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By B Vorster

Falls of Ground is one of the highest causes of incidents, accidents and fatal injuries in our mines today. These falls of ground may occur as soon as the face is exposed after blasting or after machine cutting. The falls of ground can also occur after support has been installed. There are many reasons why these falls occur before and after supporting of the face. It is therefore important to support the exposed face as soon as possible to prevent the falls of ground. It is also very important to support the face with the correct support products and to support the face as designed and required by the mining engineers. The possible reasons for falls of ground, possible support methods and the products available will be discussed in this presentation. In typical conventional narrow vein stoping operations, the use of conventional temporary support components to offer some support to workers, whilst the permanent and generally more elaborate support system gets installed or constructed, still results in injuries to people. The author wishes to discuss the following items in this paper:- ? Introduction ? Basic face behaviour after exposure ? Controllable Parameters ? Mining Engineers support designs ? Primary and Secondary Support ? Products available for prevention of falls of ground

Jan 1, 2008

By R. Butcher

Mud rushes are hazardous occurrences that have occurred frequently in mines in South Africa, and have been the cause of numerous fatalities in the past. Mud rush incidents not associated with accidents are believed to be common occurrences that are not generally reported. Many such incidents are probably associated with the operation of chutes and box fronts. This paper describes the conditions necessary for mud rush occurrences, postulated mud rush mechanisms, and methods of combating the mud rush hazard.

Jan 1, 2005

[Consider the situation where we wish to estimate the value of a block of ore W from the values of n samples wt (i = 1, 2.... n). The samples can be located anywhere inside or outside W. The blocks and the samples can have any size or shape (Fig. 8.1). We define ws as the set of all the samples wi: WS = Iw1; W2; W3.. . wn and we wish to estimate the block W using the samples ws. Let xi be the value of the ith sample and µw the unknown average value of the block. We can estimate µw from the average value of all the samples. Let µw be the estimator of µw. As the samples need not be of equal size, the sample average is: µw = wi xi/~ wi. (8.1) The mean squared error made when estimating µw by µw is known as the variance of estimation of W by ws. It is the error made when giving the value of the sample set ws to the block W and is written o2E (WS to W). By definition: o2E (ws to W) = E [(µw - µw)2]. (8.2) If n = 1, this error is known as the extension variance. Since the sum of the weights given to the sample values is equal to 1,0, the estimator µw is unbiased (the question of the absence of bias is studied in more detail in Chapter 9): E [( µw - µw)1 = 0. (8.3) The error (µw - µw) has zero mean and a variance o2E = E (W8 to W). If we assume that this error is normally distributed, we can define confidence limits for µw. Let tP be the value of the standardized normal variance t such that the probability that t is less than tP is p: (t,) = .\/27T f exp (- t2/2) dt = p (8.4) The probability that µw is larger than µw + t1-P oE is p. The probability that µw is smaller than µw- t1-P oE is p. The following approximation formulae are often used to calculate 2p central confidence limits for the block value: 68% central confidence limits (p = 16%): µw - o2E, and µw + o2E. 95 % central confidence limits (p = 2,5 %): µw - 2 oE, and µw + 2 oE. Tables of the function 0 can be found in any textbook on statistics (for example, Fraser, 1958, p. 388) (see Table 7.2). [ ] The last line of Table 2.2, corresponding to f = 00, also contains the value of tP for p = 80, 90, 95 and 97,5 %.]

