The theory of geostatistics covers a branch of .applied statistics aimed at a mathematical description and analysis of geological observations. Geostatistics can be used in pure geology (for example, for the analysis of trace elements in a metamorphic rock), in mineral exploration (for example, for the analysis of geochemical exploration data), as well as in mine valuation. This book is intended to provide a practical introduction to the theory of geostatistical methods of mineral evaluation. Over the years, various mathematical models have been developed to represent the distribution of values in mineral deposits. The simpler models are based on the assumption that the values are randomly distributed. Classical statistical methods, based on this assumption of the random distribution of values, are used to analyse mineral deposits to which these models apply or are assumed to apply. In all mineral deposits, however, one recognizes the presence of areas where the values are higher or lower than elsewhere. Also, the values of two samples in a mineral deposit are more likely to be similar if the samples are taken close together than if they are taken far apart. This indicates that there exists a degree of correlation between sample values, and that this correlation is a function of the distance between the samples. Models have been developed which take this correlation into consideration, with the degree of correlation between sample values being usually measured by the semivariogram function. In these models the fact that two samples taken next to each other will most probably not have the same value, must also be considered; even for very short distances the correlations are usually not perfect and a purely random component is present in the value distribution. The mathematical models will therefore assume the presence of two sources of variability in the values: a correlated component and a random component. Finally, one must consider the particular and very common case of mineral deposits in which the values present a systematic variation in space. This variation is usually referred to as a drift, or a trend. For example, the grade of an ore body may increase with depth of the ore, or it may decrease when one moves away from a central volcanic pipe. The earlier models did not give a satisfactory representation of drifts, and more complex models have been developed, in which three sources of variation are represented. These models are made up of: a deterministic component, a correlated component, and a random component. The deterministic component is used as a model of the drift. The correlated component explains regular changes in values which are not represented by the drift. The random component represents variations which cannot be explained by any of the above factors. The simpler models, based on the assumption of a single random component, will be described first (Chapter 2). The models based on the hypothesis of the superimposition of a correlated component on a random component, will then be analysed in detail. These models are most commonly used in the analysis of mineral deposits (Chapters 3-1 I). Finally, how to deal with the presence of a drift will be briefly described (Chapter 12). This book has been written essentially for students in mining engineering and for mining engineers who are interested in the background to the theory of geostatistics as well as its practical applications. The assumption is made that the reader has an elementary knowledge of statistics. Some knowledge of linear algebra is useful in part of Chapter 9, and is necessary to read Chapter 12. A proof is given of all the equations related to geostatistics, and which are not usually found in elementary textbooks on statistics. Understanding of these proofs is not necessary for practical application of the theory, and the reader may wish to skip them on a first reading, concentrating attention on the numerous simple practical examples given. Although the theoretical geostatistician will not find much new material in this publication, it is anticipated that he will develop some interest in the practical approach chosen to prove the various geostatistical equations. Many people and institutions contributed to the preparation and completion of this work. I am much indebted to Dr D. G. Krige and the Anglo Transvaal Consolidated In- vestment Company Limited, who gave me the opportunity to spend a considerable amount of time working on geostatistical problems, both theoretical and practical, during the time that I was in their employment. Dr Krige contributed greatly in developing my interest in studying both the theory and practice of geostatistics, always insisting that a correct balance be kept between theory and practice. I am grateful to Professor H. M. Wells and the Mining Department of the University of the Witwatersrand for inviting me to give lectures in a post- graduate course on geostatistics. The notes 1 prepared for that course became the foundation of the present work. I am also indebted to the Centre de Geostatistique of the École des Mines de Paris, where I received my first formal education in geostatistics during a summer course given by Charles Huijbregts, after many years of my lonely plodding through the published literature. Many graphs in the present volume are reproduced with the permission of the Centre de Geostatistique. The Department of Metallurgical and Mineral Engineering of the University of Wisconsin-Madison has also contributed in making this work possible, by allowing me to spend a considerable amount of time and resources in the writing, typing, and correcting of successive drafts. I am thankful to Lynn D. Kendall, who typed the entire manuscript under constant pressure.
