O. Mikhailov and M. Diament, “Some Aspects of Interpretation of Tensor Gradiometry Data,” Izvestiya, Physics of the Solid Earth, Vol. 42, No. 12, 2006, pp. 971-978. doi:10.1134/S1069351306120019 [3] A. S. Dolgal, “Geopotential Fields Approximation for Practical Tasks Using Equivalent Sources,” Geophysical Journal, Vol. 21, No. 4, 1999, pp. 71-80. [4] A. D. Gvishiani, S. M. Agayan, Sh. R. Bogoutdinov and A. A. Solovyov, “Discrete Mathematical Analysis and Applications Geology and Geophysics,” Bulletin of Kamchatka Regional Association “Educational-Scientific Center”. Earth Sciences, Vol. 16, No. 2, 2010, pp. 109-125 [5] G. V. Prostolupov and M. V. Tarantin, “Attractive Potential Full Gradient Vectors Transformation,” Proceedings of 38th Uspensky Simposium on Theoretical and Practical Aspects of Geologycal Interpretation of Geophysical Fields., Perm, 2011, pp. 245-248