Jan 1, 1978

By L. G. Stolarczyk, J. Duncan

"SynopsisLong before the environmental movement, coal miners were suffering from occupational diseases that became apparent in the later years of service, and especially during the retirement years. Chronic exposure to micro-fine dust in the respirable range (‘float’ dust) causes various lung diseases, referred to as coal mine dust lung disease. In the USA alone, 76 000 miners have died of coal mine dust lung disease since early legislation recognized the issue in 1969. Researchers believe that reducing float dust exposure limits alone will not reverse the increasing incidence of coal mine dust lung disease seen in the current generation of miners. Trace and radioactive metals are concentrated in the thin boundary layers of the coal seam (Roberts, 2013), and hence float dust includes silica and toxic trace metals. The production and quality of coal is also significantly impacted by the presence of these contaminants in the coal. In the combustion process, the trace metals are oxidized and become incorporated in the fly ash and flue gas. Since they are extremely water-soluble, they represent a significant danger to health and the environment. Coal preparation plants and power stations need to mitigate these contaminants as far as is practical, but the simple fact is that most contaminants should have been left un-mined.This paper describes an innovative coal-cutting solution to the longstanding technology gap in mining – the ability to measure uncut coal layer thickness to the boundary rock layer. Because of constant changes in geology, seam thickness, and seam undulation, the horizon sensor must be located in the bit-block of the rotating cutter drum of the mining machine. Contaminants in ROM coal must be minimized at the source – that is, at the rock/coal crushing cone directly under the bit-tips of the cutting drum. Bittip distances to the rock boundary layer must be automatically controlled in real time when mining in a complex and undulating coal bed. Horizon sensing (HS) technology enables the mining machine’s cutting picks to stop at a specified distance from undulating horizons of the boundary rock. The thin contaminated coal layer can be left in situ, significantly reducing the toxicity of the float dust. Preventing the metal picks from striking quartz-containing boundary rock also reduces the occurrence of methane ignitions. HS technology equipped with pick force vector sensing can allow optimization of the cutting pick lacing pattern for minimum coal and rock crushing, thereby reducing float dust. This technology may enable the mining industry to convert from automated machine control to autonomous during coal cutting and loading."

Jan 1, 2015

By Y. I. Yang, Y. -B. Tang, D. -J. Ma

Chlorine-containing minerals are commonly present in coal. Associated minerals such as pyrite can undergo exothermic reactions. Consequently, it is of great significance to study the effect of inorganic chloride on the spontaneous combustion of coal. In this study, the effects of five inorganic chlorides (sodium chloride, magnesium chloride, potassium chloride, calcium chloride, and zinc chloride) on the spontaneous oxidation of coal were investigated. Analysis of the gaseous products of coal oxidization at low temperatures (323K to 453K) showed that the presence of inorganic chlorine in coal markedly decreases O2 consumption and the generation of CO and CO2. Samples of raw coal and chlorine-loaded coal were oxidized for 36 hours under the same experimental conditions. Infrared diffuse reflectance spectroscopy results showed that inorganic chloride can inhibit the oxidative decomposition of some functional structure components (methyl, methylene, methine, and hydroxy) in the coal. The influence of inorganic chloride on the oxidation characteristics of the functional groups in coal during spontaneous combustion was investigated using benzyl alcohol and 1-phenylpropanol as model compounds, which were tested under the same experimental conditions as the coal samples. The oxygen consumption of model compounds with and without the addition of inorganic chloride further suggested that inorganic chloride may hinder the oxygenolysis of these structures during low-temperature oxidation. This phenomenon can be attributed to the radical reaction from the perspective of radical chemistry. It can therefore be concluded that inorganic chlorides play an inhibitory role in the spontaneous combustion of coal.

Jan 1, 2015

By C. Sahyoun

The influence of microwave treatment on copper flotation has been investigated. Comparative batch flotation tests carried out on ore treated at 5?12 kW for 0.1?0.5 s showed that improvements in copper recovery of between 6?15 % could be achieved compared with untreated ore. Both recovery and cumulative grade increased with increasing treatment time and power. A preliminary economic analysis showed that microwave treatment will be economically viable if recoveries similar to those determined on laboratory scale can be achieved on a plant. Keywords: microwave treatment, copper ore, flotation, liberation, recovery

Jan 1, 2005

By C. Wade, A. Swart, M. Dworzanowski

AngloGold Ashanti operate a pyrite flotation plant at their East Gold Plant, Acid Plant and Flotation Plant (EGAF) metallurgical complex within their Vaal River operations in the North West province in South Africa. The flotation plant feed is reclaimed pyrite rich tailings and the concentrate produced is used as the source of sulphur for the EGAF acid plant. The sulphuric acid produced is in turn used for the recovery of uranium at the Vaal River South uranium plant. The original flotation plant built in 1960 was based on the use of many small volume flotation cells and was becoming very expensive to operate and its age severely limited further operation. A decision was taken in 2005 to replace this plant with a new one based on fewer, larger volume flotation cells. This paper describes the benefits of using larger volume flotation cells in this new flotation plant when compared to the smaller volume flotation cells in the old plant. The benefits of the new plant include a smaller plant footprint, fewer flotation cells, fewer pumps, no distribution boxes, simpler piping, a greater flotation volume and a reduction in installed power. The saving in capital cost could not be quantified because of the age of the old plant. The savings in operating cost will arise from fewer operators, less maintenance and reduced power consumption. The new plant has not been in operation long enough to quantify the benefits in operating cost and metallurgical performance. However, recovery improvements can be expected given the greater flotation volume (increased residence time) and the installation of larger, more efficient flotation cells.