Applied geophysical methods such as the surface seismic method have been applied for many years and in many places, mainly for oil exploration and to a lesser extent for mineral deposits? exploration in sedimentary basins. The seismic method fundamental is based on the variations of acoustic impedance in a layered earth model and such variations at each main geological interface create reflected waves that are processed and imaged in order to output a clear picture of the subsurface structure. The geology of South Africa was historically, and even until recently, considered as unfit for seismic exploration and the mines were always reluctant to spend any portions of their exploration budgets on these techniques. Hard rocks and high P-waves velocities were creating quite a hopeless model for any mine geologist or geophysicist (if any), unsuitable for the proper use of seismic waves to image their subsurface problems. Boreholes were considered the only reliable tool to derive a geological image of the mine structural features and were linked sometimes with surface methods such as aero-magnetism. The obvious flaw of this methodology was the inability to derive a continuous image from a discrete set of measurement points. Surface 3D seismic is the tool that gives a reliable solution from the initial model extracted from the boreholes, as even the aero-magnetism mapping gives a flat image, unable to show any depth correlation from well to well. The first 3D surface seismic surveys were recorded in the early Nineties only for the gold mines of the Witwatersrand, after a series of serious new shaft sinking failures. The wrong geological locations of these shafts resulted in financial loss of several hundred million rands. The era of3D seismic just started in South Africa and till 1997, all seismic done in the country was for gold exploration with geological target depths close to the oil exploration average depth of investigation. A very important breakthrough was reached when the depth accuracy of the seismic image was tested in real scale as the stopes were surveyed. An error of amplitude of 20 m was usual when true depth was compared with the seismic image predicted depth and shape. This accuracy, completely unknown in oil exploration, started to gain supporters of seismic methods in the mining community but the cash problems and the concentration/disappearance of gold mines in the late Nineties, led to the belief that seismic would be just a very short exploration activity for the mining sector. ort exploration activity for the mining sector. But starting in 1998 with Impala, a tremendous and continuous 3D surface seismic activity occurred in the platinum mining sector. The seismic world got used to new terms such a Merensky and UG2, which have replaced the VCR and black reef. If the primary expectation of platinum surface 3D seismic was to determine and ascertain new shaft locations, as for the gold mines, the quality of seismic data led the mine geologists to require smaller and smaller imaging of geological objects. In addition to the main structural image, small faults, potholes, and shear zone were common expectations of platinum seismic. In a constant velocity environment, what saved the day was the sharp density contrast between the PGM reef and the embedding geology. A good contrast of impedance exists in the whole Bushveld and is sufficient to have enough reflected waves from the PGM main layers to build a high quality seismic image of the subsurface. Recent advances in technology have led in less than 10years to major improvements in the seismic acquisition by using high frequency vibrating seismic sources, but also in processing and interpretation. With these latest improvements, seismic can detect objects of 7.5 m size, either fault throws, flexures, etc. The PGM formations of the Eastern limb of the Bushveld Complex are now accessible for seismic imaging, with cost per square kilometre comparable to the borehole cost of the same surface unit. The economically acceptable seismic surveys can be used for UG2 structural imaging up to a depth of 210 m below surface. Linked with borehole information, 3D seismic today offers a wide range of information for mine development: structural imaging, small fault detection, pothole and shear zone identification. All users of 3D seismic have also used this technique as a tool in the process to qualify their mineral reserves and especially from the category ?inferred? to the category ?measured?. Junior mining companies, in the feasibility stage of their projects, are also quite eager to use seismic as a reserve certification tool, when they present financial statements to future potential investors. Junior mining companies, in the feasibility stage of their projects, are also quite eager to use seismic as a reserve certification tool, when they present financial statements to future potential investors. The current high demand on platinum, pushes the seismic towards new technologies to be implemented in order to improve the final image. Using surface and borehole seismic together or acquiring seismic surveys with multi-component receivers have been just introduced in South Africa. In less than 10 years, surface seismic by adapting its methods to the special case of the Bushveld, became a mandatory step in mine development and ore resources evaluation. As part of the ?seismic? world we are proud to be a major player the ?surge? of platinum exploration and production in these last years and we will certainly increase our synergy with the mine sectors in the exciting coming years.
For the past 12 years, the Universities of Stellenbosch and Cape Town have hosted an annual symposium to discuss research topics in Minerals Processing. Since 1987, this meeting has been held under the auspices of the Western Cape Branch of the South African Institute of Mining and Metallurgy, and has enjoyed much national and international support. In 1993, in place of the usual Symposium, the Branch and Universities collaborated with CSM Associates Ltd and Minerals Engineering Journal is organizing the international Minerals Engineering '93 Conference in Cape Town.
