Joao Felipe Coimbra Leite Costa

Reducing the impact of outliers in ore reserves estimation

Mining applications commonly faces surprising high values designated as outliers. These values impact dramatically statistical analysis and interpretation. A comprehensive analysis on the causes for the presence of unexpected high values was recommended. However, if an erroneous value was accepted as a part of the solution, some form of correction is recommended. A methodology based on the robust kriging (RoK) algorithm is proposed to be used in exploratory data analysis and also to deal with problems associated with the presence of outliers in the sample data set. The efficiency of RoK method as an interpolator is tested in different types of mineralizations. Importantly, the parent population from which the data was sampled is available, thus allowing direct quantitative assessment of the effectiveness of the estimation technique. The performance of the method is tested in the context of ore reserves estimation. RoK model is compared to models generated by ordinary kriging, median indicator kriging, and lognormal kriging. RoK proved to be more accurate and more precise than those methods reducing substantially the number of misclassified blocks.

Gamma-Ray Data Processing and Integration for Lode-Au Deposits Exploration

A large number of mineral deposits are associated with hydrothermal processes, especially auriferous deposits. In such processes, studies on percolating fluids may indicate the presence of potash (K), among other elements. In this study, aerogammaspectrometric data-processing methodologies are evaluated, especially those methods based on the suppression of the primary contribution of potassium, the result of lithological and soil variations, and to environmental conditions. Resulting maps point out the contribution of hydrothermal K. This processing procedure was used because of the association of hydrothermal K and auriferous mineralizations according to the deposit model defined for the studied region. Intensity maps locate the areas with great influence of hydrothermal K. Data integration required to improve a change in the gammaspectrometric data processing in order to positively correlate hydrothermalised areas. Data integration could distinguish high and medium favorable targets for mineral exploration of lode-Au deposits in the studied region.

Simulation of Geological Contacts from Interpreted Geological Model Using Multiple-Point Statistics

Applications of multiple-point statistics (mps) algorithms to large non-repetitive geological objects such as those found in mining deposits are difficult because most mps algorithms rely on pattern repetition for simulation. In many cases, an interpreted geological model built from a computer-aided design system is readily available but suffers as a training image due to the lack of patterns repetitiveness. Porphyry copper deposits and iron ore formations are good examples of such mining deposits with non-repetitive patterns. This paper presents an algorithm called contactsim that focuses on reproducing the patterns of the contacts between geological types. The algorithm learns the shapes of the lithotype contacts as interpreted by the geologist, and simulates their patterns at a later stage. Defining a zone of uncertainty around the lithological contact is a critical step in contactsim, because it defines both the zones where the simulation is performed and where the algorithm should focus to learn the transitional patterns between lithotypes. A larger zone of uncertainty results in greater variation between realizations. The definition of the uncertainty zone must take into consideration the geological understanding of the deposit, and the reliability of the contact zones. The contactsim algorithm is demonstrated on an iron ore formation.

Additional samples: Where they should be located

Information for mine planning requires to be close spaced, if compared to the grid used for exploration and resource assessment. The additional samples collected during quasimining usually are located in the same pattern of the original diamond drillholes net but closer spaced. This procedure is not the best in mathematical sense for selecting a location. The impact of an additional information to reduce the uncertainty about the parameter been modeled is not the same everywhere within the deposit. Some locations are more sensitive in reducing the local and global uncertainty than others. This study introduces a methodology to select additional sample locations based on stochastic simulation. The procedure takes into account data variability and their spatial location. Multiple equally probable models representing a geological attribute are generated via geostatistical simulation. These models share basically the same histogram and the same variogram obtained from the original data set. At each block belonging to the model a value is obtained from the n simulations and their combination allows one to access local variability. Variability is measured using an uncertainty index proposed. This index was used to map zones of high variability. A value extracted from a given simulation is added to the original data set from a zone identified as erratic in the previous maps. The process of adding samples and simulation is repeated and the benefit of the additional sample is evaluated. The benefit in terms of uncertainty reduction is measure locally and globally. The procedure showed to be robust and theoretically sound, mapping zones where the additional information is most beneficial. A case study in a coal mine using coal seam thickness illustrates the method.

O problema de amostragem manual na indústria mineral

Discrepancies in raw materials properties informed by both producer and consumer are a common problem in most areas of the industry. Commercial contracts in the mineral industry normally penalize the producer, if contaminants in the ore exceed established limits. Differences in lab analysis are due many sources of error, such as distinct practices used in two laboratories for sampling, preparation or analysis. Sampling theory provides the tools to analyze errors involved in sampling, preparation and analysis. This paper proposes a methodology to check the precision and accuracy of a given sampling protocol emphasizing the application of Gys sampling theory to broken ore. The results show the applicability of the method and its relevance to audit sampling procedures aiming at error minimization. The methodology is illustrated in a case study at a major coal producer in Brazil.