Jan 1, 2007

By P. J. van Staden, T. W. Walker

The Minfurn is a novel carbon-regeneration furnace developed at Mintek. It combines the advantages of direct resistive heating in a vertical-tube furnace with those of continuous operation, in a furnace whose capital, operating, and maintenance costs compare favourably with those of conventional rotary kilns. After successful tests under experimental conditions on carbons containing different contaminants, a 3 kg/h unit was installed on the carbon-in-pulp (CIP) plant at the Klipwal Gold Mine near Piet Retief, where it has been operating at, on average, 123 per cent of its design capacity. Since the installation of the Minfurn, monthly average losses of dissolved gold of less than 0,02 p.p.m. have been maintained for several successive months for the first time since January 1989. It is also possible that the monthly average residue values have been reduced. Further improvements to the carbon circuit are possible, and the possibility of making further savings by a reduction in the carbon-throughput rate still needs to be investigated. The mathematical modeling of the furnace has progressed to the stage where the future scale-up and design of the Minfurn can be carried out by simulation of the performance of different designs, and choosing the design that yields the desired performance.

Jan 1, 1993

By J. W. van der Merwe

Technology is advancing at a rate that makes it extremely difficult for the mining industry to keep pace. Many advances occur within a given piece of technology and often this is missed by the disciplines that could have gained advantage by its implementation. Often this may have been simply an aspect of cost exceeding benefit. However, there are some technologies that potentially have such a far-reaching impact on the mining industry that the benefits simply outweigh the cost. The application of 3D laser scanning in the mining industry has the potential of taking the concept of 'Google maps?' underground. This presents an opportunity where the virtual world of underground can be traversed with relative ease and many aspects of measurements could be obtained without having to visit the working place again, potentially saving countless man-hours and still delivering precision work with significant savings in downtime, stoppages, and exposure to safety incidents. Anglo American Platinum maintains its competitive advantage though the review and application of appropriate technology. This paper describes the 3D laser scanning trial at one of Anglo American Platinum's new shafts, and goes on to show the benefits encountered through the application and the involvement of the various MRM disciplines.

Jan 1, 2013

By J. -P. Tshibangu, A. Vervoort, A. Lavrov

Abstract: The aim of the research presented is to study the effect of complex loading schemes on the fracturing process during loading and/or unloading. A first set of experiments was done using a poly-axial cell. These experiments in combination with numerical simulations showed a difference in micro-fracturing (shear and tensile cracks), but not in macro-failure between various loading/ unloading schemes. The second set of experiments was based on the three-point bending test and several cycles with or without rotation between cycles were applied. If the specimen was rotated by 90° or 180° about its long axis between the first and second cycle, no Kaiser effect was observed. Résumé: Le but de la recherche présentée est d’étudier l’effet de schémas de charge complexe sur le processus de fracturation durant la phase de charge et de décharge. Une première série d’expériences était réalisée utilisant une cellule polyaxiale. Ces expériences combinées avec des simulations numériques ont montré une différence de micro-fracturation (fissures de cisaillements et de traction) pour les différents schémas de charge et décharge, mais en ce qui concerne la macro-fracturation ce n’est pas le cas. La deuxième série d’expériences était basée sur des essais de flexion trois points avec plusieurs cycles, avec ou sans rotation entre les cycles. Si l’échantillon est tourné de 90° ou 180° selon le grand axe entre le premier et le second cycle, l’effet Kaiser n’est pas observé. Zusammenfassung: Der Zweck der vorliegenden Forschung bestand darin, den Einfluß von komplizierten Beanspruchungsschemen auf den Bruchprozess im Laufe von Belastung und/oder Entlastung von Gesteinen zu untersuchen. Der erste hier beschriebene Satz von Experimenten wurde mit einer dreiaxialen Belastungsmaschine angestellt. Diese Experimenten zusammen mit dazugehörigen numerischen Simulationen zeigten Unterschiede zwischen Be- und Entlastungsbeanspruchungen in Bezug auf mikrobruchmechanische Mechanismen (d.h. Scher- oder Zugrisse) an, aber nicht in Bezug auf den Makrobruchprozess. Der zweite Satz von Experimenten umfasste Gesteinsbeanspruchung in mehreren Zyklen von Drei-Punkt-Biegung, indem die Gesteinsproben zwischen den Zyklen um einen angegebenen Winkel (0°, 90° oder 180°) gedreht wurden. Falls die Probe um 90° oder 180° gedreht wurde, wurde kein Kaiser-Effekt im zweiten Zyklus beobachtet.

