Document Type : Original Article
Authors
1
Faculty member of Arak University of Technology
2
Faculty of Mining Engineering, College of Earth Sciences Engineering, Arak University of Technology, Arak, Iran
Abstract
Extended Abstract
Introduction
Modeling the spatial distribution of grade and reserve estimation are the most important issues and the main goal of exploration operation. In the following situations, underground exploratory works such as exploration tunnels are carried out: 1- vertical or steep slope mineral deposits, 2- mountainous geomorphology with high altitudes and rough topography, 3- difficult or impossible situation of drilling, and 4- very high thickness or volume of overburden on the mineral deposit. In fact, in such conditions, for the most of mineral deposits there is continuity in the vertical direction whereas the changes are mostly along the horizontal surfaces.
In the present research, block modeling and geostatistical reserve estimation of the Emarat Pb-Zn deposit located in the Markazi province, have been carried out using log-kriging method with a different approach and a delicate technique. To achieve the goal, firstly, processing, modeling and geostatistical estimation of total Pb-Zn assay data obtained from exploratory tunnels drilled at the various elevation levels were performed as two-dimensional, separately. Then, using the gained results, three-dimensional estimation process for whole of the deposit was done. Such an approach for geostatistical estimation of a deposit grade and reserve discovered by underground exploratory works, has not been reported in any research before.
Materials and methods
In the Emarat Pb-Zn deposit, many activities containing drilling of horizontal exploratory- exploitational tunnels and cross-cuts with a total length of 11,000 m in six elevation levels with a height difference of about 10 m have been carried out, whereas 1,238 Pb-Zn assay data of samples taken from the tunnels are available.
From the dimensional viewpoint, in the case of two-dimensional acquisitioned data, such as assay data of surface samples, processing operation and geostatistical estimation with Kriging method is done as two-dimensional. There are also cases in which, although the data acquisition is three-dimensional, it is better to perform the geostatistical estimation first on two-dimensional surfaces, then the estimation results obtained from different levels are combined with each other and the final three-dimensional model is produced. This type of kriging estimation is called cross-sectional kriging.
If the statistical distribution of the used data is not normal, linear kriging estimation methods cannot be employed. In this case, it is better to normalize the data with a suitable transformation method such as logarithmic. Next, the estimation operation is applied on the logarithm of data with the ordinary (or simple) kriging method, and then the estimated values are converted to real values with an inverse transformation. This non-linear kriging method is called log-kriging.
Discussion and results
Based on the statistical processing of total Pb-Zn assay data for the elevation levels of 2032, 2024, 1998, 1988, 1978 and 1964-1968 m separately, data distribution was known log-normal, normalized with two and three parameters logarithmic transformation. Also, plotting standard deviation against the total Pb-Zn assay data of the various elevation levels revealed dependence of the variance with mean. Using variography of the different elevation levels and determination of ellipse search radii, grade of each elevation level was estimated with geostatistical cross-sectional log-kriging method for 10 by 10 m blocks as well as isograde map from estimation process was drawn. Afterward, the estimation process was validated through cross-validation approach with the well-known jackknife kriging method and estimation error maps of each elevation level. To create block model of the deposit, size of the blocks was set to 10*10*10 m based on the size and extension area of mineral deposit in each elevation level, as well as distance of the elevation levels. At the end, different categories of proven, probable and prospected reserves were determined for seven cut-off grades of 4, 4.5, 5, 5.5, 6, 6.5 and 7 percent.
Conclusion
In this research, a new approach was used for geostatistical estimation of grade and ore reserve, in the Emarat Pb-Zn deposit. The results of the research show that in some cases according to the conditions of the studied deposit and type of carried out exploration activities, modeling and estimation of ore reserve is possible more simply with optimal accuracy through the relatively new and accurate geostatistical methods. This scenario was performed by the approach of dimension reduction of estimation space and then converting the estimation space from two to three dimensions. The results of this research will be useful for all earth sciences users, including geologists, mining exploration and exploitation engineers.
Keywords: Emarat Pb-Zn deposit, Geostatistical estimation, Elevation level, Tunnel, Cross-sectional log-kriging
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