A conflict-free, path-level parallelization approach for sequential simulation algorithms

Pixel-based simulation algorithms are the most widely used geostatistical technique for characterizing the spatial distribution of natural resources. However, sequential simulation does not scale well for stochastic simulation on very large grids, which are now commonly found in many petroleum, mining, and environmental studies. With the availability of multiple-processor computers, there is an opportunity to develop parallelization schemes for these algorithms to increase their performance and efficiency. Here we present a conflict-free, path-level parallelization strategy for sequential simulation. The method consists of partitioning the simulation grid into a set of groups of nodes and delegating all available processors for simulation of multiple groups of nodes concurrently. An automated classification procedure determines which groups are simulated in parallel according to their spatial arrangement in the simulation grid. The major advantage of this approach is that it does not require conflict resolution operations, and thus allows exact reproduction of results. Besides offering a large performance gain when compared to the traditional serial implementation, the method provides efficient use of computational resources and is generic enough to be adapted to several sequential algorithms. HighlightsWe present a path-level parallelization strategy for sequential simulation.The proposed method does not require conflict resolution operations.The methodology is illustrated with a parallel implementation of SGS.The strategy improves performance and allows exact reproduction of results.The parallel version of SGS reproduces all the statistics of the serial SGS.

Interpolating datasets with trends: A modified median polish approach

This article investigates an alternative method to deal with data sets in the presence of trends. Median polish kriging (MPK) was introduced as an alternative solution to universal kriging or intrinsic random functions of order k (IRF-k) for estimation in the presence of trends. The maps obtained using the original MPK algorithm show banding artefacts which do not appear in the reference data set. A modified version of MPK was introduced to attempt to remove the banding artefacts. The results confirm the improvement in quality of estimate using the modified version of MPK (called MPKm), which takes into account the problems of clustered samples and boundary effect associated with the re-addition of the trend along bands. The variation introduced in the median polish algorithm proved to be satisfactory in eliminating the artefacts.

Assessing Uncertainty Associated with the Delineation of Geochemical Anomalies

A pedogeochemical exploratory survey of gold deposits was carried out in the region of São Sepé (southernmost Brazil). The region comprises a predominantly metamorphosed belt of volcanoclastics, sediments, serpentinites, basalts, gabbros, chert, tuffs, and banded iron formation of the Proterozoic age. The anomalies were identified first by stream sediment heavy mineral survey at the regional scale of exploration. Once spatial continuity was modeled, ordinary block kriging was performed to generate geochemical maps. Indicator block kriging also was used as an alternative in analyzing and interpreting geochemical data. A novel approach is proposed, which combines both ordinary and indicator kriging for delineating geochemical anomalies. Probability maps proved to be appropriate for selecting new sites for further exploration. Gold anomalies in soils trending NE were well defined by geostatistical analysis and subsequently confirmed by drilling.

Kriging with an external drift versus collocated cokriging for water table mapping

Abstract In aquifers driven by gravity, the water table resembles topographic features. Topographic data are easily obtainable at a low cost and geostatistics provides an adequate framework for incorporating exhaustive topographic secondary information to improve the estimate of a primary variable such as water table level. This incorporation results in models that better coincide with the natural phenomena being analysed. The present paper introduces collocated cokriging (multicollocated cokriging) and kriging with an external drift to incorporate topography as secondary information for mapping the water table level. The case study presented comes from a groundwater monitoring programme carried out in an underground coal mine. Incorporation of topography is aimed at diminishing the number of monitoring piezometers without deteriorating the maps of the estimates. The results of the present study show that both methodologies used improved the quality of the water table elevation maps when compared with ordinary kriging that does not introduce the topographic data. A slightly better performance obtained through collocated cokriging can be attributed to the spatial correlation taken into account by this methodology.

The effect of accumulation in 2D estimates in phosphatic ore

The geological modeling of stratiform deposits can become very complex, often making use of geological envelopes of small thickness and requiring the use of subblocks (based on Cartesian coordinates) to produce a coherent block model. However, geological events after the formation of the deposit (folds, faults, etc.) can change the direction of spatial continuity of certain attributes, with the mixing of samples belonging to different formation eras (in the case of stratiform deposits) in the same elevation. This study presents a solution for deposits with stratigraphic grades combined with samples of different origins. The solution is a two-dimensional estimate obtained by accumulating the thicknesses of P 2 O 5 in a phosphate deposit (as compared to traditional statistical analysis in three dimensions).