Jan 1, 2003

By J. Danoczi

Specially designed X-ray machines are used extensively on diamond mines for the recovery of diamonds from ores. These machines are extremely expensive and, at present, there are no reliable methods of determining if the equipment is performing efficiently. The objective of this work was to manufacture translucent X-ray diamond simulants, which would emit varying but known luminescence signals when exposed to X-rays. These X-ray diamond simulants could then be used to determine the efficiency of diamond recovery operations.

Jan 1, 2008

By Harushige Kusumi, Yuzuru Ashida, Toshiki Watanabe, Toshifumi Matsuoka

ABSTRACT: The technique of various kinds of numerical analysis offered remarkable results to explication of many rock mechanical phenomena. These techniques regarded a rock stratum as a continuum body and solved the governing equation of continuum mechanics by using finite differ-ence method, finite element method and/or others. Using numerical analysis based on continuum mechanics, however, the simulations of destruction phenomena caused by elastic waves and on the other hand, the elastic wave propagation which generated by fracturing events are quite difficult. In this paper, we express a rock stratum by a granular body model and develop a simulation tech-nique can simulate both wave phenomena and destruction phenomena at once. The DEM (discrete element method) simulation results are compared with finite difference solutions of elastic wave equation. Furthermore, we simulate Hopkinson effect by this proposed method. Hopkinson effect is famous as a destruction phenomenon caused by elastic wave propagation. ABRISS: In dieser Studie drücken wird eine Felsschicht durch ein Granularkörpermodell aus und entwickeln eine Simulationstechnik, die sowohl Wellenphänomene als auch Zerstörungsphänomene simulieren kann. Die Ergebnisse der Simulation mit DEM (Diskrete-Elemente-Methode) werden mit denen der Finit-Differenz-Lösung von Gleichungen elastischer Wellen verglichen. Desweiteren simulierten wir den Hopkinson-Effekt mit dieser vorgeschlagenen Methode. Der Hopkinson-Effekt ist als Zerstörungsphänomen berühmt, verursacht durch Fortpflanzung elastischer Wellen. RESUME: Dans cette étude, nous exprimons un lit de roches par un modèle à corps granulaire et développons une technique, permettant de simuler d'un coup le phénomène des ondes et le phé-nomène de destruction. Les résultats de la simulation DEM (méthode d'éléments discrets) sont comparés aux solutions à différence finie de l'équation d'ondes élastiques. En outre, nous simulons l'effet d'Hopkinson par la méthode proposée. L'effet d'Hopkinson est connu comme phénomène de destruction, causé par la propagation d'ondes élastiques.

Jan 1, 2003

By A. Bothma

The Impala No. 1A ventilation shaft is located approximately 15 kms north of Rustenburg and is accessed via the R510road from Rustenburg to Northam/Thabazimbi. This situation is shown on the location plan in Figure 1. The geology at the site consists of an upper layer of black turf of about 1 metre in thickness, grading into weathered norite. The depth of weathering is generally less than 5 metres. Zones of deeper weathering may occur along fracture zones associated with faults and dykes. Groundwater occurs mainly within the weathered/fractured aquifer system. The ventilation shaft is a 5.1 m diameter upcast shaft ,and forms part of a system of ventilation shafts to complement the existing infrastructure as mining progresses down the new twin decline extension of Impala 1 shaft. The principal reason for these shafts is to lessen the risk of an extended RAW and also to counter the effects of the heat build-up as the mining goes deeper, with the resultant effect that the existing cooling centre (fridge plant) becomes more remote from activities. The No. 1A shaft (upcast) is positioned approximately 1,2 km on down dip from the main shaft and the No. 1Bshaft (downcast) approximately 1,2 km further. Geological information was used from a borehole 1,2 km away on strike from the upcast shaft. The first shaft (1A) is a 5,1 m diameter hole to be fitted with two 2,2 MW fans, whilst the second shaft (1B) is 4,1 m diameter to accommodate a 7MW fridge plant.

