Weibull Model Based on the Maximum Entropy Principle and its Applications on Elements Grade Distribution

Abstract:

The distribution of metallogenic elements grade is an effective index for the quantitatively economical evaluation of mineral resources. We have defined the information entropy as a measure of randomness of metallogenic elements grade distribution, assumed its primary distribution is in an extremely random situation, and deduced the density function of the primary distribution based on maximum entropy principle. Considering the fact that elements concentration goes from a non-orderly state to an orderly one in the ore-forming process, we added restraint parameters to the primary distribution model, got a two-parameter Weibull distribution model with embedded fractal features, and then fitted metallogenic element's grade distribution of Ag-Cu-Pb-Zn from a mine in China. The results show that the Weibull model is more effective than a lognormal model to describe elements distribution, and should be applied more broadly than common lognormal models in geology discipline.

• Periodical: Applied Mechanics and Materials (Volumes 204-208)
• Pages: 4851-4854
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.204-208.4851
• Online since: October 2012
• Authors: Li Wan*, Peng Chen, Xu Yi Hu
• Keywords: Fractal, Maximum Entropy Method, Metallogenic Element, Weibull Distribution

References

[1] E.T. Jaynes. Physical Review. Vol.106(1957), p.620.

[2] J. Deng, Y.S. Zhai, J.P. Wang, L.Q. Yang. Journal of China University of Geosciences. Vol.11 (2000), p.281. (In Chinese)

[3] P.D. Zhao: Quantitative geologic method and its application. (Higher Education Press, Beijing 2004). (In Chinese)

[4] Jozef Gubač. Journal of Geochemical Exploration. Vol. 37 (1990), p.277.

[5] Q.M. Cheng, F.P. Agterberg, S.B. Ballantyne. Journal of Geochemical Exploration. Vol.51(1994), p.109.

[6] J.N. Kapur, H.K. Kesavan: Entropy optimization principles with applications. (Academic Press Inc,San Diego 1992).

[7] L.Wan, Q.f Wang, J.Deng. Resource Geology. Vol.60 (2010), p.98.

[8] J.Deng, Q.f Wang, L Wan. Journal of Geochemical Exploration. Vol.102(2009), p.95.

[9] J.Deng, Q.f Wang, L Wan. Ore Geology Reviews. Vol.40(2011), p.54.

[10] B.E. Khaledia, S. Kocharb. Journal of Statistical Planning and Inference.Vol.136 (2006), p.3121.

[11] V.P. Singh. Water Resources Management. Vol.1(1987), p.33.