On the Role of Local Structures in the Distribution of Gold Ore Deposits in Northern Kazakhstan
Abstract Generated abstract
This paper refines the geological concept of an ore shoot using statistical analysis of gold grade distributions from several Kazakhstan gold deposits. The authors argue that economic grade-based definitions are insufficient for geological and geochemical interpretation, and propose treating ore shoots as volumetric primary concentrations identified through both geological observation and polymodal grade distributions decomposed into elementary normal or lognormal populations. They derive probabilistic boundary values between such populations, discuss continuity criteria and local variability of thresholds, and outline morphological and productivity coefficients for characterizing shoots. The contribution is a more genetically oriented, quantitative framework for distinguishing ore shoots and their hierarchical orders within ore bodies.
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Toward the Definition of the Concept of an “Ore Shoot”
V. A. Narseyev, G. B. Levin, V. L. Los (KazIMS)
The term “ore shoot” has become firmly established in the geological literature (V. Lindgren, 1932, 1934; A. Bateman, 1948; M. V. Kreiter, 1956; N. I. Borodaevskii, 1960; F. N. Shakhov, 1962; F. I. Wolfson, 1960, and others). According to N. I. Borodaevskii (1960), “the principal criterion for distinguishing an ore shoot should be considered the presence of ore with a grade higher than the average for the deposit or ore body. It is incorrect to classify as ore shoots areas with ordinary average grade that stand out against a background of substandard ore...” The economic basis of most definitions is conditional and does not reflect the genetic essence of the phenomenon; for this reason it cannot be used in geological-geochemical studies. At the same time, there is no doubt that ore shoots are a reflection of the regularity in the distribution of matter in an ore body (the grade field, the geochemical field). We studied the distribution of gold grades in the ores of Kazakhstan’s proper gold-ore deposits (Akzhal, Vasilievskoye, Bakyrchik, Balazhal, Bestobe, Zholymbet, Dzhetygara, Aksu, Arkharly, Retivyi, and others).
It has been established that, in the general case, the distribution of Au grades, as well as of other elements in ores (Fe, Cu, Pb, Zn), is polymodal (the variation curve is multi-peaked), i.e., the population characterized by it is heterogeneous. Such a population may be represented as the sum of homogeneous normally or lognormally distributed subpopulations (elementary distribution—ED) [1, 2]. The density function of the grades will have the form:
\[ p(x)=a_1p_1(x)+a_2p_2(x)+\ldots+a_kp_k(x), \]
where: \(a_i\) is the “weight” of \(\mathrm{ED}_i\), and \(P_i(x)\) is the density function of a normal (lognormal) distribution.
Separation of elementary distributions is possible only under the condition: \(a_{i+1}-a_i>\sigma_{i+1}+\sigma\), where \(\alpha\) and \(\sigma\) are the mean and standard deviation of an elementary distribution.
Thus, the distribution of Au grades in deposits is stepwise. All EDs form in space areas of a definite intensity of mineralization with natural boundaries (the minima on the variation curve). These areas will constitute ore zones, shoots, etc.
Finding the boundary values \((x_r)\) of contents between two elementary distributions is possible if the parameters of these distributions are known. In this case, the boundary content will be the content at which a sample with such a content can be assigned with equal probability to any of the separated EDs. Hence we see that \(x_r\) is a stochastic quantity.
Let there be \(PЭ_i\) and \(PЭ_{i+1}\), between which it is necessary to find \(x_r[i-(i+1)]\). The condition for equally probable assignment:
\[ a_i p_j(x)=a_{i+1}p_{i+1}(x) \]
Taking logarithms and setting
\[ \frac{\lg e}{2S_i^2}=b_i, \]
in final form we obtain:
\[ Ax^2+Bx+C=0, \]
where
\[ A=b_{i+1}-b_i, \]
\[ B=2(x_i b_i-x_{i+1}b_{i+1}), \]
\[ C=-x_i^2b_i+x_{i+1}^2b_{i+1}+\lg a_i-\lg a_{i+1}-\lg S_i+\lg S_{i+1}. \]
If we wish to determine the value of \(x\) at which the probability of assigning a sample to \(PЭ_j\) differs by a factor of \(n\) from the probability of assigning it to \(PЭ_{i+1}\), i.e.
\[ \frac{a_i p_i(x)}{a_{i+1}p_{i+1}(x)}=n, \]
then the quantity \(-\lg n\) will enter into \(C\).