Jan 1, 2001

By J. M. Garcia

This paper highlights several management practices from the oil and gas industry to support the proposition that financial performance in the finite, non-renewable resource business relates more to upstream rather than downstream activities. Based on the analysis of nine oil and gas companies, this study supports a previous study involving fourteen mining companies that showed reserves growth is one of the main levers of value creation in mining. Interestingly, this study also finds that the oil and gas industry has been historically more profitable than mining. The reason, it is argued, is that oil and gas companies count on management practices that focus primarily on the upstream segments of the business, compared to the traditional downstream focus of mining. This paper delves into these ideas to conclude that what mining may need to improve its competitive advantage is a new organizational framework. Another conclusion is that the upstream management focus is vital not only for strategy formulation in the resource business, but also for policy formulation in economies based on the export of finite, non-renewable resources.

Jan 1, 2011

By K. A. G. Blendulf

The paper describes tests on horizontal-belt filters for the filtration of gold and uranium. The promising results led to the installation of 17 such filters (ten of them 120 m2 in size) in the mine's metallurgical plants, and their operation is discussed. Although several problems were encountered both in operation and maintenance, it is concluded that, with correct operation and suitable filter cloths, exceptionally good metallurgical recoveries can be achieved at filtration rates twice to three times higher than those on rotary filters.

Jan 1, 1997

By C. Botha

The South African democratically-elected government instituted policies and legislation that are intended to bring about change and transformation in the country and have drastically affected different industries, among others, the mining industry. The Mineral and Petroleum Resources Development Act 28 of 2002 (MPRDA) and the Broad-based Socio-economic Empowerment Charter (Mining Charter) were introduced in order to redress previous inequalities and to promote women's employment in the mining industry. This research evaluates the practical implementation of the MPRDA and the Mining Charter with specific reference to women in underground mining. A quantitative research paradigm was used. Data were collected through a process of a face-to-face interview surveys utilizing a structured questionnaire. The research setting was limited to the platinum-mining industry in the area of Rustenburg in the North West Province. The study population consisted of 195 available women working undergound at the mine. It is clear from the findings that mining companies are facing major challenges in their attempt to incorporate women in underground mining activities. Company policies regarding these issues must be firmly in place; however, the challenge lies in the translation of these policies into practice. In this regard, managers will have to play a leading role in the successful phasing in of women into the underground mining arena.

Jan 1, 2012

By C. Musingwini

An often overlooked factor in the analysis of mine layouts and schedules is technical operating flexibility (or tactical flexibility), mainly due to its nebulous nature. By glossing over technical operating flexibility the resultant mine layouts and schedules maybe suboptimal. The need to incorporate technical operating flexibility into the analysis and comparison of mine layouts and schedules is increasing in importance. The nature of technical operating flexibility is illustrated, previous work on valuing of operating flexibility reviewed, and a proposal made on how technical operating flexibility can be quantified for tabular reef mines by using a platinum reef deposit as a case study. Once technical operating flexibility has been quantified it becomes possible to explore its incorporation into the analysis of mine layouts and schedules and subsequent optimization processes. This paper is a revised version of a paper presented in the Proceedings of the Second International Platinum Conference, ?Platinum Surges Ahead? in 2006. The work described in this paper is part of a current PhD study at the University of the Witwatersrand. Keywords: mine plans, layouts, schedules, technical operating flexibility/tactical flexibility, ore availability.