The National Institute for Metallurgy - usually referred to as NIM - has become the Council for Mineral Technology, or Mintek. The Honourable F. W. de Klerk, Minister of Mineral and Energy Affairs, announced the change of name at the official opening of the main entrance to Mintek's premises on 30th October, 1981. Awards for bravery Two men who disregarded the dangers of fiercely burning timber and falling rocks to douse an underground fire, using their hard hats to scoop water from a drain, received the Chamber of Mines Award for bravery at a ceremony held at West Driefontein Gold Mine near the end of October.
"The determination of the oxidation state(s) of an element present in a solid sample may be required for a number of reasons, including the assessment of the degree of reduction which has taken place during a multi-step production of a metal. In addition, possible flaws in a metal may result from small amounts of oxides included in the solid. The analyte of interest may be present as a major component of a sample of interest, or as a minor impurity - beneficial or requiring removal - in another matrix.Numerous methods have been established for the analysis of species in solution samples - for example, Fe2+ and Fe3+ by titration, Cr6+ by colourimetric means, etc. With appropriate knowledge of the solution being analysed, many of these methods are fairly straightforward, extremely reproducible and accurate. In those instances where the analyte in a solution is known to be in only one form, the analysis is even more straightforward, since it can be achieved instrumentally (by AAS, rCP-OES or rCP-MS, for example).However, the situation with respect to the analysis of solids is not as simple. Various techniques - such as X-ray diffraction - are routinely used by our mineralogists to obtain information about the various minerals present in solid samples, and thus about the oxidation states of the analyte elements present. However, these techniques usually give results that are qualitative, or semi-quantitative at best. They are also usually time-consuming and expensive. One of our colleagues at Mintek, Deshenthree Chetty, has done extensive work in developing a method for the quantification of manganese species in solids using mineralogical methods, and this is no small achievement."
This paper was presented at the Coloquium on Management Techniques in the Mining and Metallurgical Industry, which was organized by The South African Institute of Mining and Metallurgy and held in Pretoria during June 1988. The author asks whether technical audits are of any use to management. Technical auditing he defines as an evaluation undertaken by an outsider of whether a technical activity is being carried out correctly. After examining the types of technical auditing, and its prerequisites and procedures, he describes its application in regard to quality, and to production processes and their adequacy. He then answers his question by saying that, not only are technical audits very useful, but they form an essential element in the provision of quality products. In addition, they give management the opportunity of testing whether the activities of the organization are being conducted correctly. This is their most important function in that they alert management to areas of potential growth, modernization, and innovation. However, the use to which technical auditing is put remains the key to its value; that is, its value depends on the positive action that each manager takes as the result of a technical audit.
"X-ray transmission (XRT) sorting has become the preferred recovery technology option in several parts of the diamond-winning flow sheet. In the De Beers Group, applications of XRT are found across kimberlite, alluvial, and marine operations. This is the result of intensive R&D conducted over the years to arrive at a suite of machine embodiments capable of sorting and auditing diamonds across all size ranges.The first applications in the marine environment used the technology in an auditing mode, and served as a useful early predictor of diamond content weeks ahead of sorthouse returns. The same machines are now available with ejection capability to produce high final product grades. The next application was tests on coarse alluvial gravels as an alternative to dense medium separation. The results were very encouraging, and tests are planned for both green- and brownfield kimberlite environments, as well as to explore an alternative to conventional techniques in final diamond recovery. At the Jwaneng mine Large Diamond Pilot Plant (LDPP), the objective is to recover diamonds in the size fraction –45 +25 mm.The technical challenge remains in the finer sizes, for high-capacitymachines as direct alternatives to conventional diamond recovery technologies. This is an area of ongoing R&D and it is only a matter of time before the breakthrough emerges. X-ray transmission fundementalsXRT makes use of X-ray imaging techniques to analyse objects and materials, and has a wide range of applications from baggage scanning for security purposes (Martz et al., 2016), to recycling of waste material (Owada, 2014). During the last decade XRT has been applied to an increasing extent in the minerals processing industry (von Ketelhodt and Bergmann, 2010; Sasman, Deetlefs, and van der Westhuyzen, 2018). Dual-energy XRT (DE-XRT), in which images of the target material are obtained at both high and low Xray energies, allows for elemental analysis and therefore can be used to discriminate between various minerals.A DE-XRT system makes use of a dualenergy X-ray line scan sensor to generate images of transmitted X-rays (Figure 1). Dualenergy refers to the camera, which contains two sensors, one responding to low-energy Xrays and one to high-energy X-rays. Feed material can be imaged either while on the belt, or while in flight."
Introduction (23e5e313-b9b2-4cd6-abaf-bc3e0988c79a)