Having determined \(x_r\) between \(PЭ_i\) and \(PЭ_{i+1}\), it is possible to calculate how many samples with contents below \(x_r\) may be assigned to \(PЭ_{i+1}\). (If we are finding the lower boundary of an ore shoot, then how many samples below \(x_r\) may be included in the contour of the ore shoot without violating its continuity.)
The calculation is performed with the aid of the function \(\Phi(z)\), tables of which are found in all mathematics textbooks:
\[ P(x>x_r)=0.5-\Phi(z); \]
\[ P(x<x_r)=1-P(x>x_r)=0.5+\Phi(z),\qquad z=\frac{x_r-\bar{x}}{S}. \]
Thus, \(P(x<x_r)\,100\%\) of samples with contents below \(x\) may be assigned to the ore shoot (without violating its continuity). At the same time, it must be remembered that samples with contents less than \(\bar{x}-2S\) will amount to \(2\%\), while samples with contents \(\bar{x}-3S\) will practically not occur at all (one sample with \(x<\bar{x}-3S\) will already cause a violation of continuity).
It should be borne in mind that the parameters of EDs at gold-ore deposits are not stable and vary within rather considerable limits.* \(x_r\) values calculated from the density of the distribution of contents for the entire deposit may not correspond to natural boundaries in some of its parts. It will be more accurate to calculate \(x_r\) for parts of the deposit. Hence it is clear that one and the same boundary within a deposit may have several different numerical values.
In light of the above, ore shoots should be understood as volumetric primary concentrations of elements (minerals), distinguished on the basis of geological observations and data from analysis of the statistical distribution of contents.
Conditions for distinguishing individual “shoots”:
- Continuity.**
- Absence of a trend over small intervals. (For the deposit as a whole, a trend is possible.)
* Within the region of even a single ED there is a trend, but without sharp gradients. Neighboring EDs may merge (\(a_i+1-a_i\), \(x_{i+1}-x_i\)) and split apart.
** “Foreign” bodies, breaks, etc., should not be considered a violation of the continuity of a shoot.
The ore shoot is a geological body and is characterized by parameters: length along strike \((l_{\mathrm{pr}})\), down dip \((l_{\mathrm{pa}})\), inclination \((l_c)\), width \((n)\), and thickness \((m)\). Derived from these, and characterizing the morphology of the shoot, are the linearity coefficient \(K_l = \frac{l_c}{n}\) and the contour-complexity coefficient \(K_{\mathrm{ck}} = \frac{L}{S}\), where \(L\) is the total length of the contour and \(S\) is its area.
Being part of an ore body, shoots, as a rule, include the main reserves of the metal. To characterize the ore-bearing capacity of ore shoots, a series of coefficients may be proposed:
\[ \text{saturation } K_n = \frac{S_{\mathrm{pc}}}{B_{\mathrm{pt}}}, \]
\[ \text{concentration } K_{\mathrm{conc}} = \frac{C_{\mathrm{pc}}}{C_{\mathrm{pt}}}, \]
\[ \text{relative productivity } K_{\mathrm{op}} = K_n \cdot K_{\mathrm{conc}} \cdot 100, \]
\[ \text{absolute productivity } K_{\mathrm{ap}} = \frac{Q_{\mathrm{pc}}}{Q_{\mathrm{pt}}}. \]
\(S_{\mathrm{pc}}, C_{\mathrm{pc}}, Q_{\mathrm{pc}}\) are the area, grade, and reserves of the ore shoot; \(S_{\mathrm{pt}}, C_{\mathrm{pt}}, Q_{\mathrm{pt}}\) are the same for the ore field as a whole.
Depending on the number of elementary distributions, shoots of different orders may be distinguished. First-order ore shoots are parts of an ore body that characterize its internal structure, contain the principal mass of reserves, and satisfy the requirement of continuity. Ore shoots of the second and higher orders are lenses, nests, and bonanzas within first-order shoots. The condition for distinguishing them can only be a definite level of mineralization intensity.