Jan 1, 2007

By Y. Guglielmi, V. Merrien-Soukatchoff, I. Kadiri

ABSTRACT: Hydraulic experiments have been conducted since 1997 within a small fractured calcareous rock mass in southeastern France, at a site called Coaraze. On this reduced-scale site closing a floodgate located on a downstream spring produces repeated hydraulic loadings. Simultaneous measurements of normal deformations and pressure in several joints have provided a better understanding of the hydromechanical behaviour of such a fractured rock mass. The present paper first describes both the site and conceptual interpretation of the measurements performed. We showed that accurate measurement reproduction requires incorporating certain features: a variable normal joint stiffness, the joint vicinity (through introducing a Z coefficient), and the initial stress state. The paper then develops an original analytical interpretation of the coupled pressure-displacement measurements carried out, which reveal the high level of measurement suitability to the non-linear behaviours examined. 2D modelling, using the discontinuous code (UDEC) was used to proceed with the calibration step. KEY WORDS: In situ test, methodology, hydromechanics, modelling, non linear behaviour ZUSAMMENFASSUNG : Hydromechanische Experimente werden seit 1997 in einer kleinen Kalksteinmasse, das sich im Südosten von Frankreich befindet durchgeführt. In diesem kleinen Standort, werden wiederholte Wasserdruck Erhöhungen durch das Schliessen eines Hahnes produziert. Gleichzeitiger Druck und normale Verformung Meßungen in mehreren Fugen haben erlaubt, das hydromechanische Verhalten einer solche gebrochene Felsenmasse besser zu verstehen. Der Artikel beschreibt zuerst den Standort und stellt die begrifflichen Interpretationen der Meßungen vor. Um die Meßungen gut zu reproduzieren ist es wesentlich, bestimmte Faktoren wie die veränderliche normale Steifheit der Fugen, die Nachbarschaft der Fugen (über einen Z-Koeffizient) und der Spannungstand zu berücksichtigen. Der Artikel erklärt die originale Methode für die Druck- und Verformungs-Meßungen Interpretation und zeigt die gute Korrelation der Meßungen mit dem nicht-linearen angenommen Verhaltens der Fugen. Die numerische 2D-Modellierung mit dem UDEC Software ist für die Verkeilung der Faktoren gebraucht worden. SCHLÜSSELWÖRTER: In-situ-test, Methodologie, Hydromechanik, Numerische Modellierung, nicht-lineares Verhalten RESUME : Des expérimentations hydromécaniques sont conduites depuis 1997 dans un petit massif calcaire fracturé situé dans le sud de la France. Dans ce site de taille réduite des mises en charge répétées sont produites par la fermeture d'une vanne située à l'aval du site. Des mesures simultanées de déformation normale et de pression dans plusieurs joints ont permis de mieux appréhender le comportement d'un tel massif fracturé. L'article décrit dans un premier temps le site et présente les interprétations conceptuelles des mesures. Pour bien reproduire les mesures, Il est essentiel de prendre en compte certains facteurs tels que la raideur normale variable du joint, le voisinage du joint (par l'intermédiaire d'un coefficient Z), l'état de contrainte initial. L'article précise la méthode originale d'interprétation des mesures pression-déplacements qui montre la bonne adéquation aux lois de comportement non linéaire proposées. La modélisation 2D, à l'aide d'un code discontinu (UDEC) a été employée pour le calage des facteurs. MOTS-CLEFS : In-situ, méthodologie, hydromécanique, modélisation, comportement non linéaire

Jan 1, 2003

By Valérie Léveillé

As new legislation drives to lower SO2 emissions from metallurgical plants, plant managers face the challenge of keeping their costs under control. The Cansolv® SO2 Scrubbing System has been broadly adopted in the non-ferrous industry as a cost effective solution for smelter operators to meet the new SO2 emissions targets. The Cansolv® SO2 Scrubbing System is an amine-based regenerable process that selectively absorbs SO2 from a variety of gases, including dilute smelter gases, such as furnace and converter gases. The system produces a pure, water-saturated SO2 byproduct stream, which can then be directed to the front end of a sulfuric acid plant for conversion to sulfuric acid. When deployed in a smelter complex, the Cansolv® SO2 Scrubbing System may also be used to process acid plant tail gas, allowing single absorption sulfuric acid plants to achieve emissions an order of magnitude lower than that of a double absorption acid plant with a lower capital investment. Depending on inlet gas temperature SO2 emissions in the treated gas can be controlled to as low as 55 mg/Nm3. This paper will describe some of the applications where customers have or are planning to use the Cansolv® SO2 Scrubbing System and what as well as which features and cost advantages for the treatment of smelter gases were key to the technology choice.

Jan 1, 2009

By V. Pawlowsky-Glahn, E. Pardo-Igúzquiza, J. J. Egozcue, R. A. Olea

Compositional data constitutes a special class of quantitative measurements involving parts of a whole. The sample space has an algebraic-geometric structure different from that of real-valued data. A subcomposition is a subset of all possible parts. When compositional data values include geographical locations, they are also regionalized variables. In the Earth sciences, geochemical analyses are a common form of regionalized compositional data. Ordinarily, there are measurements only at data locations. Geostatistics has proven to be the standard for spatial estimation of regionalized variables but, in general, the compositional character of the geochemical data has been ignored. This paper presents in detail an application of cokriging for the modelling of compositional data using a method that is consistent with the compositional character of the data. The uncertainty is evaluated by a Monte Carlo procedure. The method is illustrated for the contents of arsenic and iron in groundwaters in Bangladesh, which have the peculiarity of being measured in milligrams per litre, units for which the sum of all parts does not add to a constant. Practical results include maps of estimates of the geochemical elements in the original concentration units, as well as measures of uncertainty, such as the probability that the concentration may exceed a given threshold. Results indicate that probabilities of exceedance in previous studies of the same data are too low.

Jan 1, 2015