Stochastic Modelling and Geological Aspects of a Gold Mineralisation
ABSTRACT
Gold mineralisation is the result of physico-chemical and thermal processes of the earth’s interior. We may view a geological process of gold mineralization as a stochastic process Z(x):x∈D, where D may be considered as a mineral deposit. In the case of gold mineralization, samples drawn at regular intervals may be considered as following a discrete stochastic process. The point of interest is one of realistic estimation of mineral value property as computations based on classical methods leading to erroneous results. Modern methods based on stochastic modelling treating the process as an 1) Auto-regressive (AR), 2) Moving-average (MA) or a combination of these two viz., 3) ARMA of appropriate order k may lead to more realistic results. Yet another class of methods which consider the geometry of samples in termed as theory of Regionalised Variables. This paper analyses these classes of methods and illustrates a case study of a gold mineralization related to Strike Reef (Footwall branch) of Hutti gold mines.
Gold mineralisation is the result of physico-chemical and thermal processes of the earth’s interior. We may view a geological process of gold mineralization as a stochastic process Z(x):x∈D, where D may be considered as a mineral deposit. In the case of gold mineralization, samples drawn at regular intervals may be considered as following a discrete stochastic process. The point of interest is one of realistic estimation of mineral value property as computations based on classical methods leading to erroneous results. Modern methods based on stochastic modelling treating the process as an 1) Auto-regressive (AR), 2) Moving-average (MA) or a combination of these two viz., 3) ARMA of appropriate order k may lead to more realistic results. Yet another class of methods which consider the geometry of samples in termed as theory of Regionalised Variables. This paper analyses these classes of methods and illustrates a case study of a gold mineralization related to Strike Reef (Footwall branch) of Hutti gold mines.
KEYWORDS
Estimation; Geometry; Gold Mineralization; Stochastic Process; Regionalized Variables; Strike Reef
Estimation; Geometry; Gold Mineralization; Stochastic Process; Regionalized Variables; Strike Reef
Cite this paper
T. Ganesh, D. Sarma and P. Reddy, "Stochastic Modelling and Geological Aspects of a Gold Mineralisation," International Journal of Geosciences, Vol. 3 No. 4, 2012, pp. 790-798. doi: 10.4236/ijg.2012.34080.
T. Ganesh, D. Sarma and P. Reddy, "Stochastic Modelling and Geological Aspects of a Gold Mineralisation," International Journal of Geosciences, Vol. 3 No. 4, 2012, pp. 790-798. doi: 10.4236/ijg.2012.34080.
References
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[1] D. D. Sarma, “A Statistical Appraisal of Ore Valuation. (With Application to Kolar Gold Fields),” Andhra University Press, Waltair, Series No. 157, 1979. [2] D. D. Sarma, “Stochastic Modeling of Gold Mineralisation in the Champion Lode System of Kolar Gold Fields (India),” Mathematical Geology, Vol. 22, No. 3, 1990, pp. 261-279. doi:10.1007/BF00889889 [3] D. D. Sarma, “Geostatistics with Applications in Earth Sciences,” 2nd Edition, Capital Publishing Company, New Delhi, 2009. doi:10.1007/978-1-4020-9380-7 [4] D. D. Sarma and G. S. Koch, “A Statistical Analysis of Exploration Geochemical Data for Uranium,” Mathematical Geology, Vol. 12, No. 2. 1980, pp. 99-114. doi:10.1007/BF01035242 [5] B. K. Sahu, “Time Series Modeling in Earth Sciences,” Oxford & IBH Publications, New Delhi, 2003, p. 24. [6] B. K. Sahu., “Statistical Models in Earth Sciences,” BS Publications, Hyderabad, 2005, p. 210. [7] G. E. P. Box and G. M. Jenkins, “Time Series Analysis: Forecasting and Control,” 2nd Edition, Holden-Day, San Francisco, 1970, p. 5. [8] G. U. Yule, “On a Method of Investigating Periodicities in Disturbed Series in Spectral Reference to Wolfer’s Son Spot Numbers,” Philosophical Transactions of the Royal Society, Series-A, Vol. 226, 1927, pp. 267-298. doi:10.1098/rsta.1927.0007 [9] G. Walker, “On Periodicity in Series of Related Terms,” Philosophical Transactions of the Royal Society, Series-A, Vol. 131, 1931, pp. 518-532. [10] N. Andersen, “On the Calculation of Filter Coefficients for Maximum Entropy Spectral Analysis,” Geophysics, Vol. 39, No.1, 1974, p. 6. [11] M. Armstrong, “Common Problems Seen in Variograms,” Mathematical Geology, Vol. 16, No. 3, 1984, pp. 305-313. doi:10.1007/BF01032694 [12] G. Matheron, “Principles of Geo-Statistics,” Economic Geology, Vol. 58, 1963, pp. 1245-1266. doi:10.2113/gsecongeo.58.8.1246 [13] I. Clark, “Practical Geo-Statistics,” Applied Science Publishers Ltd., London, 1979, p. 129. [14] A. G. Royle, “How to Use Geo-Statistics for Ore Reserve Classification,” World Mining, Vol. 30, 1977, pp. 52-56. [15] S. Hayakin, “Introduction in Non-Linear Methods of Spectral Analysis,” Topic in Applied Physics, Vol. 34, 1983, p. 263. [16] T. J. Ulrych and T. N. Bishop, “Maximum Entropy Spectral Analysis and Auto-Regressive Decomposition,” Reviews of Geophysics and Space Physics, Vol. 130, No. 1, 1975, pp. 183-200. doi:10.1029/RG013i001p00183